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Biomechanical modeling and analysis of manual wheelchair propulsion 2007

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Biomechanical Modeling and Analysis of Manual Wheelchair Propulsion by Mohammadreza Mallakzadeh B.Sc, Sharif University of Technology, 1992 M.Sc, Sharif University of Technology, 1995 A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF D O C T O R O F P H I L O S O P H Y in T H E FACULTY OF GRADUATE STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA October 2007 © Mohammadreza Mallakzadeh, 2007 Abstract Users of manual wheelchairs depend on wheelchairs for most of their daily activities. Manual Wheelchair Propulsion (MWP) is an inefficient and physically straining process, which in the long term can cause injury. However, wheelchair users do benefit greatly from cardiovascular exercise with the use of manual wheelchairs. The first step in improving the low efficiency and/or preventing injuries during MWP is to be able to measure these factors. To do this, we have proposed an Equivalent Biomedical Index (EBI) and two Wheelchair Users' Joint Injury Indices (WUJII and WUJIT) for gross mechanical efficiency and injury assessments. We have fabricated and validated an instrumented wheel to measure the user's applied loads on the handrim during MWP as part of the data required for calculating the proposed indices. The wheel system has been verified by using general uncertainty analysis, and its specifications have been determined using both static and dynamic experiments. The results have ensured the reliability of the system. Also, a procedure has been developed to determine the angular position of the contact point between the hand and the handrim by using the applied loads and without the use of cameras. This study also focuses on proposing a novel method to determine the optimum seat position of the wheelchair to minimize the values of the injury indices and/or maximize the value of EBI for each user. Eight male wheelchair user subjects were recruited for the experiments. Statistical analysis showed that horizontal seat position was significantly related to all three indices (p<0.05). The response surfaces of the indices for two users were determined by using the proposed method and a Bivariate Quadratic Function. ii We developed and elaborated "Method I" for analysis of the dynamics of user joints and to calculate the joint loads as part of the factors required to define the optimum seat position. A 3 D rigid-body inverse dynamic method was used to calculate the joint loads. "Method II" for analysis of the kinetics of the upper limbs was developed and validated to simplify the experimental procedure and decrease the required post-processing. Method II showed to be reliable for measuring the joint forces. iii Table of Contents Abstract u Table of Contents iv List of Tables xi List of Figures xiii List of Symbols xix List of Abbreviations xxvii Acknowledgements xxx Dedication xxxi CHAPTER 1 Introduction 1 1.1 Foreword 1 1.2 Research Questions, Hypothesis, Objectives and Limitations 3 1.3 An Overview of the Upper Limb Joints' Anatomy 6 1.3.1 Shoulder Girdle Joints 6 1.3.2 Elbow Joint 8 1.3.3 Wrist Joint 10 1.4 Terminology 10 1.5 Previous Studies 11 1.5.1 Kinetics ofMWP 12 iv 1.5.2 Injuries Due to MWP 16 1.5.3 Effect of Seat Position on MWP 17 1.5.4 Metabolic Energy Expenditure during MWP 19 1.5.5 Instrumented Wheel 22 1.6 Possible Solutions 23 1.7 Thesis Organization 25 1.8 Concluding Remarks 26 C H A P T E R 2 The Instrumented Wheel 28 2.1 Introduction 28 2.2 Instrumentation 30 2.2.1 Wheelchair 30 2.2.2 The Instrumented Wheel 31 2.2.3 Roller-rig 32 2.2.4 A C Motor 34 2.2.5 Computers 34 2.2.6 Data Acquisition Board 35 2.2.7 Static and Dynamic Loading Setup 35 2.3 Preliminary Experimental Protocol 37 2.4 Derivation of Dynamic Equations 37 2.4.1 System Calibration 38 2.4.2 Preload Equations 38 2.4.3 Local and Global Forces and Moments 39 2.4.4 Important Kinetic Factors 45 2.4.5 Determining the Position of the Hand on the Handrim 47 2.5 Uncertainty Analysis 53 2.5.1 General Uncertainty Analysis 54 2.5.2 Uncertainty of Preloads 55 2.5.3 Uncertainty of Local Loads 57 2.5.4 Uncertainty of Global Loads 59 2.5.5 Uncertainty of cp 62 2.5.6 Uncertainty of Hand Contact Loads 64 2.6 System Verification 65 2.6.1 Experimental Setup 65 2.6.1.1 First Vertical Loading Setup 66 2.6.1.2 Second Vertical Loading Setup 67 2.6.1.3 Horizontal Loading Setup 68 2.6.1.4 Dynamic Loading Setup 69 2.6.2 Verification Tests Protocol 70 2.6.2.1 Static Verification 70 2.6.2.2 Dynamic Verification 74 2.7 Conclusions 80 C H A P T E R 3 Efficiency and Injury Assessment 83 3.1 Introduction 83 3.2 Efficiency Assessment 85 vi 3.3 Injury Assessment 87 3.4 Chapter Summary 93 C H A P T E R 4 Optimum Seat Position 95 4.1 Introduction 95 4.2 Modeling and Analysis Approach 96 4.2.1 An Overview 97 4.2.2 Study Population 98 4.2.3 Study Design 99 4.2.4 Test Protocol 100 4.2.5 Anthropometric Data 104 4.2.6 Experimental Setup 104 4.2.6.1 Motion Analysis System 104 4.2.6.2 Heart Rate Monitor 106 4.2.6.3 Blood Pressure Monitor 106 4.2.6.4 Fat Caliper 107 4.2.6.5 Speedometer 107 4.2.6.6 Weight Scale 107 4.2.6.7 Global View of the Experimental Setup 109 4.2.7 Modeling 110 4.3 Analytical Methodology 112 4.3.1 Design of Experiments 115 4.3.1.1 Grid-base Design 115 vii 4.3.2 Response Equation 116 4.3.2.1 Artificial Neural Network 117 4.3.2.2 Local Interpolation 117 4.3.2.3 Bivariate Quadratic Function 118 4.3.3 The Big Picture 119 4.4 Results and Discussion 121 4.4.1 Heart Rate, Blood Pressure, and Anthropometric Data 121 4.4.2 Fixed Seat Position 123 4.4.2 Constant Wheelchair Velocity 127 4.4.2.1 Seat Height Y l 127 4.4.2.2 Seat Height Y2 132 4.4.2.3 Horizontal Seat Position XI 138 4.4.2.4 Horizontal Seat Position X2 140 4.4.2.5 Horizontal Seat Position X3 142 4.4.2.6 Optimum Seat Position 144 4.5 Conclusions 149 C H A P T E R 5 Injury Assessment for the Upper Limb Joints 152 5.1 Introduction 152 5.2 Method I 153 5.2.1 The Kinematics of the Upper Limb 154 5.2.1.1 Velocity of the Segment 156 5.2.1.2 Z - Y - X Euler Angles 156 viii 5.2.1.3 Determining the Directional Cosines 158 5.2.1.4 Acceleration of a Segment 161 5.2.2 Kinetics of the Upper Limbs 163 5.2.3 Mass Distribution 163 5.2.4 Modeling 167 5.3 Results 175 5.4 Conclusions 185 C H A P T E R 6 A New Method for Dynamic Analysis of the Upper Limb 187 6.1 Introduction 187 6.2 Method II 188 6.2.1 Link Parameters 189 6.2.2 Link Parameters of the Model 190 6.2.3 Calculating the Joints Angles 192 6.2.4 Kinetics of Wheelchair Propulsion 201 6.3 Comparison of Methods I and II 201 6.4 Conclusions 206 C H A P T E R 7 Conclusions 208 7.1 Introduction 208 7.2 Conclusions 208 7.2.1 Research Questions and Answers 209 7.3 Limitations of the Study 214 7.3 Contributions 2 1 5 7.4 Future Research Directions 217 References 219 Appendix 232 x List of Tables 40 Table 2.2 Primary uncertainties for measured variables 56 56 56 Table 2.5 Pearson correlation coefficient r (static verification) 72 Table 2.6 Mean coefficient of variation of measured loads (%; static verification) 73 Table 2.7 Mean errors as percentage of loads (static verification) 74 Table 2.8 Pearson correlation coefficient r (dynamic verification) 77 Table 2.9 Mean coefficient of variation of measured loads (%; dynamic verification) .. 77 Table 2.10 Mean errors as percentage of loads (dynamic verification) 78 Table 4.1 Demographic data for the manual wheelchair user subjects 99 Table 4.2a Heart rate and blood pressure for the subjects 121 Table 4.2b Anthropometric data for the subjects 122 Table 4.3 Mean and Std. Dev. of WUJII for the subjects for three velocities 124 Table 4.4 Mean and Std. Dev. of WUJH' for the subjects for three velocities 125 Table 4.5 Mean and Std. Dev. of EBI for the subjects for three velocities 126 Table 4.6 Mean and Std. Dev. of WUJII for the subjects at three X-ratios and seat height Y l 129 Table 4.7 Mean and Std. Dev. of WUJII' for the subjects at three X-ratios and seat height Y l 130 Table 4.8 Mean and Std. Dev. of EBI for the subjects at three X-ratios and seat height Y l 130 Table 4.9 Mean and Std. Dev. of WUJII for the subjects at three X-ratios and seat height Y2 135 Table 4.10 Mean and Std. Dev. of WUJII1 for the subjects at three X-ratios and seat height Y2 135 Table 4.11 Mean and Std. Dev. of EBI for the subjects at three X-ratios and seat height Y2 136 Table 4.12 The coefficients and constants for the response equations that determine the indices at different seat positions for subject 7 146 Table 4.13 The coefficients and constants for the response equations that determine the indices at different seat positions for subject 8 149 Table 5.1 The coefficients and constants for the response equations that determine WUJIJ for the upper limb joints at different seat positions for subject 7 180 Table 5.2 The coefficients and constants for the response equations that determine WUJII' for the upper limb joints at different seat positions for subject 7 .....180 Table 5.3 The coefficients and constants for the response equations that determine WUJII for the upper limb joints at different seat positions for subject 8 184 Table 5.4 The coefficients and constants for the response equations that determine WUJII' for the upper limb joints at different seat positions for subject 8 185 Table 6.1 Link parameters of the model 191 Table 6.2 Average rates of over-estimation for upper limb joint loads 205 Table 6.3 Mean and Std. Dev. of the relative error (%) for upper limb joint loads 206 List of Figures Figure 1.1 Front view of acromiclavicular and glenohumeral joints (Image courtesy of medicalmultimediagroup.com [14]) 7 Figure 1.2 Front view of the bones of the right shoulder girdle, and sternoclavicular and scapuathoracic joints (Image courtesy of medicalmultimediagroup.com [14])..7 Figure 1.3 Side view of the bones and ligaments of the shoulder girdle, and section view of glenohumeral joint capsula (Image courtesy of medicalmultimediagroup.com [14]) 8 Figure 1.4 Medial view of the bones of the right elbow joint (Image courtesy of medicalmultimediagroup.com [14]) 9 Figure 1.5 Lateral view of the bones of the right elbow joint (Image courtesy of medicalmultimediagroup.com [14]) 9 Figure 1.6 Back view of the right wrist joint (Image courtesy of medicalmultimediagroup.com [14]) 10 Figure 1.7 Different phases of a complete stroke cycle and related terminology 11 Figure 1.8 Illustration of forces and moments applied on the handrim during wheelchair propulsion: (a) side view; (b) front view 13 Figure 1.9 The relationships among the direction of the applied force, joint torques, and rotation around the shoulder and elbow (modified from [9] with permission) 15 Figure 2.1 Instrumented wheel: (a) side view; (b) front view 32 Figure 2.2 Initial position and orientation of global and two local coordinate systems on the instrumented wheel 33 Figure 2.3 Encoder gear system 33 Figure 2.4 A C motor and its coupling to a shaft of the roller-rig 34 Figure 2.5 Global schematic rear view of the physical data acquisition system 36 Figure 2.6 Measurement signal flow diagram for: (a) load; (b) angular position 36 Figure 2.7 Illustration of local loads after 6 degrees of wheel rotation 42 Figure 2.8 Propulsion force components with respect to global and hand local coordinate system 43 Figure 2.9 Propulsion moment components with respect to global coordinate system ....44 Figure 2.10 Flotai and TEF with respect to the global coordinate system, and the FEF during the propulsion phase 46 Figure 2.11 Calculated q> using kinetic and kinematic methods, and the exponential of curve fit of the kinetic method 49 Figure 2.12 Mean absolute error and Std. Dev. for calculated cp using the kinetic method 50 Figure 2.13 Mean absolute error and Std. Dev. for calculated q> using the exponential curve fit for the kinetic method 51 Figure 2.14 Global propulsive and hand moments in z direction 51 Figure 2.15 Components of the user's hand moment 52 Figure 2.16 Uncertainties for local force components during possible range for propulsion phase 58 Figure 2.17 Uncertainties for local moment components during possible range for propulsion phase 59 Figure 2.18 Uncertainties for local and global force components during propulsion phase 61 Figure 2.19 Uncertainties for local and global moment components during propulsion phase 62 Figure 2.20 First vertical loading setup for static tests 66 Figure 2.21 Second vertical loading setup for static tests 67 Figure 2.22 The horizontal loading setup for static tests 68 Figure 2.23 The dynamic loading set-up 69 Figure 2.24 Measured and predicted global sample force components 79 Figure 2.25 Measured and predicted global sample moment components 79 Figure 3.1 Variation of heart rate versus time, from start to completion of a steady-state exercise and back to rest 86 Figure 4.1 A subject on the instrumented wheelchair and roller-rig during blood pressure measurement. The marker on the left hip is not shown 102 Figure 4.2 Possible seat heights and backrest horizontal positions. The wheelchair xiv variables are set at XI and Y l in this figure. Dimensions are not to scale 103 Figure 4.3 VICON infrared camera 105 Figure 4.4 Positions of six infrared cameras, a subject, the wheelchair and the roller-rig for stationary MWP 105 Figure 4.5 HR-polar heart rate monitor: (a) Heart rate sensor and transmitter; (b) recorder 106 Figure 4.6 Blood pressure monitor 106 Figure 4.7 Fat caliper 107 Figure 4.8 Speedometer: (a) Cycling computer; (b) Holding magnet; (c) Wiring kit and sensor 108 Figure 4.9 The setup for measuring the wheelchair user weight 108 Figure 4.10 Global schematic rear view of the kinetic and kinematic data acquisition system and its connections 109 Figure 4.11 The Model of the upper limbs: (a) Sagittal view of the half body; (b) the linkage model. Numbers 1-3 represent upper arm, forearm, and hand, respectively 110 Figure 4.12 Landmark positions on the upper limbs and trunk of the subject, and the wheel I l l Figure 4.13 A 3D model of the upper body and wheel, developed by using the VICON system 112 Figure 4.14 Grid-base design for two variables with four sub-areas and nine data Points. Dimensions are not to scale 116 Figure 4.15 Flowchart for the entire test process to determine the optimum positions of a wheelchair for a M W U 120 Figure 4.16 Variation of WUJII versus velocity 124 Figure 4.17 Variation of WUJJJ' versus velocity 125 Figure 4.18 Variation of EBI versus velocity 126 Figure 4.19 Variation of WUJJJ against X-ratio at Y l . Minimum values encircled 128 Figure 4.20 Variation of WUJJJ' against X-ratio at Y l . Minimum values encircled .. ..128 xv Figure 4.21 EBI with respect to the X-ratio at Y l . Maximum values encircled 129 Figure 4.22 Maximum and minimum values of WUJII and its Std. Dev. against X-ratio at Y l , among the subjects 131 Figure 4.23 Maximum and minimum values of WUJJJ/ and its Std. Dev. against X-ratio at Y l , among the subjects 131 Figure 4.24 Maximum and minimum values of EBI and its Std. Dev. against X-ratio at Y l , among the subjects 132 Figure 4.25 Variation of WUJII against X-ratio at Y2. Minimum values encircled .. ..133 Figure 4.26 Variation of WUJII' against X-ratio at Y2. Minimum values encircled .. . 134 Figure 4.27 Variation of EBI against X-ratio at Y2. Maximum values encircled 134 Figure 4.28 Maximum and minimum values of WUJII and its Std. Dev. against X-ratio at Y2, among the subjects 136 Figure 4.29 Maximum and minimum values of WUJII' and its Std. Dev. against X-ratio at Y2, among the subjects 137 Figure 4.30 Maximum and minimum values of EBI and its Std. Dev. against X-ratio at Y2, among the subjects 137 Figure 4.31 Variation of WUJII against Y-ratio at XI 139 Figure 4.32 Variation of WUJII' against Y-ratio at XI 139 Figure 4.33 Variation of EBI against Y-position at XI 140 Figure 4.34 Variation of WUJII against Y-ratio at X2 141 Figure 4.35 Variation of WUJlf against Y-ratio at X2 141 Figure 4.36 Variation of EBI against Y-ratio at X2 142 Figure 4.37 Variation of WUJII against Y-ratio at X3 143 Figure 4.38 Variation of WUJII' against Y-ratio at X3 143 Figure 4.39 Variation of EBI against Y-ratio at X3 144 Figure 4.40 Variation of WUJII versus wheelchair variables, for subject 7 145 Figure 4.41 Variation of WUJU' versus wheelchair variables, for subject 7 145 Figure 4.42 Variation of EBI versus wheelchair variables, for subject 7 146 xvi Figure 4.43 Variation of WUJII versus wheelchair variables, for subject 8 147 Figure 4.44 Variation of WUJU'versus wheelchair variables, for subject 8 148 Figure 4.45 Variation of EBI versus wheelchair variables for subject 8 148 Figure 5.1 Local and global frames for a rigid body 154 Figure 5.2 General transformation of a vector 155 Figure 5.3 Directional cosines of rotation matrix for the axes of {B} with respect to {A} 158 Figure 5.4 Frustum of conic rigid body with local frame on its center of mass 165 Figure 5.5 Rectangular prism rigid body with local frame at its center of mass 166 Figure 5.6 Free body diagram of a segment in sagittal plane 168 Figure 5.7 Free body diagram of a segment in frontal plane 168 Figure 5.8 Free body diagram of a segment in transverse plane 169 Figure 5.9 Position vectors for rpd, proximal end (p), distal end (d), and C O M of the segment 172 Figure 5.10 Variation of WUJU versus X and Y-ratios for subject 7 at wrist joint 176 Figure 5.11 Variation of WUJU' versus X and Y-ratios for subject 7 at wrist joint 176 Figure 5.12 Variation of WUJU versus X and Y-ratios for subject 7 at elbow joint.. ..177 Figure 5.13 Variation of WUJU' versus X and Y-ratios for subject 7 at elbow joint ....178 Figure 5.14 Variation of WUJII versus X and Y-ratios for subject 7 at shoulder joint .178 Figure 5.15 Variation of WUJII' versus X and Y-ratios for subject 7 at shoulder joint. 179 Figure 5.16 Variation of WUJU versus X and Y-ratios for subject 8 at wrist joint 181 Figure 5.17 Variation of WUJU' versus X and Y-ratios for subject 8 at wrist joint 182 Figure 5.18 Variation of WUJU versus X and Y-ratios for subject 8 at elbow joint ....182 Figure 5.19 Variation of WUJU' versus X and Y-ratios for subject 8 at elbow joint... 183 Figure 5.20 Variation of WUJU versus X and Y-ratios for subject 8 at shoulder joint .183 Figure 5.21 Variation of WUJU' versus X and Y-ratios for subject 8 at shoulder joint. 184 Figure 6.1 Link frames and link parameters 189 Figure 6.2 Half-body Linkage model for the upper limb with all coordinate reference systems 190 xvii Figure 6.3 Forces, moments and inertial loads on a generic link / 200 Figure 6.4 Total applied force on the wrist joint 201 Figure 6.5 Total applied moment on the wrist joint 202 Figure 6.6 Total applied force on the elbow joint 202 Figure 6.7 Total applied moment on the elbow joint 203 Figure 6.8 Total applied force on the shoulder joint 203 Figure 6.9 Total applied moment on the shoulder joint 204 xviii List of Symbols a Constant a, Distance From Z, to Z,+i Measured Along Xt aXfyiZ Linear Acceleration Components of a Segment QCOM Linear Acceleration of Center of Mass of a Segment ar Combined Linear Acceleration Matrix A Frame A A' First Intermediate Frame for Euler Transformation A " Second Intermediate Frame for Euler Transformation Ao First Constant in Durnin's Equation Atanl Return the Arctangent b Constant bo Lumped Parameter bt= i-6 Constants B Frame B Bo Second Constant in Durnin's Equation C\-l C0S(77i_7) C34 cos(773 + /74) ca cos(a) ccp cos((p) d Frame at the Center of Mass of a Link with Direction and Orientation of Link Frame i d\ Distance between Data Point Pi and Query Point P d2 Distance between Data Point P2 and Query Point P d\2 Distance between Two Data Points Pi and P2 dj Link Displacement D Lumped Parameter D1 _ 10 Lumped Parameters e Random Vector xix E\ Position Vector between Points 3 and 1 E2 Position Vector between Points 3 and 2 Ex Unit Vector of Ex E2 Unit Vector of E2 E3 Unit Vector Perpendicular to Plane of £ , and E2 fo Function 'f Exerted Force on Link i by Link i-l with Respect to Frame i fp Pushing Frequency FXtyiZ Measured Force Components Fc.XtyiZ Force Components with Respect to Wheel Center Coordinate System Fd-X,y,z External Force Components on Distal End of Segment Fg.Xiy,z Applied Force with Respect to Global Coordinate System Fh-X,y,z Force Components with Respect to Hand Coordinate System Ft Inertial Force Acting on Center of Mass of a Segment Fuj Maximum Joint Force of Propulsion Cycle / for Subject j Calculated Using Method I Fiiy Maximum Joint Force of Propulsion Cycle i for Subject j Calculated Using Method II Fi.Xty>z Applied Local Force Components Fm Maximum Total Force Applied on the Hub During Propulsion Phase Fmi Maximum Total Force Applied on the Joint / during Propulsion Phase Fp.Xty,z External Force Components on Proximal End of Segment Fp.x_y,z Force Preload Fs Centripetal Force Fs.Xiy Components of Centripetal Force g Gravitational Acceleration gi Function i h Height of Center of Mass of Frustum of Cone xx h\ Weight of Query Point with Respect to Data Point P\ hi Weight of Query Point with Respect to Data Point P2 H Height of Frustum of Cone Hh Thickness of the Hand. / Unit Vector of X-axis of Local Coordinate System / Unit Vector of X-axis of Global Coordinate System AI Inertia Tensor of a Rigid Body with Respect to Frame A °I Inertia Tensor of a Rigid Body with Respect to Local Frame C at Its Center of Mass IT Combined Mass and Inertia Matrix Ixx,yy,zz Mass Moment of Inertia Components Ixy,xz,yz Mass Product of Inertia Components j Unit Vector of Y-axis of Local Coordinate System J Unit Vector of Y-axis of Global Coordinate System k Weight Factor of Length ^1,2,3,4 Lumped Parameters K11-44 Lumped Parameters k Unit Vector of Z-axis of Local Coordinate System K Unit Vector of Z-axis of Global Coordinate System L] i_44 Lumped Parameters and Components of 2T La Length of Upper Arm Lai Length of Segments Connected to Distal part of Joint i Ld Combined Distal Load Matrix Lf Length of Forearm Lg Matrix of Global Force and Moment Components Lh Length of Hand Li Matrix of Local Force and Moment Components Lp Combined Proximal Load Matrix m Mass of a Segment mw Mass of a Weight xxi MXiyfZ Measured Moment Components Mc.Xi%z Moment Components with Respect to Wheel Center Coordinate System Md.x,y,z External Moment Components on Distal End of Segment Mg.x,y,z Applied Moment with Respect to Global Coordinate System Mh-X,y,z Moment Components with Respect to Hand Coordinate System Mjy Maximum Joint Moment of Propulsion Cycle i for Subject j Calculated Using Method I Mjuj Maximum Joint Moment of Propulsion Cycle / for Subject j Calculated Using Method II Mr.-X,y,z Applied Local Moment Components Mm Maximum Total Moment Applied on Hub during Propulsion Phase Mmi Maximum Total Moment Applied on Joint i during Propulsion Phase Mp.XyiZ External Moment Components on Proximal End of Segment Mp.X:y,z Moment Preload Mz Average Propulsive Moment Applied on Hub n Number of Variables Exerted Moment on Link / by Link i-l with Respect to Frame i N Number of Cases Ni Inertial Moment Acting on Center of Mass of a Segment Preload p /?-value, The Probability of the Null Hypothesis Po Query Point APBORG Position Vector of Origin of Frame B with Respect to Frame A 'Pa Position Vector of Origin of Center of Mass with Respect to Frame i APE Position Vector of Point E with Respect to Frame A BPE Position Vector of Point E with Respect to Frame B Pt Data Point i 'Pi+x Position Vector of Origin of Frame i+l with Respect to Frame i xxn Pwx,wy,wz Position Components of Wrist q Random Vector Q Skew-symmetric Matrix of Vector q r Pearson Correlation Coefficient ro Smaller Radius of Frustum of Cone r\i_33 Components of Rotation Matrix—Directional Cosines rh Mean Radius of Handrim Directional Cosines R Larger Radius of Frustum of Cone g R Rotation Matrix Describing Frame B in Frame A *R Rotation Matrix Describing Frame C in Frame A R(Po) Response at Query Point PQ R(PX) Response at Data Point P\ R(P2) Response at Data Point P2 RA Inverse of Matrix R RT Transpose of Matrix R s\-i sin(/7i_7) S34 sin(^3+^4) sx Standard Deviation of Independent Variable sx Variance of Independent Variable sy Standard Deviation of Dependent Variable sa sin(a) s(p sin(^) Siotai Total Value for Skinfold Test '~XjT Denavit-Hartenberg Matrix for Links i-1 and i u Function Ui Uncertainty of Parameter / 'Vj+\ Linear Velocity of Link /+1 with Respect to Frame i 'VM Linear Acceleration of Link i+1 with Respect to Frame i ' Vc Linear Acceleration of Center of Mass of Link / with Respect xxm to Frame / Linear Velocity of Point E with Respect to Frame A AvE Linear Acceleration of Point E with Respect to Frame A Linear Velocity of Point E With Respect to Frame B Y E Linear Acceleration of Point E with Respect to Frame B v, Average Linear Wheelchair Velocity W\ Normalized Weight of Query Point with Respect to Data Point P\ Normalized Weight of Query Point with Respect to Data Point P2 wh Width of Hand X-position of Points 1, 2 and 3 XQ X-position of Center of Mass Xdp Distance between Points d and p in X-direction Xi Case Value for Independent Variable XCOM Linear Acceleration of Center of Mass in X-direction X Mean of Independent Variable X Horizontal Seat Position with Respect to Wheel Axle xB Unit Vector for X-axis of Frame B AxB Unit Vector for X-axis of Frame B With Respect to Frame A Unit Vector for X-axis of Frame / on the Link / ^1,2,3 Y-position of Points 1, 2 and 3 y c Y-position of Center of Mass ydP Distance between Points d and p in Y-direction yt Case Value for Dependent Variable ycoM Linear Acceleration of Center of Mass in Y-direction y Mean of Dependent Variable Y Vertical Seat Position with Respect to Wheel Axle YB Unit Vector for Y-axis of Frame B Ay Unit Vector for Y-axis of Frame B With Respect to Frame A t Unit Vector for Y-axis of Frame i on the Link i xxiv z 1,2,3 Z-position of Points 1,2 and 3 z c Z-position of Center of Mass Zdp Distance between Points d and p in Z-direction zCOM Linear Acceleration of Center of Mass in Z-direction Zo_9 Z-direction of Local and Global Coordinate Systems for Upper Limb Model ZB Unit Vector for Z-axis of Frame B AZB Unit Vector for Z-axis of Frame B with Respect to Frame A Zi Unit Vector for Z-axis of Frame i on the Link i z Average Value for Index Az Offset Distance between Plane of Handrim and Origin of Global Coordinate System in Z-direction a First Euler Angle a Time Derivative of a 0Ci Link Angle P Second Euler Angle Time Derivative of /? y Third Euler Angle y Time Derivative of y 5j Partial Derivative of Function fo with Respect to j]i Joint Variable of Frame / fji First Derivative of Joint Variable of Frame / fjj Second Derivative of Joint Variable of Frame i 6 Angular Position of Wheel during Test 6 Angular Velocity of Wheel during Test A0 Angular Displacement of Wheel during Test A, Transformation Matrix from Local to Global Coordinate System £ Phase Difference p Radius in Polar Coordinate System xxv az Standard Deviation of Index z zd Induced Moment Due to External Forces at Distal Point of Segment. tp Induced Moment Due to External Forces at Proximal Point of Segment. (p Instantaneous Angular Position of Hand on Handrim in Global Coordinate System (x-y plane) Measured Clockwise with Respect to the +x Axis <p0 Angle in Polar Coordinate System <pc Calculated <p O Formatted Skew-symmetric Segment Length Matrix 'coM Angular Velocity of Link i+l with Respect to Frame i (Dx,y.z Angular Velocity Components of a Segment a>r Formatted Angular Velocity Matrix ldJM Angular Acceleration of Link i+l with Respect to Frame i c0)xyz Angular Acceleration Components of a Segment With Respect to Frame C *P, Measured Variables AQ.B Angular Velocity of Frame B with Respect to Frame A AQ.c Angular Velocity of Frame C with Respect to Frame A BQc Angular Velocity of Frame C with Respect to Frame B AQB Angular Acceleration of Frame B with Respect to Frame A AClc Angular Acceleration of Frame C with Respect to Frame A BClc Angular Acceleration of Frame C with Respect to Frame B QT Formatted Skew-symmetric Angular Velocity Matrix xxvi List of Abbreviations 3D 3 Dimensional {A} Frame A AD Autonomic Dysreflexia A/D Analog-To-Digital %BF Percentage of Body Fat ANN Artificial Neural Network ANOVA Analysis of Variance {B} Framed BMI Body Mass Index BQF Bivariate Quadractic Function cm Centimeter {C} Frame C {Cj} Frame C, COM Center of Mass CT Contact Time CTS Carpal Tunnel Syndrome d Distal End of a Segment DEXA Dual Energy X-ray Absorptiometry E A Randomly Selected Point on a Segment EBI Equivalent Biomedical Index EBI Mean value of EBI EMG Electromyogram FEF Fractional Effective Force GME Gross Mechanical Efficiency h Hour HC Hand Contact HR Hand Release TV Intravenous xxvii kg Kilogram kHz KiloHertz km Kilometer log logarithm m Meter m' Number of Unknown Constants in Response Equation m3 Cubic Meter M Male MEE Metabolic Energy Expenditure Min Minute MWP Manual Wheelchair Propulsion MWUs Manual Wheelchair Users n Number of Subjects n' Number of Data Points or Tests N Newton N.m Newton.Meter p Proximal End of a Segment PCI Physiological Cost Index PEF Partial Effective Force rad Radian ROM Range of Motion ROT Rotation RSI Repetitive Stress (Strain) Injury RT Release Time s Second (Time Unit) SCI Spinal Cord Injury SPADI Shoulder Pain and Disability Index ST Stroke Time Std. Dev. Standard Deviation T3 Third Vertebrae of the Thoracic Part of Vertebral Column T4 Forth Vertebrae of the Thoracic Part of Vertebral Column xxviii T5 Fifth Vertebrae of the Thoracic Part of Vertebral Column T6 Sixth Vertebrae of the Thoracic Part of Vertebral Column TEF Total Effective Force THB Total Heart-Beats THBI Total Heart-Beats Index Tn nth Vertebrae of the Thoracic Part of Vertebral Column UBC University of British Columbia USB Universal Serial Bus VICON Brand Name of a Motion Analysis System WPSR Wheelchair Propulsion Strength Rate WUJII Wheelchair User Joint Injury Index (using BMI) WUJII Mean Value of WUJII w u j i r Wheelchair User Joint Injury Index (using %BF) WUJJJ' Mean Value of WUJII' WUSPI Wheelchair User's Shoulder Index Xo-9 X-direction of the Local and Global Coordinate Systems for Upper Limb Model XI First Horizontal Seat Position with Respect to Wheel Axle X2 Second Horizontal Seat Position with Respect to Wheel Axle X3 Third Horizontal Seat Position with Respect to Wheel Axle X-ratio Ratio of X-position to Arm length Yo-9 Y-direction of Local and Global Coordinate Systems for Upper Limb Model Y l First Vertical Seat Position with Respect to Wheel Axle Y2 Second Vertical Seat Position with Respect to Wheel Axle Y3 Third Vertical Seat Position with Respect to Wheel Axle Y-ratio Ratio of Y-position to Arm length xxix Acknowledgements In the name of God, the Compassionate, the Merciful First I would like to express my gratitude to my supervisor Dr. Farrokh Sassani. I am deeply indebted for the endless help, support and guidance he has given me, and his countless efforts in advising me throughout the different stages of this research. His profound knowledge and sprit of scientific exploration, have contributed significantly to the fulfillment of my academic goals, and will benefit me in my future pursuits. I am particularly grateful to my very active supervisory committee member, Dr. Bonita J. Sawatzky, for her invaluable support and many hours of engaging and inspiring discussions about this study. I would like to thank Dr. Thomas R. Oxland, Dr. Antony J. Hodgson, and Dr. Michiel van de Panne for supporting this research and providing access to facilities. I am also grateful to Dr. Thomas R. Oxland and Dr. A. William Sheel for their great suggestions for this dissertation. I would also like to thank, Mr. Mohammad Sepasi, Mr. Amin Karami and Mr. Edward Cheung for their kind assistance during the tests. I wish to thank my colleagues in the Process Automation and Robotics Laboratory: Dr. Reza Tafreshi, Dr. Reza Ghodsi, Dr. Tao Fan, Ms. Pirmoradi, for their moral support. I am grateful to my dear parents, for their constant encouragement and prayers, and to my sisters and brother for their great emotional support when I was far from them. I wish to thank my wife's family for their endless moral support, too. Last but not least, I wish to express my deepest gratitude to my dear wife, Sima Sajjadi, for her understanding, patience, encouragement and support during all the hard times that I went through; and my adorable children, Amirali and Melika, who were inexhaustible sources of motivation for me, and without whose sacrifices I would never have been able to complete this project. xxx T(? my dear parents Ho my dear wife and lovely children xxxi CHAPTER 1 Introduction 1.1 Foreword A survey conducted by Canadian Community Health reported that about 155,000 Canadians were using a wheelchair for mobility in 2000/01 [1]. hi the USA, statistics reported by researchers and official sources indicated that the number of wheelchair users had grown from 1.2 million in 1987 [2] to approximately 2.1 million in 2003 [3]. These people rely on wheelchair for locomotion and other daily activities. Manual Wheelchair Propulsion (MWP) is inefficient and physically straining. It is a natural expectation for Manual Wheelchair Users (MWUs) to be comfortable, when they use their wheelchairs for mobility and accomplishing various activities. Normally, upper limbs are used for prehensile and manipulation tasks, whereas MWUs have to use their upper limbs for additional functions such as moving between the wheelchair and 1 other essential locations (bed, car seat, bathtub etc.), the pressure-relief raising to eliminate the pressure sore, reaching overhead objects, and propelling wheelchair. The nature of wheelchair propulsion is such that MWUs are essentially walking with their upper limbs [4]. It has been reported that, on average, a M W U performs about 3,500 propulsive strokes per day [5]. Considering the millions of strokes during the lifetime, MWP can be categorized as a serious repetitive motion. Repetitive Stress (or strain) Injuries (RSI) are "a variety of musculoskeletal disorders, generally related to tendons, muscle, or joints, as well as some common peripheral-nerve-entrapment and vascular syndromes [6, pp. 943]". It is known that the repetitive stroke to manually propel a wheelchair is related to RSI in the shoulder, wrist, and elbow [2]. It has also been reported that the propulsion technique plays a role in the mechanical efficiency of the propulsion [7, 8]. MWP is a form of ambulation, whose mechanical efficiency is about 10% at best [8-10]. As a consequence, MWP is associated with a high mechanical load on the upper limb joints, which may lead to overuse injuries in shoulder, elbow and wrist. A reliable efficiency assessment must consider both the mechanical and biological aspects of MWP [9]. Therefore, Gross Mechanical Efficiency (GME) must be used to determine the efficiency of the physiological systems. The position of the wheelchair seat with respect to the wheel axle is one of the most important factors that is related to MWP [11], and can cause injuries to the upper limbs [12, pp. 270-271]. Simply stated, changing the seat position will change the joint loads [13]. The subsequent chapters will have more detailed review for each section to extend the discussion and make connection to the chapters' contents. 2 This study considers that a major part of RSI incidences in wheelchair users is the result of forceful motions and awkward postures that MWUs experience during wheelchair propulsion, and proposes a method to determine the optimum seat position to minimize injury for individual users. To accomplish this, an instrumented wheel as part of the required experimental setup was designed, fabricated and validated to measure the loads applied on the hand of the user during MWP. Also, two methods were developed and elaborated to determine the dynamic loads on the user's joints as part of the parameters needed by the proposed method to define the optimum seat positions. The thesis layout is presented at the end of this chapter. 1.2 Research Questions, Hypotheses, Objectives and Limitations This study was performed to assess the feasibility of answering the following research questions in a cross-sectional study: • Is the PY6 load transducer a suitable and sufficiently accurate measuring device for determining 3-Dimensional (3D) forces and moments in the handrim of a wheelchair during propulsion? • How can the optimum horizontal and vertical seat positions with respect to the wheel axle (X,Y) be determined for each wheelchair user? • Can one propose some generic rules to estimate the optimum seat position for various users? 3 • Is there a relationship between the average linear wheelchair velocity (simply referred to as velocity) and the degree of injury of the wheelchair user? • Is there a relationship between the velocity and the propulsion efficiency of the wheelchair users? • How can one estimate the probable injuries to upper limb joints? • To what extent will a 3D simulation of the upper limb joints be reliable, if in a vision system only two markers are used for kinematic tracking and analysis? (A smaller number of markers allows a convenient and speedy process.) To answer these research questions, we considered and focused on the following hypotheses and objectives, respectively: We hypothesized that: • The fabricated instrumented wheel system, using the PY6 load sensor, will prove to be a reliable and valid instrument for measuring 3D forces and moments at the hub of a standard wheelchair during MWP. This hypothesis is based on the assumption that the specifications reported by the manufacturer are dependable. • Changing the seat position of the wheelchair can alter the Gross Mechanical Efficiency and the upper limb joint loads of MWUs. This hypothesis is based on the assumption that the combination of the human and the manual wheelchair presents a closed-loop linkage-system during the propulsion. Changing the seat position, will change the length of the virtual link between the center of the wheel hub and the hip of the user. This apparently 4 simple kinematic change affects the kinetics of the system during propulsion and has a host of other influences. The objectives of this study were then set to: • Develop, fabricate and validate a versatile instrumented wheel. • Propose three new indices for efficiency and injury assessment, which consider both mechanical and biological aspects of MWP. • Propose a method to prescribe the optimum wheelchair seat position for a user, based on the efficiency and injury indices. • Assess the injury at upper limb joints during MWP by using the inverse dynamic method and the new injury indices. • Develop and verify a new model for analysis of the dynamics of the upper limb. The limitations of this study are as follows: • Small sample size of the subjects. Eight MWUs were recruited in this study. • The study was focused on male subjects with Spinal Cord Injury (SCI) and lesion below the fifth thoracic vertebrae (T5). • The subjects used the instrumented wheelchair not their own. • The data from the dominant side of the subjects were used for the analysis. • The propulsion techniques were not necessarily the same for all subjects. • Limited range of variation for the seat position. 5 1.3 An Overview of the Upper Limb Joints' Anatomy In this section, the important joints of the upper limb, which are: shoulder girdle, elbow, and wrist joints are introduced. The hand joints are not discussed here, as minimal concerns and injuries have been reported by MWUs. 1.3.1 Shoulder Girdle Joints The shoulder girdle consists of three true joints and one articulation or false joint: glenohumeral, acromioclavicular, sternoclavicular, and scapulothoracic joints, respectively. The glenohumeral joint is formed where the ball of the humerus fits into a shallow socket on the scapula, which is called the glenoid cavity (Figure 1.1). The acromioclavicular joint is where the clavicle meets the acromion. The sternoclavicular joint provides the only connection of the arms and shoulders to the main skeleton on the front of the chest (Figure 1.2). The scapulothoracic joint helps to keep the gleniod cavity lined up during shoulder movements. The glenohumeral joint is the most important joint in the shoulder girdle and the most mobile ball-and-socket joint in the human skeleton because the size of the semi- spherical humeral head is much larger compared to the shallow and relatively flat cavity of the glenoid [15] (Figure 1.3). The possible movements and Range of Motion (ROM) of this joint are as follows: Flexion (0-90°) , extension (0-45°) , internal rotation (0-40°) , external rotation (0-55°) , adduction (0-45°) and abduction (0-180°) [16, page 87]. 6 CMMIi 2003 Figure 1.1 Front view of acromiclavicular and glenohumeral joints (Image courtesy of medicalmultimediagroup.com [14]). Figure 1.2 Front view of the bones of the right shoulder girdle, and sternoclavicular and scapuathoracic joints (Image courtesy of medicalmultimediagroup.com [14]). 7 Acromion Acromio- clavicular ligament Joint capsule (cutr End View of Scapula Coraco- lavicular ligament Tendon of biceps muscle Coraco- acromial ligament racotd process ' M M * . : W I I Figure 1.3 Side view of the bones and ligaments of the shoulder girdle, and section view of glenohumeral joint capsula (Image courtesy ofmedicalmultimediagroup.com [14]). 1.3.2 Elbow Joint The elbow joint is a hinge joint composed of three separate joints: humeroradial, humeroulnar and proximal radioulnar (Figures 1.4 and 1.5). The joints between the humerus and both the ulna and radius (Figure 1.5) act as a typical hinge joint, allowing only flexion and extension, but the head of the radius and ulna is a pivot joint [16, pp. 91-93]. The possible movements and ROM of this joint are as follow: Flexion (140°), extension (0°), pronation (90°), and supination (90) [16, pp. 91]. 8 C.VIMG 2001 Figure 1.4 Medial view of the bones of the right elbow joint (Image courtesy of medicalmultimediagroup. com [14]). C M M G 2001 Figure 1.5 Lateral view of the bones of the right elbow joint (Image courtesy of medicalmultimediagroup.com [14]). 9 1.3.3 Wrist Joint The proximal wrist joint (radiocarpal joint) is a typical condyloid joint. It is Figure 1.6 Back view of the right wrist joint (Image courtesy of medicalmultimediagroup.com [14]). 1.4 Terminology MWP is a stroke cycle whose Stroke Time (ST) is divided into two main phases: (a) propulsion phase, and (b) recovery phase. The propulsion phase or the Contact Time (CT) occurs when the hand of the user has contact with the handrim. The recovery phase, or Recovery Time (RT), occurs when the hand has no contact with the handrim. The sum of CT and RT is equal to ST. The Hand Contact and Hand Release are abbreviated as HC and HR, respectively. The propulsion phase consists of pull and push phases. The located between the radius and ulna on one side, and the wrist on the other (Figure 1.6). Wrist movements include flexion, extension, abduction, and adduction. Proximal row Distal row 10 recovery phase is divided into four parts: follow through, retrieval, preload and pre- impact. Figure 1.7 illustrates the complete six phases of standard manual wheelchair propulsion [12]; role of the push phase should not be confused with the propulsion phase. In some research reports, these two terms have been incorrectly used interchangeably. Stroke C y c l e puisio Recovery Phase Pull phase Push Phase Follow through Retrieval Preload Pre- impact P C ) 0 % - (HR) Hand Contact Hand Release (HQ 100% Hand Contact Hand Has Contact Hand Is Released Recovery Time (RT) Stroke T i m e (ST) Figure 1.7 Different phases of a complete stroke cycle and the related terminology. 1.5 Previous Studies There are many published studies related to MWP. Some of the previous research related to the present work is presented in this section. Due to the vast area of these studies, they are classified into four specific topics: Kinetics of MWP, Injuries Due to MWP, Effect of Seat Position on MWP, and Metabolic Energy Expenditure (MEE) during MWP. 11 1.5.1 Kinetics of M W P Some of the previous studies focused on the kinetics of MWP [7-9,17-23]. In this Section, some of the key kinetic factors during MWP are reviewed. Figure 1.8 illustrates the most important forces and moments applied by the hand of the manual wheelchair user on the handrim and thus on the wheel center. Ff,.x, y, z, Fc.Xi y> z, Mh-X, y, z, Mc.Xp y> z are the force and moment components with respect to the hand and wheel center coordinate systems, respectively. Fc, Mhy and Mcy are not shown in Figure 1.8. The origin of the hand coordinate system is placed at the contact point between the hand and the handrim. The origin of the wheel coordinate system is placed at the center of the wheel, r/, is the mean radius of the handrim and (p is the angular position of the hand at the handrim contact point. Total applied force (F,olai) on the handrim is obtained by using the force components and either Equation 1.la or 1.1 .b. Total Effective Force (TEF), which is the virtual force required to produce propulsion, is obtained by using Mcz, the moment around the z-axis, and Equation 1.2 (1.1a) (1.1b) [8,9,17-19]: TEF = Mcz • r'h -i (1.2) 12 Handrim (a) (b) Figure 1.8 Illustration of forces and moments applied on the handrim during wheelchair propulsion: (a) side view; (b) front view. Fractional Effective Force (FEF) is an important factor because it shows the ratio of the required force for propulsion to the force produced by the wheelchair user during the propulsion phase [8,9,20-22]. FEF is related to Ftotai and TEF as follows: FEF = T E F • F~Jal • 100 (1.3) 13 Partial Effective Force (PEF) is the tangential part of the total force applied on the hand rim. PEF is related to Fcx, Fcy and <p as follows: PEF = Fa • sin<p-F' • cos«p (1.4) The torque around the wheel center (M c z) is dependent on the torque around the hand (Mhz) and PEF as [9] From the mechanical point of view, if we increase TEF, we should expect FEF and the mechanical efficiency to increase, but we still cannot say that G M E will also increase. de Groot et al. [9] found that using feedback-based learning, TEF increases, but G M E decreases. This could be because of a conflict around the elbow that arises with the direction of application of the tangential force. Figure 1.9 illustrates that applying tangential force on the handrim could lead to a contradictory situation. The flexor muscles should act to mechanically balance the resultant moment around the elbow resulting from tangential force, whereas the extensor muscles must act to extend the elbow. This co-contraction may help the stability of the motion in some cases, but it will Mcz = Mhz + PEF • rh (1.5) Mhz can be obtained by using Equations 1.4 and 1.5, and is given by Mhz=Mcz-(Fcx-sm(p-Fcy-cos(p)rh (1.6) 14 produce negative power from the physiological point of view. To arrive at an optimum situation, one should avoid this conflict by redirecting the applied tangential force [9]. One should consider both mechanical and biological aspects of wheelchair propulsion to be able to analyze this motion properly before offering any suggestions for its improvement. However, there is no guarantee that the more efficient propulsion is the safer one for the user. A concurrent optimization of GME and probable injury prevention can lead to a breakthrough in this field. Shoulder Shoulder Elbow Direction of the actual \ force in the plane Figure 1.9 The relationships among the direction of the applied force, joint torques, and rotation around the shoulder and elbow (inspired by [9]). 15 1.5.2 Injuries Due to MWP Statistics reported by researchers indicate that a considerable number of wheelchair users suffer from pain in their upper limb joints. In MWUs, the most commonly reported site of musculoskeletal injury is the shoulder (rotator cuff injuries, etc.), and the most common neurological cause of upper limb pain is Carpal Tunnel Syndrome (CTS), with prevalences of between 31 and 73% [2,7, 24-27] and between 49 and 73%, respectively [7,28-33]. Another common musculoskeletal injury is elbow tendonitis, being most prevalent in this site. Boninger et al. [4] reported that the prevalence of elbow pain in MWUs is about 16%. Prolonged use of a wheelchair could result in upper limb overuse injury [2], however, MWUs do benefit from the cardiovascular exercise associated with propulsion [34]. Efficient wheelchair propulsion with minimum injury pain is related to the manner and level of the loads that a user applies to the handrim during MWP [12]. Median nerve damage has been associated with high-force and high-repetition wrist motions. It has been found that weight loss of MWUs may prevent such nerve injury, which is the fundamental pathophysiology behind the development of CTS [23]. Su et al. [17] reported in 1999 that high upper limb joint loads may imply the risk of joint over-use injury. Boninger et al. suggested that reducing the forces during wheelchair propulsion may minimize developing shoulder injuries [18]. None of the previous studies on MWP introduced an injury index, which covers different factors that can cause injury during propulsion. An index that considers different aspects of the propulsion and anatomical specification of a user may help to estimate the probable injury due to MWP. 16 1.5.3 Effect of Seat Position on MWP The wheelchair seat is one of the interfaces between the user's body and the wheelchair in the closed-loop linkage model of the human body and the wheelchair during MWP. Changing the wheelchair seat positions will alter the position and orientation of the upper limb segments of the user. This alteration affects the dynamics of MWP. It has been reported that there is a relationship between wheelchair seat height, and both cardio-respiratory and kinematic parameters [19]. For example, differences in the kinematics and kinetics of the upper limbs appear at different seat positions, significantly affecting the Wheelchair Propulsion Strength Rate (WPSR) (p<0.05). Su et al. [17] used WPSR in their study as an index, and concluded that optimal alignment of the wheelchair for the user could reduce joint loads and prevent injury. They used nine positions for the user during the tests, by considering three horizontal positions of the seat with respect to the wheel axle and three elbow angles when the hand is on the top of the handrim. Boninger et al. [35] determined that the pushing angle was related to the horizontal and vertical distances of the subject's shoulder from the wheel axle. Their study showed that the frequency of propulsion and the rate of rise of the resultant force were significantly correlated to the horizontal distance of the subject's shoulder from the wheel axle— p<0.0\ andp<0.05, respectively. Richter [13] suggested that the seat position of the wheelchair affects the torques on the shoulder and elbow joints, the push angle, and the push frequency during MWP. 17 Richter considered the length of the position vector from the hub of the wheel to the user's shoulder as the variable for seat position. Van der Woude et al. [19] evaluated the effect of seat height on the cardio- respiratory system and kinematics of nine non-wheelchair users. They concluded that seat height adjustment is critical, and is related to the anthropometric dimensions of the user. They considered elbow angle as a measure for seat height. This angle was measured when the user put his hand on the top of the handrim. They suggested that the seat height is optimum when the elbow angle is between 100° to 120°. In another study, Wei et al. [36] reported that the seat position is a critical factor affecting the MWP movement and wrist kinematics. The wrist joint angle and range of motion varied according to seat height. However, they did not indicate the ideal seat position in their study. Kotajarvi et al. [11] in a recent study investigated the effect of seat position on wheelchair propulsion biomechanics. They used thirteen experienced wheelchair users to propel an instrumented wheelchair over a smooth level floor at a self-selected speed. They changed the seat position horizontally and vertically and performed the tests at nine different positions. They reported that a shorter distance between the axle and shoulder (low seat height) improve the push time and push angle (p<0.0001). They did not normalize the horizontal and vertical positions for the subjects. The above studies indicated that there is a relationship between the seat position and the parameters of the dynamics of MWP. All of these studies referred to the effect of changing the seat position on different factors. Actually, most did not consider two- dimensional variations for the seat position, and those who used two-dimensional 18 changes for the seat position did not determine the optimal seat position for each individual. 1.5.4 Metabolic Energy Expenditure during MWP Researchers and designers have made numerous attempts to improve the efficiency of MWP. They have tried to better understand this activity and improve its efficiency by using new propulsion techniques, new wheelchair designs, or both. One category of related research focuses solely on the mechanical energy and efficiency of MWP [10,37,38]. In fact, mechanical efficiency is not a good measure to verify the degree of suitability of a wheelchair's seat position. As MWP is produced by the combination of a human being and a mechanical device, one cannot determine the efficiency of MWP by using the mechanical efficiency equation only. To define the optimum seat position, G M E must be used [9]. To determine G M E , the physiological cost, or Metabolic Energy Expenditure (MEE) must be measured. M E E can be measured by indirect calorimetry, which assumes that all energy produced in the body depends on oxygen uptake. The most common method of measuring oxygen uptake is by spirometry, which analyzes exhaled air for its oxygen content [9]. Another method of measuring M E E is counting the heartbeats. It has been reported that there is a very good linear relationship between the heartbeat and the oxygen uptake profile for both steady and non-steady state situations [39,40]. Hood et al. 19 [39] studied both steady-state and non-steady-state human gait, and proposed a Total Heart-Beat Index (THBI) as THBI = Total heartbeats during exercise period / Total distance traveled (m) (1.7) They used repeatability statistics and found the THBI is comparable to the oxygen cost, and that it is more reliable than the Physiological Cost Index (PCI) given by PCI = (HR(SS)-HR(R)) / velocity (1.8) where HR(SS) is the average steady-state working heart rate, HR(R) is the average resting heart rate, and velocity is the average linear velocity of the wheelchair. Hood et al. also reported that THBI can be considered as a reflection of the metabolic energy expenditure and may be used in comparative studies, as long as the same subjects are involved. Andrea Natali et al. [41] asked 12 young healthy individuals to use a cycloergometer. They reported a relationship close to linear for heartbeat and oxygen uptake during a cycling test after a bolus intravenous (TV) injection of either carnitine or saline was administered 10 min before the test. Their study consisted of 5 periods: (1) 30 min baseline period; (2) 40 min of cycling (aerobic exercise); (3) 2 min pause; (4) 2 min of intense (anaerobic) exercise; (5) 50 min of recovery. Izerman et al. [42] reported that during paraplegic gait analysis, they observed a good correlation (r = 0.86) between the oxygen cost and the change of heartbeat (steady state minus rest). However, Schmid et al. [43] performed a study using different groups 20 of Spinal Cord Injury (SCI) and able-bodied subjects and reported that the slope of the line that represents the linear relationship between the oxygen consumption and the heart rate, changes for different groups of the subjects. Bot et al. [40] investigated the validity of using heart rate response to estimate oxygen uptake during various non-steady-state activities. They studied interval tests on a cycloergometer by using 16 able-bodied subjects, and took simultaneous heart rate and V02 measurements. Linear regression analysis revealed a high correlation between heart rate and V02 (r - 0.90 ± 0.07). In the second experiment they used 14 non-wheelchair- bound subjects and performed a wheelchair field test. A significant relationship was found for all subjects (r = 0.86 ± 0.09). They suggested that V02 may be,estimated from individual Heart rate- V02 regression lines during non-steady-state exercise. Sawatzky et al. [44] reported in a recent study that heart rate has a very good correlation with oxygen consumption (r - 0.82) in SCI individuals with lesions below the fifth thoracic vertebrae (T5). For subjects with higher lesions, the correlation was weaker. They reported that this may be caused by the effect of the autonomic parasympathetic nerves on heart rate. They indicated that it is important to consider that heart rate does have its limitation and it should only be used to measure within-subject differences. hi another study, Tolfrey et al. [45] performed steady-state wheelchair propulsion of 16 paraplegic, elite male wheelchair racers with the classification of T3 and T4 lesions and reported that the group mean of the individual correlation coefficient for the V02- heart rate relationship was 0.99. The above studies give enough confidence to assume a relationship close to linear between oxygen consumption and the heart rate of SCI subjects with lesions below T5. 21 Therefore, heart rate can be used as an alternative to oxygen consumption to estimate the variation of the G M E in these subjects for within-subject analysis. 1.5.5 Instrumented Wheel Knowing the forces and moments that a wheelchair user exerts on the handrim is necessary for an inverse dynamics approach to calculate the forces and moments in the upper limb joints. Collecting reliable 3D kinetic data, especially the forces and moments applied to the handrim of a manual wheelchair, is one of the most challenging aspects of gaining an in-depth understanding of the biomechanics of wheelchair propulsion. A number of research groups have fabricated and instrumented wheels to measure the forces and moments applied on the handrim by the wheelchair user [46,47-51]. Although it is advantageous to develop and fabricate an in-house system, which allows greater flexibility in adding hardware and obtaining various signals, it is important to determine the specifications of such an instrument. Detailed specifications determine the system's level of reliability and usefulness. The collected data cannot be useful if they are unreliable. Uncertainty analysis is a method that helps the researcher to calculate the level of uncertainty of the acquired data. This method can estimate the expected errors for different results obtained from the system. Cooper et al. [52] determined the uncertainties for the data acquired from their instrumented wheel (Smartwhee l). They determined the uncertainty for the forces and moments as 1.1-2.5 (N) and 0.03-0.19 (N.m) in the plane of the handrim, and 0.93 (N) and 2.24 (N.m) in the wheel axle direction, respectively. As uncertainty analysis is an analytical method, one will have greater confidence when an 22 experimental technique uses the actual output of the system to determine the specification of the respective instrumented device. Wu et al. [48] performed static and dynamic analyses for their fabricated instrumented wheel and determined the degree of linearity and drift of their system. They determined part of the specification of their system by using the experimental method. In this section, the previous studies have been presented to explain the motivations regarding the related topics. As this study consists of different aspects of M W P , such as fabrication of an instrumented wheel, clinical experiments, modeling of the upper limb, and analytical analysis, additional related published studies are presented in the corresponding chapters that follow. 1.6 Possible Solutions Our review of the previous studies indicated that determining the optimum seat position for a user is still a challenge and warrants further investigation. One of the main purposes of the present study is to develop a method to increase efficiency and prevent or reduce probable injuries during MWP. In this research, three new indices for manual wheelchair propulsion analysis are proposed, as follows: • Equivalent Biomedical Index (EBI) reflects the behavior of G M E . The total heartbeats of the subject represents the pattern of M E E , and is one of the factors used in EBI equation. The above literature review indicates that there is a reliable relationship between the heart rate and the oxygen uptake. Heart rate can then be a good alternative to oxygen uptake for estimating G M E . 23 • The Wheelchair User Joint Injury Index (WUJII) reflects a value that is representative of the MWU's joint injury, and uses the joint loads, pushing frequency, Body Mass Index (BMI), and total weight of the user and the wheelchair. If WUJII has a high value, the risk of injury is also high. • The third index is WUJII', which is the same as WUJII except that Percentage of Body Fat (%BF) is used instead of the BMI in the relation. Comparing the results of the two injury indices will help to determine the role of BMI and %BF on the probable injury. The effects of changing the two seat-position parameters on the value of the proposed indices are investigated to find the optimum position. In this study, an instrumented wheel is fabricated, and validated through a general uncertainty analysis method. The specifications of the instrumented wheel are determined by using both static and dynamic experiments. The loads that a user applies on the handrim during MWP are part of the data required to calculate propulsion efficiency and analyze the optimum seat position for wheelchair users, in order to improve performance and develop injury-prevention techniques. The values of the proposed indices for six possible seat positions are calculated and the results are analyzed to derive some generic rules that can be used to estimate the optimum seat positions for all users. Some of the data needed to determine WUJII or WUJII' at each of the upper limb joints are the values of the loads at these joints. To calculate the net joint forces and moments of the upper limb during MWP, an algorithm necessary for an inverse dynamics solution is developed. Considering probable priorities for injury prevention at specific 24 joint, corresponding injury index for the joint of interest will be used to determine the optimum position. To make the testing procedure and post-processing of the acquired data more convenient, a new model for the dynamics of the upper limb is introduced that only needs the geometric positions of two anatomical sites to perform kinematic analysis. This model has some advantages and some limitations (see discussion in Section 6.4). However, it makes data acquisition noticeably more convenient compared with other models that use more anatomical sites [12,46]. 1.7 Thesis Organization The thesis is organized as follows. The current chapter has provided a general background and the motivation for this study, and outlined the research questions, hypothesis and objectives. It has also presented an overview of MWP kinetics to open the related discussions. Numerous studies have analyzed MWP. Some were reviewed in this chapter; additional related work will be referred to in subsequent chapters. Chapter 2 describes the design, fabrication and validation of an instrumented wheel. Uncertainty analysis for the instrumented wheel is presented, and the required static and dynamic experiments for determining the specification of the instrumented wheel are described. One book chapter [53] and two journal papers [54,55] have been published based on the results presented in this chapter. In Chapter 3, an assessment of the efficiency and injury potential during MWP is presented. Three new indices, EBI, WUJII, and WUJII' are proposed and described for this purpose. 25 Chapter 4 outlines the proposed method for determining the optimum seat position of a manual wheelchair, involving experiments conducted on eight wheelchair user subjects. This is followed by an analysis of the results to extract generic rules to estimate the optimum seat position for all users. Also, the optimum positions are prescribed for two subjects. One conference paper has been prepared based on part of the results of this chapter and presented as poster [56]. In Chapter 5, a 3D rigid-body model for the dynamics of the upper limb is presented, and a method of calculating the upper limb joint forces and moments is described. This chapter also addresses the injury-assessment method for the upper limb joints during MWP. Chapter 6 provides a new model for analysis of the dynamics of the upper limb. The reliability of the new model is investigated by determining the relative error for the calculated loads. The advantages and limitations of the new model instead of the method used in Chapter 5 are then presented. In Chapter 7, a summary of the main conclusions drawn from the research, its limitations and contributions, and suggestions for future work are presented. 1.8 Concluding Remarks Many of the studies cited in this chapter used able-bodied or non-wheelchair user individuals as subjects. The absence of actual manual wheelchair user subjects eliminates most of the external validity of the results [57]. Also, the repeatability of the tests for each individual is an important factor and is not considered in most of the studies. However, they do shed light on new trends and approaches, and some suggest innovative 26 i d e a s f o r a n a l y z i n g M W P . In t h i s t h e s i s , a r e l i a b l e i n s t r u m e n t e d w h e e l f o r m e a s u r i n g the l o a d s a p p l i e d b y the u s e r o n the h a n d r i m i s f a b r i c a t e d . A m e t h o d o l o g y i s d e v e l o p e d f o r p r e s c r i b i n g the o p t i m u m seat p o s i t i o n f o r e a c h i n d i v i d u a l , u s i n g th ree n e w i n d i c e s p r o p o s e d to p e r f o r m e f f i c i e n c y a n d i n j u r y a s s e s s m e n t s . A 3D r i g i d - b o d y i n v e r s e d y n a m i c s m e t h o d w a s u s e d t o c a l c u l a t e the l o a d s at the u p p e r l i m b j o i n t s as pa r t o f t he d a t a r e q u i r e d to c a l c u l a t e the v a l u e s o f the p r o p o s e d i n d i c e s at e a c h j o i n t . T h e o p t i m u m seat p o s i t i o n s w e r e d e t e r m i n e d f o r t w o s u b j e c t s t o p r e v e n t i n j u r y at s p e c i f i c j o i n t s b y u s i n g the j o i n t i n j u r y i n d i c e s . F i n a l l y , a n e w m o d e l f o r the a n a l y s i s o f t he d y n a m i c s o f t he u p p e r l i m b w a s d e v e l o p e d a n d v a l i d a t e d to s i m p l i f y t he e x p e r i m e n t a l p r o c e d u r e a n d t h e r e q u i r e d p o s t - p r o c e s s i n g . 2 7 CHAPTER 2 The Instrumented Wheel 2.1 Introduction In Chapter 1, the importance of the instrumented wheel for kinetic analysis of MWP was explained, and a review of the relevant literature was presented, to emphasize that this equipment is an essential device for kinetic analysis of MWP. In the present work, an instrumented wheel system is fabricated and validated by using the general uncertainty analysis. Also, the specifications of the wheel system are determined using both static and dynamic experiments. This system enables the forces and moments applied by the wheelchair user on the handrim to be determined. It is important to understand how these forces and moments are generated and what factors influence them. The applied loads are part of the data required to calculate propulsion efficiency and analyze the optimum seat position for wheelchair users, in order to 28 improve performance, identify the probable causes of injuries, and develop injury prevention techniques. This chapter also presents a procedure for calculating the essential dynamic variables used in the study of manual wheelchair propulsion. An important feature of the force/moment calculation procedure is that, together with encoder data analysis, it allows one to determine the angular position of the contact point between the hand and the handrim without the use of cameras. This angular position is a critical factor in determining moments and the effective tangential force acting on the wheelchair user's hands and upper limbs, which can result in discomfort or injury. The general uncertainty analysis was performed for different outputs of the instrumented wheel, and the system's level of reliability was determined. The results indicated that the uncertainty for the forces and the moments of interest were in the range of 1.4—1.7 N and 0.58-0.68 N.m in the plane of the handrim, and about 3.40 N and 0.25 N.m in the wheel axle direction, respectively. For the developed system, however, the uncertainty values for the important load components, namely the planar forces and axial moment, were low. The resulting uncertainties represent an estimation of the expected errors in future data gathering and analysis. The static and dynamic test protocols were designed to cover all loading conditions. To determine the specifications of the system, the linearity, repeatability and mean error of the measurement system in both static and dynamic situations were calculated. These specifications allow one to determine the level of the system's reliability, and gain confidence in the results and future applications. 29 2.2 Instrumentation To conduct an uncertainty analysis, as well as static and dynamic verification for manual wheelchair propulsion, stationary tests were performed to measure the forces and moments applied by the wheelchair user on the handrim, and the angular position of the wheel during propulsion. Currently, there is no sensor available that can measure the required forces and moments directly. Instrumented wheels are mechatronic systems (a combination of hardware and software) that process the data acquired by the sensors and calculate the desired values. In this research, an instrumented wheel assembly was designed and fabricated and the required setup for the tests was prepared to accurately determine uncertainties and system specifications. The setup for this part of the study consisted of a wheelchair, the instrumented wheel, a platform with two rollers to allow stationary tests (roller-rig), an A C motor, two Personal Computers (PCs), an Analog-to- Digital (A/D) data acquisition board, and four different static and dynamic loading set- ups. 2.2.1 Wheelchair A Quickie (Sunrise Medical Inc.) 40-cm-wide wheelchair with standard spokes was used in this study. The wheelchair had solid gray rubber tires 58.25 cm in diameter and 3 cm in width. The handrim was 54 cm in diameter, and the positions of the backrest and axle of the wheels (thus the seat) were adjustable. 30 2.2.2 The Instrumented Wheel The instrumented wheel system itself consisted of a standard-spoke wheel from Quickie wheelchair, a six-component load transducer (Model PY6-500, Bertec Inc., Measurement Excellence™), an A M 6500 external amplifier, a signal conditioning circuit, a power supply, a handrim assembly, an encoder (Sl 360 IB), a slip ring (AC 6373), two gears, and insulated shielded cables (Figure 2.1). As some of the data acquisition components had to be mounted within the wheelchair, counterweights were used to maintain the wheel's rotational balance. The PY6 load transducer came with a digitally stored calibration matrix and used 16-bit digital signal acquisition and conditioning with a sampling rate of 1 kHz. The digital signal output could be plugged directly into the standard Universal Serial Bus (USB) port of a personal computer via the A M 6500 amplifier without requiring an additional PC board for A/D signal conversion. The transducer had sensitivity levels of 2 mV/N and 2 mV/(N.m), an accuracy of 99.5%, ±1.0% cross-talk, a full mechanical load rating of 1250 N for in-plane forces Fx and Fy, 2500 N for the out-of-plane force Fz, 60 N.m for moments Mx and My, and 30 N.m for moment Mz with respect to the first local coordinate system (Figure 2.2). The load cell was mounted on the wheel with its z-axis aligned with the axle of the wheel. The origins of the global and first local coordinate systems were concentric. The handrim assembly had three parts: a handrim, a 3-mm thick round aluminum face-plate, and six reinforced aluminum spokes. The encoder had three input-output channels, and its resolution was 1°. Gears were used to transfer the wheel rotation, and, with a gear ratio of 8 to 1, increase the resolution of the measured angular position (0) to 31 0.125°. The first (large) gear was mounted on the wheel shaft and the second (small) gear was mounted on the encoder shaft (Figure 2.3). A slip ring aligned with the wheel axle allowed continuous transfer of the transducer signals to the computer during wheel rotation (Figure 2.1). (a) (b) Figure 2.1 Instrumented wheel: (a) side view; (b) front view. 2.2.3 Roller-rig The roller-rig was a platform with two parallel rollers to allow stationary tests. The entire wheelchair was placed on the roller-rig, which had adjustable legs to maintain a horizontal position (Figures 2.1 and 2.4). 32 Figure 2.2 Initial position and orientation of global and two local coordinate systems on the instrumented wheel. Figure 2.3 Encoder gear system. 33 2.2.4 AC Motor The AC motor was connected to the shaft of one of the rollers to rotate the instrumented wheel during some of the tests. The motor speed was adjustable, and three different wheelchair angular velocities (3.0, 3.8 and 4.8 rad/s) close to required speeds for the subject tests, in this study, were used for the dynamic tests (Figure 2.4). The equivalent linear velocities were 3.15, 3.98 and 5.03 km/h, respectively. 2.2.5 Computers The experimental setup included two personal computers. The transducer interface software, Digital Acquire , used one computer to record the load exerted on the handrim by the user. The LabVIEW™ software on the second computer calculated the wheel's angular position as the load data was collected on the first computer. The 34 output of the encoder was analog voltage. Therefore, the angular position of the wheel was calculated using the Lab VIEW™ software and its counting option, where the value of the output increased 360 counts per revolution of the shaft of the encoder. A single PC was not used for both measurements because running two different software programs at the same time on one PC caused the measured times to be incompatible and shifted. 2.2.6 Data Acquisition Board A 12-bit AID signal conversion board (PCI-6025E) transferred the encoder's analog output data to the computer (note: the encoder had built-in hardware that converted the encoder pulses into an analog output). For consistency, when tests were set up, a specially wired push-button was used to activate both PCs at the same instance. Figures 2.5 and 2.6 give global views of the system as a schematic sketch and a block diagrams, respectively. 2.2.7 Static and Dynamic Loading Setups To perform the tests, three different static loading setups and one dynamic loading setup were used. These setups are elaborated in Section 2.5.1. In the next section, three coordinate systems for the instrumented wheel are introduced and the required dynamic equations are derived to determine the forces and moments applied by the user on the handrim. 35 Common mouse Connected to 110 volt power A C Motor Coupling • Bearing y y y y y y y y y y y y " " y y Figure 2.5 Global schematic rear view of the physical data acquisition system. PY6 , Signal processor • Slipring A M 6500 USB PCI (a) Encoder Screw terminal AID PC2 (b) Figure 2.6 Measurement signal flow diagram for: (a) load; (b) angular position. 36 2.3 Preliminary Experimental Protocol In this part of the study, one 27-year-old able-bodied male subject was used for the stationary tests because we were interested in testing the system rather than acquiring specific information related to the subject himself. The main idea was to propel the wheelchair, measure loads, and calculate uncertainties to verify the system. The subject had a daily training of 5 min for one week to become familiar with the experimental setup. For the main test, the subject propelled the wheelchair for 2 min, increasing his speed as much as conveniently possible and maintaining it steady for 1 min [49]. The data were then collected for the final minute of the test. 2.4 Derivation of Dynamic Equations To characterize and measure the forces and moments applied by the user on the handrim, three different coordinate systems were used (Figure 2.2). The global and first local coordinate systems have the same origin at the center of the wheel and the same direction at the beginning of the propulsion, which is the direction of the transducer coordinate system. The first local coordinate rotates with the wheel. The origin of the second local coordinate system (hand-coordinate system) is at the contact point between the hand and the handrim and moves with the handrim, but its axes remain parallel to the global coordinate axes. 37 2.4.1 System Calibration As indicated before, the PY6 load transducer came with the calibration matrix digitally stored within and interfaces to the PC through software (Digital Acquire™). Therefore, there was no need to determine this matrix, due to the automatic conversion of voltages to forces and moments, and the cross-coupling involved. Using this transducer, the digital signal output was plugged directly into the standard USB port of a personal computer without requiring an A/D signal conversion board. During the propulsion phase, in addition to the loads produced by the user, the system experienced dynamic preloads due to the rotating weight of the measurement system and the balancing weights, which should be taken into account to eliminate their effects. 2.4.2 Preload Equations The instrumented wheel was mechanically turned by the A C motor on the rollers without applying any force on the handrim to measure the net preloads. As the preloads changed sinusoidally with the rotation of the wheel, their values were calculated and their equations were determined with respect to the global coordinate system. All of the preloads can be described by the following generic periodic equation: P = asm(0 + £) + b (2.1) In this equation, P represents preload forces or moments, a and b are constants wkh dimensions [N] or [N.m], 6 is the wheel's angular position [radian] (which is a function of time), and % is the phase difference [radian] for the output of the x, y, and z 38 channels. Table 2.1 shows the preload equation constants for various load components. They were obtained by using the measured preloads, Fp.x>yiZ and MP.x<y<z, with respect to the first local coordinate system. 2.4.3 Local and Global Forces and Moments Forces and moments measured by the data acquisition software are not the values directly required for the MWP analysis. The effects of preloads must be considered, and by using the following equations, one can calculate the net local forces and moments with respect to the first local coordinate system: Fix ~ Fx Fpx (2.2a) Fiy ~Fy~ Fpy (2.2b) FLZ = Fz — FPz (2.2c) M l x = M x ~ M P x (2.2d) Mly= My ~MPy (2.2e) MLz=M2-MPz (2.2f) where FL.XiyZ and ML.x,y,z are the force and moment components applied by the wheelchair user, and FXtytZ and Mx-y>z are the measured force and moment components. All values are with respect to the first local coordinate system at the center of the wheel. 39 Table 2.1 Constants for different preload equations. p (preload) a [N, N.m] b [N, N.m] [radian] Fpx -26.5 2.5 0 Fpy 25.5 24.5 -7T/2 FPz 1 ~0 0 MPx 1.05 -1.05 nil Mpy -1.2 -0.2 0 MPz -0.1 ~0 0 The first local coordinate system is fixed to the wheel and rotates with it. The global coordinate system must therefore be used to calculate the forces and moments with respect to a fixed reference system. It should be emphasized that the origin of the global coordinate system coincides with that of the first local coordinate system, and that their z- axes are aligned. To calculate forces and moments in the global coordinate system, the following transformation relations, with reference to Figure 2.7, were used: = cos# • - sin 0 • FLy (2.3a) Fgy=sin0Fh:+cos0 -FLy (2.3b) Fv=Fu (2.3c) Mgx = cos 6 • Mu - sin 6 • MLy (2.3d) M& = sin 6 • Mu + cos 6 • MLy (2.3e) M^^M^ (2.3f) 40 where, Fg.x,y,z and Mg.Xiyz are the applied force and moment components with respect to the global coordinate system. These relations can be expressed in matrix form as F*' cos# — sin 0 0 0 0 0~ Fsy sin# COS0 0 0 0 0 F, 0 0 1 0 0 0 Ms* 0 0 0 COS0 -s in# 0 M, 0 0 0 sin# COS0 0 MLy M, 0 0 0 0 0 1 Mu. (2.4) and in the compact form: Lg=X.-LL (2.5) where X is the transformation matrix for transforming the local into global values, Lg is the matrix of global force and moment components and LL is the matrix of local force and moment components (Figures 2.8 and 2.9). 41 First local coordinate system: x', y\ z' Global coordinate system: x, y, z Figure 2.7 Illustration of local loads after 6 degrees of wheel rotation. Using Equations 2.1, 2.2 and 2.3, the global forces and moments during the propulsion phase were calculated. The global forces are the same as the local (hand- coordinate system) forces. Figure 2.8 shows the forces produced by the wheelchair user during the pushing phase on the handrim with respect to the global coordinate system. It is postulated that the dips on the curves for Fgx and Fgy and the spike on the curve for Fgz during the primary time of the propulsion phase are due to the contact impact between the hand and the handrim. These dips and spikes appeared in the results because an able- bodied subject (inexperienced wheelchair user) was used in this set of experiments. The presence or absence of the dip or spike has also been reported by other researchers who employed inexperienced or experienced wheelchair users in their investigations, 42 respectively [8, 49]. However, the spike or dip may happen for experienced users because of the bad propulsion technique or seating position, as well. 20 -30 H 1 1 1 1 ' 1 1 r——J 1 0 20 40 60 80 100 Propulsion phase (%) Figure 2.8 Propulsion force components with respect to global and hand local coordinate systems. Figure 2.9 shows the moments produced by the wheelchair user with respect to the global coordinate system. These moments were calculated using Equations 2.1, 2.2 and 2.3. The curves of Mgz and Mgx (the moment about the global coordinate system's z and x-axis) show a spike, and the curve of Mgy shows a dip in the early phase of the propulsion. The only important moment for manual wheelchair propulsion is M^, which is the effective moment. The other two moments are undesirable and reduce the propulsion efficiency. 43 Since we need to determine the forces and moments at the contact point between the hand of the wheelchair user and the handrim during the pushing phase, another transformation from the global coordinate system to the parallel-moving local hand (second local) coordinate system is required. These forces and moments, with reference to Figures 1.8 and 2.7, are as follows: Fhx - Fgx (2.6a) F>>y = Fgy (2.6b) ***** (2.6c) Mhx = Mgx-Fg2Xrhxsin<p + FgyxAz (2.6d) Mhy=Mgy+Fg:xrhxcos(p-FgxxAz (2.6e) 44 Mhz =Mgz+rhx (Fgx x sin <p - x cos <p) (2.6f) where 77, is the mean radius of the handrim, and Az is the offset distance between the plane of the handrim and the origin of the global coordinate system in the z direction. Also, the angle (p is the instantaneous position of the hand on the handrim in the global coordinate system (x-y plane) measured clockwise with respect to the +x axis. 2.4.4 Important Kinetic Factors In Section 1.5, some of the most important kinetic factors during MWP were introduced. In this section, the kinetic factors are elaborated by presenting the results of a sample test. Figure 2.10 illustrates F,otai, Total effective force (TEF) and Fractional Effective Force (FEF), which were calculated using Equations 1.1, 1.2 and 1.3, and the data from the test. All calculations were made with respect to the global coordinate system. The figure shows a spike on the curve for F,otai during the early part of the propulsion phase. It is postulated that this spike has resulted from the contact impact between the hand of an able-bodied or inexperienced wheelchair user and the handrim. The hand of the wheelchair user is in contact with the handrim for the entire propulsion phase, but the nature of the grip changes and affects the level of the loads transmitted. At the beginning and end of the propulsion phase the grip is partial and soft, but during the rest of the propulsion phase the user has a firm grip. During part of the early period of the propulsion phase, the strength of the grip increases sharply for able-bodied or inexperienced wheelchair users, which produces the spike. 45 Propulsion phase (%) Figure 2.10 Ftotai and TEF with respect to the global coordinate system, and the FEF during the propulsion phase. The location or the time of the spike is not exactly the same during different tests. The shape of the spike depends on the propulsion style of the wheelchair user. This spike represents a loss of energy that the user should learn to avoid. TEF is a virtual force that produces the propulsive moment. Considering the generally low levels of efficiency for manual wheelchair propulsion, it is reasonable to expect a lower value for the total effective force compared with the total force produced during the propulsion phase. To improve manual wheelchair propulsion, one should attempt to reduce the total force as much as possible, closer to the total effective force, by choosing the proper seating position, and propulsion technique. 46 FEF is an important factor in determining the effectiveness of manual wheelchair propulsion and is used as an alternative to efficiency [49,58,59]. Figure 2.10 shows that FEF was less than 60% during approximately the first 25% and the last 10% of the propulsion phase. There is not high reliability in the early and late phases of the propulsion phase because of the vibrations due to the initial contact between the hand and the handrim, and releasing the handrim. So, except for the early and the late parts of the propulsion phase, FEF has its lowest value at the time the spike was produced, which verifies the moments stated earlier. 2.4.5 Determining the Position of the Hand on the Handrim The angle <p can be obtained in a number of ways, but some assumptions must be made [49]. Equations 2.6d and 2.6e can be used to obtain Equation 2.7. First, if and Mhy are assumed to be zero (their values are small and have less importance compared with Mhz) Equation 2.8 is obtained. Although this is a viable approach, it was not used because Equation 2.8 is based on five parameters, of which only Az is directly measurable. This poses a high risk of accumulation and propagation of error within the different equations that are needed to calculate cp. (p - tan" ^-M^+M^+F^xAzj (2.7) With Mhx ~ Mhy ~ 0, one has 47 Instead, Equation 2.6e was used to obtain Equation 2.9. By assuming that only Mhy is zero, Equation 2.10 is derived for q>. This equation is also based on five parameters, but three are directly measurable (Az, F^, r )̂. Therefore, the risk of error accumulation and propagation is less. <p = cos 1 (2-9) With Mhy ~ 0, which is a reasonable assumption (see later discussion on this assumption), <pc is calculated as (pc = cos" (2.10) <pc is the "calculated <p," but for simplicity we will continue to use the symbol (p in our derivations. To evaluate the above procedure as a kinetic method, the VICON motion analysis system was used to acquire the kinematic data from the wheel center and a point on the handrim to calculate (p. The VICON system is described in Chapter 4. Figure 2.11 shows the calculated #>by using kinetic and kinematic methods, and the exponential curve fit of the kinetic method. The results show that one does not have sufficient reliability at the beginning and end of the propulsion phase for the calculated cp, 48 as similarly reported by Cooper et al. [52]. This is likely because of the lack of constant stability during the initial period of the propulsion phase (roughly the first 20%) when the hand impacts the handrim. During the later part of the propulsion phase (roughly the last 15%) the grip on the handrim becomes soft, and the propulsive moment begins to decrease. Therefore, it is reasonable to attribute these instabilities to the making and breaking of the hand contact with the handrim. During much of the propulsion phase, there is a reasonable relationship between the two calculated (p by using the kinetic and kinematic methods. To improve the reliability of the results, <p was estimated by using the exponential curve fit of the kinematic method. The equations in the Figure were automatically generated by the Excel® software. It gives the relation between (p and the propulsion phase. 0 -1 1 h — — ^ 1 1 1 1 1 1 1 0 20 40 60 80 100 Propulsion phase (%) Figure 2.11 Calculated cp using kinetic and kinematic methods, and the exponential curve fit of the kinetic method. 49 The kinematic method was considered as a more reliable way to calculate <p. The other two methods were validated by comparing their calculated values for (p with those determined by using the kinematic method. Five consecutive propulsion cycles were used to determine the absolute error and its standard deviation (Std. Dev.) for calculated q> by using the kinetic method and the exponential curve fit of the kinetic method, respectively (Figures 2.12-13). The figures show an absolute error of about ±3° for <p, or ±1.5 cm, for the hand-contact point during most of the propulsion phase. -20 Mean Mean ± Std. Dev.! 20 40 60 Propulsion phase (%) 80 100 Figure 2.12 Mean absolute error and Std. Dev. for calculated q> using the kinetic method. Now, using q> and Equation 2.6f one can calculate M/,z. Figure 2.14 illustrates the behavior of the global propulsive moment and the hand moment in the z direction during the propulsion phase. It can be seen that they act in opposite directions, meaning that Mhz reduces the propulsive moment. This situation is unavoidable and necessary for the natural stability of the propulsion. 50 40 30 <u I 20 § i < 10 0 -10 -20 0 —I 1 1 1 1 20 40 60 Propulsion phase (% - - ' Mean Mean± Std. Dev. 80 100 Figure 2.13 Mean absolute error and Std. Dev. for calculated cp using the exponential curve fit for the kinetic method. 10 8 6 f C <D 6 2 o 2 1 . i / . SX. If » V vV »\ * \ »\ f\ if i l If If */. # * \ t \ 1 1 " T " " - " " I 0 20 40 60 80 Propulsion phase (%) 100 Mgz Mhz •Curve fit for Mgz Curve fit for Mhz Figure 2.14 Global propulsive and hand moments in z direction. 51 Figure 2.15 shows the components of the user's hand moment, calculated by using the kinematic method to determine <p. The figure indicates that considering Mhy as zero in the kinetic method for calculating q>, is a reasonable assumption. 20 40 60 Propulsion phase (% 80 100 Mhx Mhy Mhz •Curve fit for Mhx •Curve fit for Mhy •Curve fit for Mhz Figure 2.15 Components of the user's hand moment. Microsoft Excel , MATLAB and LabVIEW software were used to calculate all forces, moments, and <p. In this section, the transformation matrix between the local and global values was determined, and the applied forces and moments between the wheelchair user's hand and the handrim were calculated. The angular position of the hand on the handrim during the pushing phase was calculated by means of the kinetic parameters without using cameras or a motion analysis system. <p was validated and its mean absolute error and standard 52 deviation (Std. Dev.) were determined. Finally, the propulsion moment with respect to the hand coordinate system was calculated using the determined (p. The negative value of Mhz is significant and has been addressed by other researchers [9, 60]. This negative value shows that Mhz is against the propulsive moment. However, from another point of view it is believed to stabilize the transmission of loads to the handrim. In the following section, the experimental errors of the system will be estimated using the general uncertainty method. 2.5 Uncertainty Analysis The concept of uncertainty describes the degree of goodness of a measurement or an experimental result [61]. Kline defines uncertainty as "what we think the error would be if we could and did measure it by calibration" [62]. Uncertainty is thus an estimate of the experimental error. Uncertainty analysis is a necessary and powerful tool, particularly when used in the planning and design of experiments. There are cases in which all of the measurements in an experiment can be made with 1% uncertainty, yet the uncertainty in the final experimental result could be greater than 50% [61]. Uncertainty analysis, used in an experiment's initial planning phase, can identify such situations and save the researcher much time. 53 2.5.1 General Uncertainty Analysis In the planning phase of an experimental program, one focuses on the general, or overall, uncertainties. Consider a general case in which an experimental result, fo, is a function of n measured variables *F,- [61]: fo ~ fo ' ^2 »"•) ) (2.11) Equation 2.11 is the data reduction equation and is used to determine fo from the measured values of the variables The overall uncertainty in the result is then given by Jo Ul +...+ ul (2.12) where Uv are the uncertainties in the measured variables *F,-. It is assumed that the relationship given by Equation 2.11 is continuous and has continuous derivatives in the domain of interest, that the measured variables *F,- are independent of one another, and that the uncertainties in the measured variables are also independent of one another. If the partial derivatives are interpreted as absolute sensitivity coefficients such that S,= (2.13) 54 then Equation 2.12 can be written as Ul=Y.SiK (2-14) ;=1 2.5.2 Uncertainty of Preloads The general uncertainty equation for preloads is obtained by using Equations 2.12 and 2.1 as follows: Up = [(sm(0 + ^)2U2a +(acos(0 + ^))2U2g +U2b]l/1 (2.15) where Up represents the uncertainty for different preloads [N or N.m], Ua and Ub are the primary uncertainties for the constants a and b [N or N.m.], and Ug is the uncertainty for the wheel angular position [radian]. Uncertainty equations for different preload components are then calculated by using Equation 2.15, as follows: UFpx = [(sim? + )fUlFi + (aFx cos(0 + ^ )fU2e + ] 1 / 2 (2.16a) UFpy =[(sHe + £Fy))2Ky + K cos(0 + ^ ) ) 2 £ / j +U2bfy ]"2 (2.16b) UFpi = [(sm(0 + ^ ) ) 2 ^ +(aFi cos(0 + ^ ) ) 2 £ / 2 ] 1 / 2 (2.16c) UMpx =l(smW+£„, ))2U]Ux +(aMx cos(0+{Mx )fU2g ] l / 2 (2.16d) UMpy =[(sin(^+^)) 2f/ 2^ H*M,™*0+tM,))2U}+Uir2 (2.16e) UUm =[(sin(^ + ^ ) ) 2 C / ^ +( f l j # i cos(0 + ^))2U2d + (2.16f) 55 Tables 2.2, 2.3 and 2.4 show the values for primary uncertainties. These values were determined in static tests and on the basis of parameter resolution as reported by the manufacturer of the transducer. Table 2.2 Primary uncertainties for measured variables. Variable uncertainties Ue [radian] U [m] Value used 0.001745 0.001 0.001 Table 2.3 Primary uncertainties for measured loads. Load UF UF Up . UM . UM . UMprim2 uncertainties [ N ] [ N ] [ N ] [ N m ] [N.m] Value used 1 1 2 0.4 0.4 0.2 Table 2.4 Primary uncertainties for constants. Constant U^U^ U^&U^ U^U^ Ua uncertainties UaFy ^aMy &lJbMy &Ub [N] [N] [N.m] [N.m] Value used 1 2 0.4 0.2 The values of UF ,UF ,UF ,UM ,UM and UM were calculated by using 1 px 1 py 1 pz iV* px py pz w Equations 2.16 and Tables 2.2 and 2.4, when 0 varies between 0° and 180°, the possible interval for the propulsion phase. 56 2.5.3 Uncertainty of Local Loads The uncertainties of the local forces and moments were obtained by using Equations 2.2 and 2.16, and Table 2.3, as follows: uF =[U2F +U2P ] 1/2 (2.17a) U =[U2F +U2F ]' bLy L hpy . bprimy J UF =[U2F +U2F ] 1/2 (2.17b) 1/2 (2.17c) uMu=lulpx+u2Mp^] 1/2 (2.17d) J/2 (2.17e) uMu=[u2M^u2Mp^] 1/2 (2.17f) These uncertainties are shown in Figures 2.16 and 2.17. The uncertainties for different outputs of the system were determined with respect to the local and global coordinate systems. The uncertainties for the preloads and local loads were calculated with the primary uncertainties for the measured variables and with Equations 2.15, 2.16 and 2.17, and the values are given in Tables 2.2, 2.3 and 2.4. The results show that there is not much difference between the uncertainties of the preloads and the local loads. Therefore, only the uncertainties of the local loads appear in the presented results. Figure 2.16 shows the uncertainties for the local forces in the interval during which the propulsion phase can occur (from +x to -x direction of the global coordinate system). The figure indicates that and FLZ have their highest uncertainties (about 1.75 N for FLX and about 3.40 N for FLZ) in the + y direction of the global coordinate system, 57 and that FLy has its highest uncertainty (about 1.75 N) in the +x and -x directions of the global coordinate system. Fu and FLy are the components of the applied force, which produces the propulsive moments. The above information indicates that the highest uncertainties for Fu and FLy are both low and acceptable. i 1 r •) I I I I I I I 1 I 1 0 20 40 60 80 100 120 140 160 180 The interval during which the propulsion phase can happen (degree) Figure 2.16 Uncertainties for local force components during possible range for propulsion phase. Figure 2.17 shows the uncertainties for local moments in the interval during which the propulsion phase can take place (from +x to -x direction of the global coordinate system). The figure shows that Miy and MLz have their highest uncertainties (about 0.70 N.m for MLy and about 0.30 N.m for Mu) in the + y direction of the global coordinate system and that Mu has its highest uncertainty (about 0.70 N.m) in the + x 58 and -x directions of the global coordinate system. Miz is the moment, which produces the propulsion; its highest uncertainty is comparatively very low. 0.8 I [ 1 1 1 1 1 r J 0 .3 - Q> - "" O c ••" 3 0.2 0 1 I i i i i i i i i 0 20 40 60 80 100 120 140 160 180 The interval during which the propulsion phase can happen (degree) Figure 2.17 Uncertainties for local moment components during possible range for propulsion phase. 2.5.4 Uncertainty of Global Loads The following relations were obtained by calculating Fu, Fiy, Fiz, M^, Miy, Miz and UFu,UFLy,UFu,UMu,UMiy and UMu using Equations 2.2, 2.12 and 2.17, respectively, and employing Equations 2.3 and 2.12: UFgx = [(-sm&xFLc-cos 9xFLy)2 U2 + cos 02 xU2Fu + sin 02 xU2FJ12 (2.18a) UF =[(cost9xFijc -smdxFLy)2U2 +sin02 xU2Fu +cos02 XU2FL ] 1 / 2 (2.18b) 59 UFg!=UFu (2.18c) uu„ =[(-sin(9xML i -cos0xMLy)2Ue2 + cos02 xU2Mu + sin02 x£/£ ]"2 (2.18d) UMgr =[(cos0xMu -sin0xMLy)2U2 + sm02xU2Mu +co%02 xU2MJ12 (2.18e) Uum=UUiM (2.18f) These uncertainties for the global forces and moments are shown in Figures 18 and 19. F^, FLy, Mu, MLy and 6 are the parameters calculated from the data measured in the tests. Figure 2.18 shows the uncertainties for the local and global forces. These uncertainties were calculated for the normal propulsion phase of 80°, covering a range from 75 to 155° of the possible propulsion phase. The local uncertainties were compared with the global uncertainties in the same graph and for the same period. This figure shows that the global uncertainty of Fz is the same as its local uncertainty. The global uncertainty of Fx shows a small increase compared with the local one, but its highest value of about 1.60 N is not near the end of the propulsion phase; it reaches its highest point at about 60° into the propulsion phase. The global uncertainty for Fy shows a small decrease compared with the local value. Its highest value of about 1.70 N is around 10° after the beginning of the contact between the hand and the handrim. It decreases to a minimum at about 60°. 60 3.5 i 1 1 1 1 1 r -| I I I I I I I I I 0 10 20 30 40 50 60 70 80 Propuls ion phase (degree) Figure 2.18 Uncertainties for local and global force components during propulsion phase. Figure 2.19 shows the uncertainties for the local and global moments. These uncertainties were also calculated for the normal propulsion phase. This figure shows that the global uncertainty of Mz is the same as its local uncertainty. The global uncertainty of My shows a modest increase compared with the local values. It starts to decrease after its peak of about 0.63 N.m at around 60° after the beginning of the contact between the hand and the handrim. The global uncertainties for Mx decrease to some extend compared with the local value, whose peak value of about 0.70 N.m occurs near 10° after the beginning of the contact between the hand and the handrim. It drops to a minimum at about 60°. Above results showed that the maximum uncertainties for the global loads appeared at early or late phases of the propulsion. In this study, the maximum applied 61 loads during the propulsion were calculated. These loads never occur at the early or late parts of the propulsion. 0.8 0.7 7 0.6 | 0.5 o | 04 C 'co •c o 0.3 c Z) 0.2 0.1 — 1- Loca l x — 2- Loca l y » 3- Loca l z . . . 4. G loba l x 5- G loba l y 6- G loba l z 3 and 6- 10 20 30 40 50 60 70 Propuls ion phase (degree) 80 Figure 2.19 Uncertainties for local and global moment components during propulsion phase. 2.5.5 Uncertainty of (p The uncertainty of (p is obtained using Equations 2.9 and 2.12, as Uf=^(D,+D2) (2.19a) where Dx =(d<p/dMhy)2U2Mhy +(d<p/dMgy)2U2Mgy +(d<p/dFgx)2U2gx (2.19b) 62 D^idp/dF^fUl +(d<p/dAz)2Ulz+0<p/drh)2Ul) ( 2 . 1 9 c ) a re l u m p e d p a r a m e t e r s t o s i m p l i f y the E q u a t i o n 2 . 1 9 a . T h e d e r i v a t i v e s o f <p w i t h r e s p e c t to d i f f e r e n t v a r i a b l e s a re c a l c u l a t e d as f o l l o w s : £>3 = d<p/dMhy = - 1 / D ( 2 . 2 0 a ) D4=dq>/BMgy=l/D ( 2 . 2 0 b ) D5 = d<p/dFgx = - Az/D ( 2 . 2 0 c ) D6 = dcpjdF^ = (Mhy -M^ + Fgx x Az)/D x F^ ( 2 . 2 0 d ) 7J>7 = d<p/dAz = -F^ JD ( 2 . 2 0 e ) D% = d<p/drh = (Mhy -M^+F^x Az)/D x rh ( 2 . 2 0 f ) T h e l u m p e d p a r a m e t e r s D3-& a n d D i n E q u a t i o n s 2 . 2 0 a re u s e d to s i m p l i f y s o m e r e p e t i t i v e t e r m s , a n d D i s g i v e n b y D = ^(Fgzxrh)2- (Mhy - M& + Fgx x A z ) 2 ( 2 . 2 1 ) Uq, i s t h e n d e t e r m i n e d as E q u a t i o n 2 . 2 2 o n the b a s i s o f E q u a t i o n s 2 . 1 9 a n d 2 . 2 0 as U, = J(D3 xUMJ2+ (D4 xUMgy)2 + (D5 xUFJ2+ (D6 xUFJ2+(D7xU^)2 + (Dt xUj ( 2 . 2 2 ) 63 Using the above relations and data from measured tests, one can obtain the time- dependent uncertainty for (p. As the absolute error of the calculated <p was determined and presented in Section 2.4.5, the value of the uncertainty of (p was not calculated. 2.5.6 Uncertainty for Hand Contact Loads Equations 2.6a-2.6f show that the forces are the same in both the second local and global coordinate systems for the hand contact with the handrim (Figure 2.18). Using Equation 2.12, the uncertainties for forces in the second local coordinate system are determined as Knowing the uncertainties for rh and Az, and calculating the other required uncertainties, one can obtain the uncertainties for the moments with respect to the local hand coordinate system as follows: Uu„ =[UMJ Hr, sin<p)2Ul +{Fgz *m<p?U\ + ( F ^ cos^ -V 2 + A z 2 C / ^ +Fgy2U2J12 (2.24a) Uu„ =[UMgy2 Hrh costfUl HFP cospfU-l + (Fg2rh sin^)2f/2 +&z2U2Fr +Fgx2U2J'2 (2.24b) (2.23a) (2.23b) (2.23c) A =UUJ Hr„ tmtfUl HFP *uup)2U\ + ( F ^ cos?>)2£/2 Ao =(rh cos(p)2Ul +(F^ cosr^)2^2 +(Fgyr/l sin„) 2t/ 2 (2.24c) (2.24d) UMtt=[D9+Dl0] 1/2 (2.24f) 64 As the results of the tests presented low values for hand moments (Figure 2.15), their uncertainties were not calculated. In the next section, the instrumented wheel system is verified by using an experimental technique, and system specifications are determined by applying statistical methods. 2.6 System Verification To obtain the degree of reliability of the results obtained from the designed and fabricated instrumented wheel, an experimental technique was used to determine the system specifications by performing static and dynamic tests. Four different setups were used for these tests, and both qualitative and quantitative analyses were conducted. Pearson correlation and coefficient of variation techniques were used to determine linearity and repeatability, respectively, as key system specifications. Also, the error for quantitative analysis was estimated. Three different angular velocities were used in the dynamic tests. The static and dynamic tests were performed at different levels of loading on the handrim at four different loading positions. 2.6.1 Experimental Setup The following four different loading setups were used: a first vertical loading for static tests, a second vertical loading for static tests, a horizontal loading for static tests, and a dynamic loading. 65 2.6.1.1 First Vertical Loading Setup The first vertical loading setup for static tests was used to apply the selected vertical loads at four loading points (one at a time) when they were placed in turn at the loading position of point 1 (Figures 2.20 and 2.21) on the handrim. Points 1 and 2 were at the intersections of a horizontal line passing through the handrim and its center. A loading disk was connected via a wire cable to the handrim with a clamp. Six different weights (22.27, 44.48, 66.76, 89.04, 111.50 and 133.30 N) were used in this setup. The level of resolution for the weights depends on the resolution of the sensor—in our case, 0.01 N. The range of weights covers the typical loads applied on the handrim during the propulsion. The first local coordinate system, which is attached to the load transducer, turned in unison with points 2, 3 or 4, when they turned into the position of point 1. Rotation of the wheels during the static loading was prevented by locking the shaft of one of the rollers. Figure 2.20 First vertical loading setup for static tests. 66 2.6.1.2 Second Vertical Loading Setup The second vertical loading setup for static tests applied the selected vertical loads at the four points when they were placed at the position of point 3 (Figure 2.21) on the handrim. Points 3 and 4 were at the intersections of the handrim and a vertical line passing through its center. A load-holding disk was hung from a horizontal bar 2 m in length and 1.5 cm in diameter. One side of the bar was hung from the handrim using a rope so that only a normal load was transmitted. The other side of the bar rested perpendicularly on a bar 2 cm in length and 0.5 cm in diameter, which itself rested on a smooth horizontal surface. This combination provided a rolling effect and eliminated horizontal frictional loads on the long bar due to deformation and shortening of its span after loading. The set of six weights used in this setup was the same as the set used in the initial vertical loading setup. Figure 2.21 Second vertical loading setup for static tests. 67 2.6.1.3 Horizontal Loading Setup The horizontal loading setup was used to apply horizontal static test loads at four different points located 90° apart from each other on the handrim's outer circumference. In fact, these were the same four points used in the previous tests. Four loading points were used to cover the entire circumference of the handrim. These points were at the intersections of the x and y axes of the first local coordinate system and the handrim, and were used to apply pure axial loads. A loading disk was connected to the loading point on the handrim through a pulley using a 2 mm wire cable (Figure 2.22). Six different weights (4.50, 9.02, 13.49, 16.41, 19.31 and 22.23 N) were used in this setup for each point. During manual wheelchair propulsion, the subject applied a lower load in the direction of the axle of the wheel compared with the loads in the plane of the wheel. Therefore, we used a new set of the loads in the horizontal static tests. Figure 2.22 The horizontal loading setup for static tests. 68 2.6.1.4 Dynamic Loading Setup The dynamic loading setup applied centrifugal test forces at four loading points, which were also the same as the loading points in the static setups. Three different weights (4.50, 8.95 and 13.39 N) were used as loads. The loads were attached individually to the handrim's lateral surface with a very powerful magnet (Figure 2.23). The AC motor was used to mechanically turn the wheel at three different speeds. Figure 2.23 The dynamic loading setup. Increasing the number of weights, loading points and tests can yield more data for different parts of the system, but it also increases the calculation time. Therefore, the 69 number of weights, loading points and tests were chosen such that proper statistical analysis could be performed within a reasonable time and with sufficient accuracy. The test loads were not meant to reproduce the level of the loads applied by the wheelchair user. 2.6.2 Verification Tests Protocol After the design and fabrication of the instrumented wheel and determining the transformation equations for the applied forces and moments [56], the system had to be verified. For this purpose, both qualitative and quantitative analyses were performed for the output of the experiments. Two of the most important system specifications for qualitative analysis—linearity and repeatability-— were determined using Pearson correlation and descriptive analysis, respectively. The error for the quantitative analysis was also estimated. Given the dynamic nature of the real situations, both static and dynamic conditions had to be considered to verify the system. 2.6.2.1 Static Verification To verify the system under static conditions, the wheelchair was placed on and securely strapped to the roller-rig. Three different test setups, described in Section 2.6.1, were used to apply loads in three different directions (x, y and z) of the first local coordinate system (Figure 2.2). For vertical loading in the static tests, six different weights (22.27, 44.48, 66.76, 89.04, 111.50 and 133.30 N) were suspended independently from points 1,2,3 and 4 on the handrim circumference using two vertical loading setups (Figures 2.20 and 2.21). The loading positions were 90° apart in the -x', -y', x', and y' 70 d i r e c t i o n s o f t he f i r s t l o c a l c o o r d i n a t e s y s t e m ( F i g u r e 2 .2 ) . T h e b a s e l i n e o f t he l o a d h o l d i n g d i s k ' s o w n w e i g h t w a s m e a s u r e d b y p e r f o r m i n g a n o - l o a d test , a n d the r e s u l t s s u b t r a c t e d f r o m the m e a s u r e d l o a d s a c c o r d i n g l y . M e a s u r e m e n t s w e r e r e p e a t e d th ree T o d e t e r m i n e the s p e c i f i c a t i o n s f o r q u a l i t a t i v e a n a l y s i s , t he P e a r s o n c o r r e l a t i o n c o e f f i c i e n t ( r ) w a s u s e d , w h i c h i s d e f i n e d as w h e r e sx a n d sy a re the s t a n d a r d d e v i a t i o n s o f the i n d e p e n d e n t a n d d e p e n d e n t v a r i a b l e s a n d the v a l u e bo i s d e t e r m i n e d as w h e r e x , i s t he c a s e v a l u e f o r the i n d e p e n d e n t v a r i a b l e , x i s the m e a n o f t he i n d e p e n d e n t v a r i a b l e , yt i s t he c a s e v a l u e f o r the d e p e n d e n t v a r i a b l e , y i s the m e a n o f t he d e p e n d e n t v a r i a b l e , N i s t he n u m b e r o f c a s e s a n d sx i s t he v a r i a n c e o f the i n d e p e n d e n t v a r i a b l e [ 6 3 ] . I n t h i s s t u d y , d e p e n d e n t v a r i a b l e s a re the m e a s u r e d f o r c e s a n d m o m e n t s a n d i n d e p e n d e n t v a r i a b l e s a re the a p p l i e d l o a d s at d i f f e r e n t l o a d i n g p o i n t s . T h e P e a r s o n c o r r e l a t i o n c o e f f i c i e n t m e t h o d w a s u s e d t o o b t a i n t he l i n e a r i t y o f t h e s y s t e m . T h e c o e f f i c i e n t o f v a r i a t i o n w a s u s e d f o r a l l d i f f e r e n t tes ts t o d e t e r m i n e s y s t e m r e p e a t a b i l i t y , a n d t o c o m p a r e the v a r i a b i l i t y o f d i f f e r e n t p a r a m e t e r s w i t h d i f f e r e n t u n i t s . t i m e s at f o u r d i f f e r e n t l o a d i n g p o i n t s w i t h r e s p e c t to t he f i r s t l o c a l c o o r d i n a t e s y s t e m . r = b0x(sx/sy) ( 2 . 2 5 ) ( 2 . 2 6 ) 71 The coefficient of variation expresses the standard deviation as a percentage of the mean. This allows one to compare the variability of different parameters. The coefficient of variation is given by Coefficient of variation = {^tandard deviati°^mear^100 (2.27) where mean is the mean of the variable of interest. To determine the specifications of the instrumented wheel from the quantitative analysis, the actual values were compared with the measured values. SPSS® 11.0 and Microsoft Excel® software were used to analyze the data and calculate the system specifications. All r values were calculated by using the results of the first series of tests. Table 2.5 shows r due to static verification. The "Position" column gives the different load application points, and the "Channel" row gives different measurements. The values of r show high linearity (above 0.9) at different loading points and for different measuring channels in the static situation. Table 2.5 Pearson correlation coefficient r (static verification). ~̂~"~~~----~̂ _____Channel Position Fx Py Fz Mx My Mz 1 1.000 1.000 0.999 1.000 1.000 1.000 2 1.000 0.994 0.998 0.993 1.000 0.985 3 1.000 1.000 0.997 1.000 1.000 1.000 4 1.000 1.000 0.999 1.000 1.000 1.000 72 Table 2.6 shows the mean of the percentages of the coefficient of variation for different measured loads at the four loading points. The "Load" column gives the different loading forces used during the tests. The loads differ for channel Fz because they did not reach high values during propulsion. These values indicate low coefficients of variation (less than 2%), and were calculated using the measured values of the three different tests. The entries in Tables 2.6 show high repeatability of the instrumented wheel. Tables 2.5 and 2.6 present the results for the qualitative analysis and collectively show reliable values for system specification. The average of the results from three series of the repeated tests has been used to calculate the mean errors. Table 2.6 Mean coefficient of variation of measured loads (%; static verification). ^•^^Channel L o a d ( N j ^ \ Fx Fy My Mz "~^~~^Channel L o a d ( N ) ^ \ Fz 22.273 0.110 0.166 1.547 1.784 0.133 4.50 1.736 44.482 0.045 0.147 1.545 0.398 0.166 9.02 1.293 66.755 0.059 0.174 1.401 0.289 0.082 13.49 0.863 89.043 0.070 0.053 1.314 0.355 0.067 16.41 0.747 111.504 0.102 0.117 1.192 0.381 0.563 19.31 0.895 133.299 0.096 0.106 0.234 0.485 0.117 22.23 1.325 Table 2.7 presents the results of the quantitative analysis and lists the mean errors of the measured forces and moments as percentages of the loads. The values indicate low mean error (mostly less than 5%) for different loads on all channels. Some errors were 73 expected because of the effect of other sources of errors, such as human or experimental errors. The low levels of the errors indicate that the parameters measured by the instrumented wheel are reliable. Table 2.7 Mean errors as percentage of loads (static verification). ^ ~ \ C h a n n e l L o a d ( N T \ ^ Fx Fy Mx My Mz " ^ \ ^ C h a n n e l Load ( N T \ ^ Fz 22.273 0.857 0.070 1.608 2.969 0.344 4.504 3.572 44.482 0.583 0.291 8.422 4.556 0.113 9.015 1.374 66.755 0.640 0.144 2.586 1.088 0.179 13.489 2.037 89.043 0.576 0.170 1.922 1.420 0.081 16.406 2.680 111.504 0.726 0.074 3.187 0.881 0.259 19.308 3.718 133.299 0.666 0.097 3.383 0.614 0.128 22.225 7.401 The results of qualitative and quantitative analyses for the mstrumented wheel in the static situation show a reliable range of the values for all system specifications. 2.6.2.2 Dynamic Verification Dynamic verification was more challenging than static verification. The local coordinate system of the transducer spun with the wheel and the loadings were weights, so the loads (in the global coordinate system) could not be measured directly. An encoder was used to determine the position of the load attached to the wheel with respect to the global coordinate system. The wheelchair was placed on the roller-rig, and the A C motor 74 rotated the driving roller. Three different angular velocities (3.0, 3.8, and 4.8 [rad/s]) were used for the dynamic tests to cover the wheeling speeds of the user. Three different weights (4.50, 8.95 and 13.39 N) and one powerful magnet were used for loading at points 1 to 4 (Figures 2.20, 2.21 and 2.22) on the handrim lateral surface. The loading positions were the same as for the static verification tests. The measured forces and moments of three successive cycles were used to verify the system repeatability. The baseline of the attachment's own weight was set to zero by using the method described in the static verification tests. The actual values were compared with the measured values to obtain the specifications for quantitative analysis. The actual values were determined using the inverse dynamics method. The angular motion of the loaded wheel was considered in the vertical plane, where the centripetal force, Fs was determined as Here, mw is the mass of the weight that was attached to the wheel, o, is the moment arm (handrim radius), 0 is the wheel angular velocity and g is the acceleration of gravity. There was no force component in the z direction because the object had a planar motion (x-y) and the wheel camber angle was zero with respect to the global coordinate system. The x and y planar components are as follows: Fs =rnwrhe2+mwg (2.28) (2.29a) F —m ru02 cos0 — m g sy w h wo (2.29b) 75 where 6 is the angular position of the wheel (or load for these tests), and Fs.Xwy are the components of the centripetal force. Equations 2.25, 2.26 and 2.29 were used to determine the specifications for qualitative analysis in the dynamic tests with three different angular velocities. As the nature of the manual wheelchair propulsion is dynamic, qualitative and quantitative analyses were performed for the instrumented wheel under dynamic situations. These analyses were carried out for three different angular velocities (3, 3.8 and 4.8 rad/s). Table 2.8 shows the Pearson correlation coefficient for the tests conducted. These values mostly show high correlation (r above 0.9) between different angular velocities and loadings implying very good linearity. Channel Fz was not considered for dynamic verification because there was no appreciable load on this channel, due to the nature of dynamic loading. The values in Tables 2.9 show a low mean coefficient of variation for different measured loads (less than 4%) at four loading points, and high repeatability of the instrumented wheel. Tables 2.8 and 2.9 show the results of the qualitative analysis. They indicate reliable values for system specification in the dynamic verification tests. The mean errors produced by the instrumented wheel as a percentage of loads are presented in Table 2.10 (quantitative analysis). The low mean error values (mostly less than 6%) indicate that, the parameters measured by the instrumented wheel are equally reliable for the dynamic situations. 76 Table 2.8 Pearson correlation coefficient r (dynamic verification). ^•^^Channel Position"""---^ Fx Fy Mx My Mz 0= 3 rad/s 1 1.000 1.000 0.999 1.000 1.000 2 1.000 1.000 1.000 1.000 0.992 3 1.000 1.000 1.000 0.997 0.998 4 1.000 1.000 0.993 1.000 0.987 (9=3.8 rad/s 1 1.000 1.000 0.999 1.000 1.000 2 0.999 1.000 0.999 0.996 0.982 3 1.000 1.000 0.994 1.000 0.995 4 1.000 1.000 0.996 1.000 0.989 (9=4.8 rad/s 1 1.000 1.000 0.993 0.985 1.000 2 0.998 1.000 0.993 0.989 0.991 3 1.000 1.000 0.998 1.000 0.989 4 0.997 1.000 0.999 0.999 0.991 Table 2.9 Mean coefficient of variation of measured loads (%; dynamic verification). ^^-^Qiannel L o a d ( T ^ T ) \ ^ Fx Fy Mx My Mz 0=3 rad/s 4.50 2.170 1.467 1.547 0.967 0.842 8.95 1.871 1.752 1.236 1.226 0.144 13.39 1.230 0.954 0.638 0.761 0.115 (9=3.8 rad/s 4.50 2.511 3.196 2.892 1.475 0.445 8.95 2.144 1.498 2.781 1.915 0.300 13.39 1.054 0.968 0.896 0.937 0.078 .9=4.8 rad/s 4.50 3.986 3.404 2.191 3.051 0.844 8.95 2.529 1.604 2.247 3.695 0.456 13.39 1.691 0.856 3.380 1.721 1.347 77 Table 2.10 Mean errors as percentage of loads (dynamic verification). ^^^--^Channel L o a d ( N 5 ^ \ Fy Mx My Mz 0=3 rad/s 4.50 5.675 7.724 3.276 4.514 4.395 8.95 6.532 6.820 1.924 5.227 6.005 13.39 6.723 7.038 2.944 6.878 5.638 (9=3.8 rad/s 4.50 4.115 4.833 3.762 4.116 3.134 8.95 5.581 6.636 4.798 2.867 5.530 13.39 7.430 6.909 5.579 3.259 5.640 •9=4.8 rad/s 4.50 5.837 6.200 3.079 6.189 4.643 8.95 5.675 7.211 5.794 4.329 4.300 13.39 5.590 8.079 2.281 3.467 4.639 Given the actual performance for the instrumented wheel and its measurements, Figures 2.24 and 2.25 show the measured and predicted values for Fx, Fy, Mx, My and Mz with respect to the global coordinate system. As mentioned previously, Fz was not considered in the dynamic measurements because there was no significant load on this channel due to the nature of loadings for dynamic tests. These figures show that the patterns of the measured and predicted curves of the data for forces and moments are highly compatible with typical results measured by other researchers [49]. 78 .-| 0 I 1 1 1 ! I 1 ! I I L 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (s) Figure 2.24 Measured and predicted global sample force components. 2.5 _2 51 i i i i i i i i i i_ 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (s) Figure 2.25 Measured and predicted global sample moment components. 2.7 Conclusions In this chapter, a general uncertainty analysis was performed to determine the uncertainty equations for the local and global forces and moments, the local hand forces and moments, and the hand-contact angular position in MWP. The uncertainty values for the local and global forces and moments and the hand-contact forces were then calculated. The results provided an estimation of the errors and uncertainty in the output of the instrumented wheel. The uncertainties were found to vary from 1.40 to 3.40 N for the local forces and from 0.20 to 0.70 N.m for the local moments. The maximum and minimum of the uncertainties for global values were about the same as the uncertainties for the local values, but the patterns of variation were different. Uncertainties determined by Cooper et al. [52] for the forces and moments are in the range of 1.1-2.5 N and 0.03- 0.19 N.m in the plane of the handrim, and 0.93 N and 2.24 N.m in the wheel axle direction, respectively. Our results show uncertainty for the forces and moments in the range of 1.40-1.70 N and 0.58-0.68 N.m in the plane of the handrim, and about 3.40 N and 0.25 N.m in the wheel axle direction, respectively. For our system, however, the uncertainty values for the important load components, namely the planar forces and the axial moment, are low. The absolute error for hand-contact position was determined as ± 3° or ± 1 cm for most of the propulsion phase. Cooper et al. reported uncertainties between 1.8° and 16° for the hand-contact position using their Smart w h e e l [52]. A complete experimental technique was designed and performed under different static and dynamic conditions to determine the specification of the instrumented wheel. The verification techniques, which were highlighted and demonstrated step-by-step, can be implemented in similar wheelchair instrumentation setups. The results of the static and 80 dynamic tests were used for both qualitative and quantitative analyses to determine the system specifications. The static tests showed high linearity (r above 0.9), very low standard deviation (mostly close to zero) and a low mean coefficient of variation for measured loads (less than 2%). These results indicate high repeatability and low mean error (mostly less than 5%) due to the different loading for all load channels. Two cells of Table 2.6 show mean errors above 5%, with one at the maximum horizontal load. Usually, the horizontally applied loads are not so high during manual wheelchair propulsion, and the main idea is that the users try to apply planar loads. Therefore, the system is not proportionally responsive to higher horizontal loading due to its structure, but it had mean errors less than 5% for all other lower horizontal loadings. The other mean error above 5% corresponded to Mx. All of the mean errors for this column were close to 2% or more. Generally, higher values of the mean error (%) were obtained for Mx compared with the mean errors (%) for the other channels. Dynamic tests were performed at three angular velocities and at four loading positions for all measuring channels. The results also showed high linearity (r above 0.9). The low mean coefficient of variation for measured loads (less than 4%) confirmed high repeatability (reliability) of the instrumented wheel. The results showed that most of the mean errors were around 5%. The resultant specifications showed high linearity, repeatability and a low percentage for errors. The results presented in this chapter collectively show that it is possible to reliably obtain the essential information required for manual wheelchair propulsion analysis, including the applied forces and moments, using the designed and fabricated instrumented wheel. The tests with one able-bodied subject reproduced patterns and 81 overall behavior comparable to the available data, ensuring that the system can be used for the designed experiments. It is worth emphasizing that a system developed in-house allows flexibility in enhancing the experimental scope. The instrumented and verified wheel can now be used to determine the kinetic aspects of wheelchair propulsion. Varying the seat position with respect to the wheel axle affects all the forces and moments, as well as the mechanics, of propulsion. Determining and prescribing optimum positions is expected to reduce pain and help prevent injury of manual wheelchair users, and may improve the gross mechanical efficiency of propulsion. In the next chapter, the proposed indices for efficiency and injury assessment of MWP are described. These indices are used as criteria to determine the optimum wheelchair variables. 82 CHAPTER 3 Efficiency and Injury Assessment 3.1 Introduction Previous studies have reported a low value of about 10% for the efficiency of Manual Wheelchair Propulsion (MWP) [22]. The Gross Mechanical Efficiency (GME) for human movement is defined as the ratio of the work accomplished to the amount of the corresponding Metabolic Energy Expenditure (MEE) [23]. However, few studies have focused on the mechanical factors only and have not considered the physiological aspects of the MWP in calculating the efficiency [64]. Although the reasons for this low efficiency have not been sufficiently addressed in many studies [8, 65,66], Veeger, et al. [8] reported that it can be partially attributed to nonoptimal tuning of the wheelchair to the functional abilities of the user. Braking torques at the start and end of the propulsion phase [21], and suboptimal direction of the propulsion force [8] are reported as the other possible causes for the low efficiency of 83 MWP. Whereas, de Groot et al. [9] reported that even the applied tangential force acting in the optimal direction tends to decrease G M E because of the conflict that was explained in Section 1.5.1. Injuries due to MWP are usually consistent with pain. It has been determined that the pain is a limiting factor in the daily activities for MWUs [67]. Roach et al. [68] developed the Shoulder Pain and Disability Index (SPADI) to quantify shoulder pain and difficulties during the functional activities in an ambulatory population. Curtis et al. [67] developed the Wheelchair User's Shoulder Pain Index (WUSPI) to measure the severity of the shoulder pain associated with functional activity in the individuals who use wheelchairs. SPADI and WUSPI are in fact 38-item and 15-item questionnaires, respectively. A score is given for the response to each item. The higher the total score, the greater pain interference of activities. These indices do not measure pain intensity, but pain interference. Wheelchair Propulsion Strength Rate (WPSR) is a reported injury index and is the ratio of the joint moment generated during propulsion and during the maximum isometric strength test in different directions [17]. It has been hypothesized that larger values of this ratio indicates a high risk of injury. In this chapter, a new index for efficiency assessment during MWP is proposed. This index uses the heart rate of the subject as a factor to estimate the variation of the M E E . This is followed by developing two new injury indices to estimate the level of the probable injury due to MWP. 84 3.2 Efficiency Assessment Wheelchair-user system is a combination of a mechanical device and a human body. A major requirement for reliability of the efficiency assessment for MWP is to consider both physiological and mechanical aspects of the motion. Measuring the oxygen uptake is one way of estimating M E E , but some of the subjects may feel uncomfortable to have the device on their face during the tests, which may affect their natural performance. Finding an alternative method could be helpful for some of the studies that have above consideration for the subjects or do not have access to the respective equipment. However, one should consider that the calculated results using the heart rate can be used for within-subject analysis. hi Section 1.5.4, we reviewed some studies, which reported that the physiological cost of the body can be predicted by measuring heart rate. Figure 3.1 shows the variation of heart rate versus time, during the start, performance and finishing a steady-state exercise [39]. Area 2 represents the total number of the subject's heartbeats above the resting level during the steady-state phase of the test. The area 2 is determined by subtracting the numbers of heartbeats during the exercise from the resting level, multiplied by the seconds of the test period. In this study, the area 2 will be determined for the tests. While the areas 1 and 2 represent the total heartbeats during the exercise above the resting level, the areas 1, 2 and 4 show the total number of the heartbeats during the exercise, including the resting level. Area 3 represents the extra heartbeats during the recovery phase. Areas 3 and 5 together represent the total heartbeats during the recovery. The resting heartbeats during the exercise and recovery are defined by areas 4 and 5, respectively. 85 Gross Mechanical Efficiency (GME) considers the biological aspects of the manual wheelchair propulsion [9], and is defined as Gross Mechanical Efficiency = Useful Energy Out / Metabolic Energy Expenditure or: GME = Mz • A0/MEE (3.1) where Mz is the average propulsive moment applied on the hub of the wheel, and AO is the angular displacement of the wheel; both during the test period. Heart rate Steady-state heart rate Resting heart rate Figure 3.1 Variation of heart rate versus time, from start to completion of a steady-state exercise and back to rest (inspired by [39]). 86 Methodology— The linear relationship between the heartbeats and the oxygen uptake profile for steady state and non-steady state situations allows us to use an alternative and convenient method for measuring M E E . We prefer the heart rate measurement over oxygen uptake measurement because it is more comfortable, cheaper and the equipment is lighter. Continuous heart rate monitoring is now possible with the development of portable heart rate monitors. We have proposed Equivalent Biomedical Index (EBI) for efficiency assessment, which reflects the behavior of G M E and is given by Equivalent Biomedical Index = Useful Energy Out / Total Heartbeats or: EBI = M Z A0 /THB (3.2) where THB is the area 2 in Figure 3.1. A comparison of the Equations 3.1 and 3.2 shows that their numerators are the same and their denominator have linear relationship with one another. Therefore, EBI can reflect the behavior of GME. 3.3 Injury Assessment The referenced studies in Chapter 1 indicated that MWP is associated with injuries. To predict probable injuries during MWP, two injury indices were proposed. These indices consist of the important factors that may lead to injury. 87 As reported by other researchers, higher applied forces and moments on the handrim may increase the risk of RSI or over-use injury [17,69]. Therefore, the applied forces and moments can be considered as key factors that can cause the injury. It has been reported that the subject's weight is related to pushrim forces and the median nerve function [23]. Also, previous studies have shown that the Body Mass Index (BMI) is significantly related to the shoulder injury [70,71]. BMI is based on the anthropometric data of the subject and can be considered as another factor in injury assessment. As it is assumed that repetitive motion puts a person at the risk of RSI, therefore the pushing frequency of the M W U has direct influence on the wheelchair user's joint injury. Boninger et al. [35] suggested that decreasing the frequency of propulsion may help to prevent median nerve injury and thus CTS. Methodology—Wheelchair User Joint Injury Index (WUJH) is our first proposed injury index and reflects a value that is representative of the level of possible M W U joint injury. A general idea for linking WUJII to the above factors can be expressed as WUJn = F m M m B M I - / p (3.3) Variables Fm and Mm are the maximum total force and moment applied on the hub of the wheel during the propulsion phase, respectively, and fp is the pushing frequency. BMI is defined as 88 BMI = mjh2s (3-4) where ms and hs are the mass and the height of the subject, respectively. Substituting Equation 3.4 in Equation 3.3, WUJU is related to individual parameters as follows: WVm = Fm-Mm-fp-ms/h> (3.5) To be able to compare this index between different subjects, the index is normalized with respect to the subject arm length (anthropometric parameter), and the total weight of the subject and the wheelchair, which affect the applied moment and force on the upper limb's joints: F Mm — —-fp^s W W • L w u j n = — — - — T x IOO A, (3.6a) or F -Mm • fn • m;. WUJII= m 2 m 2 J p sxl00 ( 3.6b) where La is the arm length, and Wt is the weight of the user and wheelchair combined. The index was multiplied by 100 to avoid presenting the values as a percentage. A pre- test showed small numerical value of the index without using a hundred as a coefficient. 89 WUJII can be used for estimating the injury at the shoulder, elbow or wrist joints by using the joint loads instead of the applied loads in Equation 3.6b. The modified form is presented as WUJII, = m-ms-fp-Fmi-Mn ^•h)-Lai (3.7) / = 1,2,3 Variable / represents the corresponding joint as follows: 1-shoulder, 2-elbow, and 3-wrist. Fmi and Mmi are the maximum total force and moment applied on the joint / during the propulsion, and Lai is the length of the upper limb segments connected to the distal part of the joint /, such that La\ is the total length of the arm and hand, La2 is the total length of the forearm and the hand, and Las is the length of the hand. As BMI is not a perfect index for all cases (compare BMI between two persons, who have the same height and weight but one has more fat, and the other has stronger muscles), WUJIT is proposed by using calculated %BF as equations 3.8a and 3.8b for general form and the joints injury analysis, respectively. , 100 • %BF • f • F • M WUJII'= ^ — - (3.8a) W, • L„ WUJII ; = i = 1,2,3 100-%BF-/ / ,F W J . -M„ W,2-Lai (3.8b) Percentage of Body Fat is the ratio of the fat to the total body mass, and therefore is unitless. A variety of techniques have been developed to measure this parameter such 90 as using calipers (skinfold measurements - anthropometry), bioelectrical impedance analysis, hydrodensitometry weighting, near-infrared interactance, magnetic resonance imaging, computed tomography, total body electrical conductivity, and Dual Energy X - ray Absorptiometry (DEXA) [72-80]. The hand-held caliper that exerts a standard pressure was used in the previous studies for SCI subjects, and the skinfold thickness was measured at following body locations: Triceps, Biceps, Subscapula and Supraspinal [72-74]. In this study, the same method and measuring sites were used. Linear regression equation for the estimation of body density (kg/m ) has been reported by Dumin et al. [75] as follows: Density = A0-B0x log Stotal (3.9) where Ao and Bo are the constants and their values differ for different genders and ages, and Stotai is the sum of the skinfold measurements at four sites. In the same report, %BF has been determined as %BF ( s k i n f o l d )  = ( 5 ^ - 4 - 5 0 ) - 1 0 0 (3-10> where %BF( S k i nf 0i d) is the value of %BF that is measured by using the skinfold method. Maggioni et al. [73] reported that measured %BF for people with spinal cord injury using the skinfold method is under-estimated. They introduced Equation 3.11 that shows the relationship between %BF calculated by the skinfold and D E X A methods. 91 D E X A is known as the best method to determine % B F . In this study, the values of % B F were modified by using the following equation as % B F , (DEXA) = 1 . 4 5 % B F , (Skinfold) + 2.58 (3.11) where %BF(DEXA) is the value of % B F that is measured by using the D E X A method. Wheelchair velocity has also been reported as a factor that can affect the efficiency of MWP [4]. Veeger et al. [8] performed manual wheelchair exercise tests on a stationary ergometer for nine able-bodied subjects and determined that G M E increases with lower tangential velocities of the handrim, whereas another study reported that propulsion speed slightly lower than the freely chosen speed is energy efficient [38]. In this study, to verify the effect of velocity on the indices, several tests were performed, which, are described in the next chapter. It was found that the injury indices increase by raising the Average Linear Wheelchair Velocity (would be referred as velocity) during the propulsion phase. Considering the dependency of the injury indices on the velocity, the relations of the injury indices were modified to include the velocity as one of their parameters. This allows the injury indices to be stand alone measures for the level of possible joint injury due to MWP. The modified injury indices for general evaluation are then stated as WUJII = lOO-Fm-Mm-fp-Vrms (3-12) 92 wu jn , lOO-%BF-fp-VrFm-Mn 2 (3-13) where V, is the symbol that represents the velocity. To determine the level of the possible injury at the joints, the modified injury indices are given by WUJIL = \00-ms-fp-VrFmrMmi W2-h)-Lai (3.14) t "s "ai i = 1,2,3 , 100 • %BF • fp-V, • F j • M WUJII = Jp I m W,2.Lai (3.15) »" = U,3 The units of WUJII and WUJII' are kg/(m.s2) and m/s2, respectively. The risk of the injury may increases with higher values of WUJII or WUJII'. The effects of changing the seat position on the proposed indices were investigated in this research. The minimum value for each injury index corresponds to the optimum seat position. We think that WUJII' can be a more realistic index and will discuss it more in Chapter 5. 3.4 Chapter Summary Most of the previous research on the efficiency assessment has been conducted for sport wheelchairs, and some did not consider the physiological aspects of MWP. All 93 of the previous studies about MWP that we found have used oxygen uptake to determine MEE for efficiency assessment. Two reported indices in the previous studies measure the interference of the pain, and they are based on questionnaires. Previous reported injury index was based only on the joint moments during MWP and the maximum isometric strength of the muscles. This injury index does not consider the other factors like the applied force, the frequency of the propulsion, and the weight of the subject that have effects on the injury during MWP. In this chapter, a new index was presented for efficiency assessment of MWP. The use of the subject's heart rate in the proposed index represents the biological factors. EBI was considered as a good alternative to estimate the efficiency of MWP because it uses the heartbeats of the user to estimate the variation of the MEE. Measuring the heartbeats by using the newly developed heart rate monitors is cheaper, more comfortable and the required equipment is lighter. To measure the level of the possible injuries, two indices were proposed. The general forms of the indices determine the level of the probable injury totally at the upper limb of the subject. The indices were modified to be used for injury assessment at each joint of the upper body of the user. Also, there is a choice of using BMI or %BF to calculate the injury indices. In the next chapter, the test procedures are explained and the calculated values of the proposed indices are given. The sensitivities of the indices are verified, and the optimum seat positions for two users are determined by presenting the values of the indices in 3D graphs. 94 CHAPTER 4 Optimum Seat Position 4.1 Introduction The wheelchair-user interface, based on the design and settings of the wheelchair and the physical and habitual characteristics of the user, will affect the pattern of the applied loads, cardio-respiratory factors, kinetic and kinematic parameters, pushing angle, pushing frequency, and joint loads during MWP [13,17,19,35,36,81]. Inappropriate settings can lead to RSI [82]. Furthermore, the results from at least one study have confirmed the possibility of reducing, or even eliminating, back pain and discomfort related to wheelchair seating by individually adjusting the settings of the subjects' wheelchair (p<0.001) [83]. Actually they did not explain their adjustment procedure. Also, another study presented a significant relationship between the wheelchair seat's tilt angle and the biomechanical efficiency [84]. 95 Determining the optimal seating positions for MWUs is a major challenge for researchers. Masee et al. [85] found a low position to be optimal for smoother upper limb motion, less electromyogram (EMG) activity and lower pushing frequency, while another study reported greater upper limb motion in a low position [86], and Kotajarvi et al. [11] did not find lower pushing frequency at the low seat height positions. These contradictions imply that more work is required in this area. In this chapter, a new method for determining the optimum seat position for a user is described, followed by explaining the experimental setup and a subject model. Also, the optimum seat position is determined using an analytical method, and the reliability of the indices are investigated by sensitivity analysis. Four research questions concerning the optimum seat position and the relationship between linear wheelchair velocity and the proposed indices are addressed. 4.2 Modeling and Analysis Approach The data acquired from this study covers the kinetic, kinematic, and part of the anthropometric and physiological information for the subject group of the manual wheelchair users. The above parameters were measured and/or monitored using several devices and instruments that we provided in the Human Measurement Studio at the Institute for Computing, Information and Cognitive System (ICICS), the University of British Columbia (UBC). All measurements were taken at the same time to acquire synchronized data. A medical student assisted in the measurement of the heart rate, blood pressure and the %BF of the subjects. 96 The following method was devised and applied to determine the optimum seat position for each user by analyzing the calculated values of the indices at different seat positions. The subsequent sections of this chapter describe in details the study population, study design, test protocol, setup and modeling. 4.2.1 A n Overview In this research, new injury and efficiency indices were proposed as criteria to determine the optimum wheelchair variables for each manual wheelchair user. To accomplish these, the parameters that are measurable and have significant effect on the factors in the proposed indices were investigated. Possible wheelchair parameters are the horizontal and vertical positions of the seat with respect to the wheel axle, the backrest position or angle, the seat angle, the footrest position and the camber angle of the wheels. Choosing the proper parameters depends on the situations and characteristics of different wheelchairs. If the specifications of the wheelchair are flexible enough for setting and measuring these variables, and the subjects can handle the requirements of the tests, one can use the new method with different combinations of the parameters listed above to determine the optimum position. In this study, the vertical and horizontal positions of the seat with respect to the wheel axle were considered as the adjustable variables of the seat position, which have significant effects on the factors in the proposed indices. The lower and upper bound values of the seat position can be different for various manual wheelchairs. 97 4.2.2 Study Population This study was approved by the Clinical Research Ethics Board at U B C (Appendix). Subjects were recruited through a database provided by Dr. Bonita Sawatzky and the Spinal Cord Injury Research Registry at the GF Strong Rehabilitation Center (Vancouver, BC). All of the subjects were of legal age (> 18 years) and they signed a consent form. Subjects were provided with a $50 honorarium upon completion of the protocol to primarily cover transportation related expenses. All of the subjects met the inclusion and exclusion criteria for the study. The inclusion criteria for the subjects in this study were as follows: • Males with a spinal cord injury for longer than one year. • Age between 19 and 59 years. • Height ideally between 160 and 190 cm. • Dominant right hand side. • Fit into a 16" wide wheelchair or use the same size wheelchair. • Can independently use a manual wheelchair for 50% of the day. Potential subjects were excluded from this study if they: • had been previously diagnosed with any kind of heart or lung disease. • had lesion level higher than the sixth thoracic vertebrae (T6; see Section 1.5.4). • had significant shoulder pain during wheeling. • have had surgery within three months prior to the tests. • were unable to transfer themselves independently from their wheelchair to the test wheelchair. 98 In Chapters 1 and 3, the linear relationship between the heart rate and M E E was explained. Also, it was discussed that among SCI subjects, this linear relationship only works for the individuals with lesions at T6 or lower. Eight adult male MWUs (n= 8) participated in this study. Demographic data are given in Table 4.1. Table 4.1 Demographic data for the manual wheelchair user subjects. Subject code Gender Age (years) Diagnosis Level of lesion 1 M 52 Paraplegia Tll-12 2 M 27 Paraplegia T10 3 M 20 Spina Bifida Lumbar 4 M 48 Paraplegia T10 5 M 59 Paraplegia Tll-12 6 M 49 Paraplegia T6-7 7 M 24 Paraplegia T6 8 M 34 Paraplegia T10 M = Male; Tn = The nth thoracic vertebrae. 4.2.3 Study Design In this research, the relationship between the proposed indices and the seat position for eight MWUs were analyzed and their sensitivity was evaluated. To do this, experiments were designed and implemented in two categories: 1- Fixed seat position; 2- Constant wheelchair velocity. 99 I n t he f i x e d seat p o s i t i o n tes ts , the e x p e r i m e n t s w e r e p e r f o r m e d at th ree d i f f e r e n t v e l o c i t i e s f o r a l l s u b j e c t s i n s e a r c h o f a m e a n i n g f u l r e l a t i o n s h i p b e t w e e n t h e i n d i c e s a n d the v e l o c i t y f o r M W U s . I n t he c o n s t a n t v e l o c i t y tes ts , the e x p e r i m e n t s w e r e p e r f o r m e d at t w o v e r t i c a l a n d th ree h o r i z o n t a l p o s i t i o n s o f t he seat ( s i x tests) f o r a l l s u b j e c t s , to c o n d u c t s e n s i t i v i t y a n a l y s i s a n d to v e r i f y t he p o s s i b i l i t y o f e s t a b l i s h i n g s o m e g e n e r i c r u l e s to e s t i m a t e the o p t i m u m seat p o s i t i o n s f o r a l l u s e r s . P e r f o r m i n g at l eas t n i n e tests e n a b l e s o n e to a c q u i r e the r e q u i r e d d a t a f o r a r e s p o n s e s u r f a c e , w h i c h re l a tes the i n d i c e s t o t he seat p o s i t i o n . T o d e t e r m i n e the r e s p o n s e s u r f a c e , t w o s u b j e c t s p a r t i c i p a t e d i n n i n e tes ts . T h e m e t h o d o l o g y i s e l a b o r a t e d i n S e c t i o n 4 . 3 . 4.2.4 Test Protocol F i r s t , t he s t u d y p r o c e d u r e w a s e x p l a i n e d i n d e t a i l e d a n d a n e a s y t o f o l l o w f o r m a t to t he s u b j e c t s , a n d t h e y w e r e a s k e d to s i g n t he e t h i c a l c o n s e n t f o r m . S o m e i n d i v i d u a l s w i t h s p i n a l c o r d i n j u r y h a v e a c o n d i t i o n k n o w n as " A u t o n o m i c D y s r e f l e x i a ( A D ) " , w h i c h a f f e c t s t h e i r h e a r t ra te i f t he b l a d d e r i s f u l l [ 8 7 , 8 8 ] . A l t h o u g h , w e c h o s e s u b j e c t s w i t h l e s i o n l e v e l s b e l o w T 5 , w h i c h i s the cu t o f f l e v e l f o r a p o s s i b i l i t y o f A D , w e s t i l l a s k e d t h e s u b j e c t s t o v o i d t h e i r b l a d d e r s b e f o r e t he tests . T h i s w a s c o n s i d e r e d as a m a t t e r o f c o n v e n i e n c e f o r t e s t i n g , as w e l l as to p r e v e n t i t s p r o b a b l e e f f ec t s o n the b l o o d p r e s s u r e , a n d to a v o i d d i s t r a c t i o n d u r i n g the tes ts . T h e s u b j e c t s ' a n t h r o p o m e t r i c d a t a ( h e i g h t , a r m l e n g t h , j o i n t c i r c u m f e r e n c e , a n d h a n d w i d t h ) w e r e m e a s u r e d . T h e y w e r e a s k e d t o s t r e t c h t h e i r a r m s s t r a i gh t to t he s i d e s s u c h that the d i s t a n c e f r o m the t i p o f t h e i r l e f t m i d d l e f i n g e r t o t he t i p o f right m i d d l e f i n g e r c a n b e m e a s u r e d . T h i s m e a s u r e m e n t i s a g o o d 100 representative of the height of a subject, which is normally hard to measure in seated individuals. Previous studies have reported a high correlation (0.73-0.89) between the arm-span and height for different genders and ethnicities [89,90]. The subjects' %BFs were determined using a caliper for skinfolds test at Triceps, Biceps, Subscapula and Supraspinale. The measurements were taken three times and the average values were used. Then using a custom made scale the weights of the wheelchair users were obtained. Ten semi-spherical passive markers were attached to the upper limb and trunk landmarks, and two markers were attached to the instrumented wheel (Figure 4.1). The markers reflected the infrared waves emitted from the six surrounding cameras of an advanced Motion Analysis System (VICON). The joint positions and the motion of the upper limb of the subjects were determined by tracking the markers through the VICON system and a digital camcorder. All measurements were non-invasive. The subjects wore sleeveless shirts (tank top) during the tests. They transferred themselves onto the stationary instrumented test wheelchair. As part of subject calibration for the motion analysis system, they were asked to take a "T" pose (stretch arms horizontally) for a few seconds; and turn their upper limb segments starting from their hand, forearm, and upper arm around their joints for about a minute in front of the cameras. The base line of the heart rate and the blood pressure of the subjects were measured just prior to the tests (Figure 4.1). The wheelchair seat could be positioned at three vertical positions (Y l , Y2 and Y3) and three horizontal positions (XI, X2 and X3) (Figure 4.2). There were two different sets of the tests. In the first set, three velocities of 0.9, 1.1 and 1.3 m/s were used, at a fixed position (X2 and Y2) for eight subjects. The 101 selected velocities are typical wheeling velocities for MWUs. In the second set, the tests were performed at a fixed velocity of 0.9 m/s. In this category, the tests were conducted at six different combinations resulting from two incremental vertical seat positions (Yl and Y2) and three incremental horizontal seat positions (XI, X2 and X3) for all eight subjects. Two subjects had three more tests at three different combinations of the seat position (XI, X2, and X3; all at Y3). A speedometer measured the speed of the wheelchair. The order of the tests was selected randomly for each subject. The magnitude of X I , X2, and X3 were 11, 14, and 17cm, and Y l , Y2, and Y3 were 15, 18, and 20cm with respect to wheel axle, respectively. X values were negative. Figure 4.2 illustrate these positions with respect to the wheel axle. Figure 4.1 A subject on the instrumented wheelchair and roller-rig during blood pressure measurement. The marker on the left hip is not shown. 102 To change the seat position, it was necessary for the subjects to transfer themselves in and out of the wheelchair a number of times. Each test took 3 minutes and the data was collected during the final minute of the test. The subjects rested between the tests, and prior to each test their heart rate and blood pressure were measured to ensure they had returned to the baseline levels. Figure 4.2 Possible seat and backrest positions. The seat position is set at XI and Y l in this figure. Dimensions are not to scale. 103 The forces and moments that the subjects apply during propulsion are needed for the analysis, and were measured with the instrumented wheel. During the tests, the heart rate, and the kinetic and kinematic data of the subjects were recorded, simultaneously. 4.2.5 Anthropometric Data The anthropometric dimensions of the upper limb were obtained using a tape measure. A platform was designed for this study to determine the weight of the subjects as well as the weight of the instrumented wheel, separately (see Section 4.2.6.6). BMI and %BF were calculated using the Equations 3.4 and 3.11, respectively. 4.2.6 Experimental Setup In this study, it was necessary to measure a number of physical and biological parameters; therefore several devices were used to acquire such data. The wheelchair, the instrumented wheel, the roller-rig and the two computers for kinetic data acquisition were described in Chapter 2. This section outlines the rest of the equipment used. 4.2.6.1 Motion Analysis System ®VICON Motion Analysis System was used to acquire the kinematic data. VICON is equipped with infrared cameras, which are more accurate compared with the conventional video cameras (Figure 4.3). To conduct a 3D kinematic study of the upper body during MWP, at least four cameras are necessary for a good all around coverage of the subject for data acquisition, with less possibility of any marker being missed. Figure 4.4 illustrates a schematic view 104 of the multi-camera setup. We used six cameras in our tests to have more confidence in covering all landmarks and to ensure redundancy in data acquisition. Figure 4.3 VICON infrared camera. Figure 4.4 Positions of six infrared cameras, a subject, the wheelchair and the roller-rig for stationary MWP. 105 4.2.6.2 Heart Rate Monitor A heart rate monitor (HR-Polar S610™) was used to measure the heart rate of the subjects. This was one of the data required to determine EBI for the subjects (Figure 4.5). (a) (b) Figure 4.5 HR-polar heart rate monitor: (a) Heart rate sensor and transmitter; (b) recorder. 4.2.6.3 Blood Pressure Monitor An automatic blood pressure monitor (© 2005 A&D Medical) was used to determine the blood pressure of the subjects at rest and prior to each test (Figure 4.6). Figure 4.6 Blood pressure monitor. 106 4.2.6.4 Fat Caliper Skinfold tests were performed using a Slim Guide fat caliper (SLrMGUIDE®) to determine %BF for each subject (Figure 4.7). Figure 4.7 Fat caliper. 4.2.6.5 Speedometer A speedometer (Filzer dB4L) was used to measure the linear propulsion speed of the wheelchair during the tests (Figure 4.8). The subjects were able to see the speed on the digital display of the speedometer. This online feedback helped them to adjust their propulsion and maintain the desired constant speed during the tests. 4.2.6.6 Weighting Scale A special scale was designed and fabricated to determine the combined weight of the wheelchair and the sitting subject (Figure 4.9). We then subtracted the weight of the wheelchair from the total weight to obtain the net weight of the subject. 107 (a) (b) (c) Figure 4.8 Speedometer: (a) Cycling computer; (b) Holding magnet; (c) Wiring kit and sensor. Figure 4.9 The setup for measuring the wheelchair user weight. 108 4.2.6.7 Global View of the Experimental Setup Figure 4.10 is a schematic sketch of the physical experimental setup and its electronic connections. The subject wears the heart rate monitor not shown in this diagram. Common mouse Figure 4.10 Global schematic rear view of the kinetic and kinematic data acquisition system and its connections. 109 4.2.7 Modeling Although, there may be some differences between the left and right side of the subjects, but since we had a right-side instrumented wheel, we studied subjects with dominant right hand side. The right upper limb was emulated as a linkage system with three links (upper arm, forearm, and hand) and three joints (shoulder, elbow, and wrist) (Figure 4.11). (a) (b) Figure 4.11 The Model of the upper limbs: (a) Sagittal view of the half body; (b) the linkage model. Numbers 1-3 represent upper arm, forearm, and hand, respectively. Twelve semi-spherical passive camera markers were used to determine the positions of 10 anatomical landmarks (cervical 7, acromion, medial and lateral epicondyle, radial and olnar styloid, second and fifth metacarp, left and right greater trochanter), and 2 points on the wheel (wheel axle and wheel angular position) (Figure 110 4.12). The neck and hip information were used to construct the "prismatic-box model" in the VICON software system, and the wheel markers were used to determine the angular position of the wheel. Al l of the markers were attached on the skin of the subject. The prismatic-box model was designed using the subjects' anthropometric dimensions. The VICON system resizes the designed model using the acquired data through a subject calibration test as explained in Section 4.2.4. Cervical 7 Medial epicondyle Lateral epicondyle Radial styloid Olnar styloid Second metacarp Fifth metacarp Figure 4.12 Landmark positions on the upper limbs and trunk of the subject, and the wheel. Figure 4.13 shows the designed 3D model of the upper body of the subject, which was used for kinematic data acquisition. VICON IQ2 software was used to construct this model and re-play animations of the tests. During the re-play mode, it was possible to turn the viewing camera around the prismatic-box model to see the details of the wheelchair propulsion. I l l Acromion Two markers on both Greater trochanters (The left marker, which is not shown, is on the opposite side of the right one). Wheel angular position Wheel center Figure 4.13 A 3D model of the upper body and wheel, developed by using the VICON system. 4.3 Analytical Methodology To determine the optimum seat position for each user, focusing on the efficiency aspect, it is necessary to obtain an equation, which relates seat position (Xand Y) to EBI. It has been reported that heart rate and propulsive moment are related to seat position [19]. Considering Equation 3.2, it is assumed that THB and Mz are related to X and Y, whereas AO is a constant, because the experiments are conducted for a pre-determined period of time and velocity. THB and Mz are related to X and Y as follows: 112 THB = gl(X,Y) Mz=g2(X,Y) (4.1a) (4.1b) where gt stands for function /. EBI is the related to THB and Mz as EBI = g i (THB, Mz) (4.2) EBI is now obtained using Equations 4.1 and 4.2: EBI = g 4 (X,7) (4.3) To determine the optimum seat position for each user considering the injury aspect, it is also necessary to obtain an equation that relates X and Y to WUJII or WUJIF. In Equations 3.12-3.15, ms, W,, hs, La, V,, and %BF are constant. Also, Fm, Mm, and fp are related to Xand Y. Fm, Mm and fp are related to A!"and Fas follow: Fm=g5(X,Y) (4.4a) Mm=g6(X,Y) (4.4b) fp=g7(X,Y) (4.4c) Equation 4.5 shows the relationship amongst WUJII, Fm, Mm and fp. 113 WUJII = gs(Fm,Mm,fp) (4.5) Using Equations 4.4 and 4.5, WUJU is re-stated as WUJII = g 9 ( X , T ) (4.6) In a similar fashion, WUJII' is determined as Wjm' = g10(X,Y) (4.7) Human responses are not exactly the same in repeated tests. Therefore, determining the Std. Dev. (tr) can provide a measure of the variability of the results. We defined z as a general function of Xand Y, which represents EBI, WUJII, or WUJII'. The test were repeated five times at each position with the same velocity to determine the average value for each index (z ) and its standard deviations (az). z and <7Z are functions of X and Y (Equations 4.8), and we called them the response model. One needs these equations to determine the optimum position for a wheelchair user. z = g(X,Y) (4.8a) oz=u(X,Y) (4.8b) 114 4.3.1 Design of Experiments Clearly, a large number of physical experiments requires long time and costs more. Also, because of the physiological and/or anatomical limitations of the subjects, it is not always possible to perform many experiments. Specially, the number of the experiments has to be reduced to a practical one. In statistical analysis, the problem of choosing a suitable sample of design variables is referred to as Experimental Design or Design of Experiments (DOE) [91,92]. When a required parameter is related to two variables the resulting function is called the response surface. To have a more reliable response surface, one has to increase the number of tests and have the variables reasonably distributed over the possible range. In this study, the subject fatigue, total test time, and the possible range for X and Y were the factors that constrained the number of the experiments. Therefore, a DOE method was used to build the response model that related the biomedical indices to the seat position. DOE methods reduce the number of the experiments required. Using a DOE method, one can generate a set of representative input parameters that uniformly cover the entire design surface. The response model is used as a surrogate model to substitute the actual response. 4.3.1.1 Grid-base Design In this study, three levels for the vertical and horizontal positions of the seat were considered. As the number of the experiments was limited, four sub-areas were defined with four data points (JP,) on the corners of each sub-area. The grid for this experimental design is shown in Figure 4.14. The values of the variables have been normalized. 115 This model presents nine data points for the experiments. Two more tests with different velocities at position X2 and Y2 were needed that increased the total number of the tests to eleven. It was not possible for all subjects to follow all eleven tests continuously, due to considerations given to possible fatigue. Therefore, the above model was used for two subjects, who could complete the eleven tests, and another design was used with two vertical seat positions (Yl and Y2) and three horizontal seat positions (XI, X2 and X3) for the rest. The other design required eight tests consisting of six experiments at six different positions and two additional tests at the position X2 and Y2 for different velocities. LOO 1 Normalized Y P4 0.00 Pi 0.00 T;t. p2 Ps P 3 Pe P9 1.00 Normalized X Figure 4.14 Grid-base design for two variables with four sub-areas and nine data points. Dimensions are not to scale. 4.3.2 Response Equation Using the results of the experiments, the responses were calculated at the designed data points. The response equations can be determined using one of the following three approximation methods: 116 • Artificial Neural Network (ANN) • Local interpolation of the discrete database [93] • Bivariate Quadratic Function (BQF) 4.3.2.1 Artificial Neural Network ANN method is very versatile approach and there are many applications of it in areas such as signal processing, controls, pattern recognition, medicine, business, speech recognition and production. ANN is an information-processing system, and is a generalization of mathematical models of human cognition or neural biology [94]. In this research, ANN was not used because there was insufficient data to train and check the network. 4.3.2.2 Local Interpolation In this method the response at a query point (Po) is calculated as follows. First the closest pair of data points of the database (Pi, Pi) are identified and the distances d\2 between them, and d\ and d2 from the points P\ and P 2 to the query point P 0 are determined. The weights h\ and h2 are calculated as hx =d2ldn h2=djdn ( 4 - 9 ) Normalized weights are shown by w\ and w2 and given as 117 w2 = h2l{hx +h2) (4.10) The response is obtained as R(P0) = wlR(Pl) + w2R(P2) (4.11) where R(Po) is the response at the query point P0, and R(P\) and R(P2) are the known responses at data points Pi and Pj, respectively [93]. In this method, if the database is sufficiently dense and if the query point Po is located such that the distance d\ or di are less than dn, the calculated response is a good approximation of the real case. Again, since the database was not sufficiently dense, this method was not used. 4.3.2.3 Bivariate Quadratic Function (BQF) In this study, each of the response equations was estimated by using a BQF [95] as follows: where b\, bz, bj, b$, bs and be are unknown constants and were determined by having the values of X, Y, and z for n' data points or tests and m' unknown, and using the m'- equation-n'-variable method, z represents the response surface and gives the value of the corresponding index at different seat positions. BQF is a practical method that can be z=g{X,Y) = bxX2 +b2Y2 +b3X + b4Y + b5XY + b6 (4.12) 118 used for the cases with a small number of the data points. However, increasing the number of the tests will increase the reliability of the results. Although, this method can be used with equal number of the equations and the variables, in case the data points are at the border of the sampling region there is no solution and more data points are needed. This conflict is because of the singularity that may occur in the solution. 4.3.3 The Big Picture The big picture of the entire test process is given as a flowchart in Figure 4.15. It shows the steps, which are followed to determine the optimum seat position of a manual wheelchair for a user. This method determines the procedure, which can be used to prescribe a more suitable manual wheelchair considering the injury priorities, conditions and concerns, of the subject. 119 Recruit the subject Measure anthropometric data of the subject Set the seat position (Xand Y) Train the subject 3 £ Record the data of at least five consecutive propulsions at this seat position Let the subject rest, and check his blood pressure and heart rate to ensure he is back to the baseline level Return to the third block and set a new seat position, continue the process until all planned positions have been used Post-process the raw kinematic data Measure Fm Mm, THB, and %BF Calculate z and oz at each data point Obtain the response equations using BQF Determine the values of Xand Tat optimum z Figure 4.15 Flowchart for the entire test process to determine the optimum positions of a wheelchair for a M W U . 120 4.4 Results and Discussion In the sections that follow, different categories of the results are presented. First, the heart rate, blood pressure and the anthropometric data of the subjects are given. Then, four research questions are explained and answered by addressing the following issues: • Relationship between the biomedical indices and the propulsion velocity. • Sensitivity of the biomedical indices to the seat position. • Generic rules for estimating the optimum seat position for all users. • Optimum seat position for a particular user. 4.4.1 Heart Rate, Blood Pressure and Anthropometric Data The measured and calculated resting level of heart rate and blood pressure, and anthropometric data for the subjects are presented in Tables 4.2a and 4.2b, respectively. These data were used in the kinetic and kinematic analysis. Also, the subject's limb segment lengths were required to design the prismatic-box model (see Sections 4.2.5 and 4.2.7). Table 4.2a. Heart rate and blood pressure for the subjects. Subject Heart rate Systolic blood pressure Diastolic blood pressure (Beats/min) (mmHg) (mmHg) 1 72 129 76 2 94 141 85 3 45 130 82 4 71 122 78 5 100 173 91 6 87 94 66 7 80 112 64 8 76 118 62 121 Table 4.2b Anthropometric data for the subjects. Subject Height Upper arm Forearm Hand Hand Shoulder joint Elbow joint Wrist joint Mass BMI % BF code length length length width circumference circumference circumference (m) (m) (m) (m) (m) (m) (m) (m) (kg) (kg/m2) ~T~ 1.85 0.32 0.29 Ojfl 0.10 0.45 0.26 0.16 ~88 25.71 28.9 2 1.62 0.28 0.25 0.08 0.09 0.38 0.26 0.15 58 22.10 27.1 3 1.65 0.27 0.26 0.08 0.09 0.40 0.25 0.17 53 19.47 21.5 4 1.93 0.29 0.30 0.10 0.09 0.42 0.28 0.17 100 26.85 24.0 5 1.80 0.30 0.26 0.10 0.09 0.44 0.29 0.19 94 29.01 32.2 6 1.80 0.28 0.28 0.09 0.09 0.42 0.29 0.18 80 24.69 29.5 7 1.77 0.29 0.27 0.09 0.08 0.36 0.25 0.16 58 18.51 8.8 8 1.91 0.31 0.30 0.10 0.10 0.43 0.30 0.19 87 23.84 22.8 4.4.2 Fixed Seat Position In this category, the fixed positions at X2 and Y2, and the velocities of 0.9, 1.1 and 1.3 m/s for eight subjects were used to determine the relationship between the biomedical indices and the speed. The mean and Std. Dev. of five consecutive pushing phases were analyzed for each test. In this study, because of the small sample size of the subjects we performed the statistical analysis for estimating the Type I or Alfa error. The results from statistical analysis using repeated-measures Analysis of Variance (ANOVA) showed that velocity alter the injury indices significantly (p<0.01). Figures 4.16 and 4.17 illustrate the variation of the mean values of WUJII and WUJII' (WUJII and WUJII') with respect to the velocity using Equations 3.6b and 3.8a, respectively. The figures show that these two indices increase by increasing the velocity for all subjects. Tables 4.3 and 4.4 present the mean and Std. Dev. of WUJII and WUJII', which confirm the above finding. So, the relations of the injury indices were modified to include the velocity as one of their parameters. The results from repeated-measures A N O V A did not show significant relationship between the velocity and the mean value of EBI (EBI). Figure 4.18 presents the variation of EBI with respect to the velocity. The figure shows that EBI increases for five subjects by increasing the velocity up to about 1.1 m/s. Three subjects have their maximum EBI at the middle speed. As this seems case dependent, we cannot determine a specific rule for variation of EBI with respect to the velocity. This result confirm the findings of Mukherjee et al. [38] that efficient propulsion velocity is case dependent and is not related to lower or higher speeds. The mean and Std. Dev. of EBI are shown in Table 4.5. 123 5 8 7 6 5 4 3 2 1 0 0.85 - 0.95 1.05 1.15 Velocity (m/s) 1.25 — Subject 1 — « — Subject 2 A Subject 3 — X - Subject 4 — Subject 5 - : - Subject 6 — r - — Subject 7 - Subject 8 1.35 Figure 4.16 Variation of WUJII versus velocity. Table 4.3 Mean and Std. Dev. of WUJU for the subjects for three velocities. Subject code Velocit (m/s) 1.553 1.809 2.453 2.970 2.416 1.608 0.869 2.369 0.9 ±0.195 ±0.396 ±0.576 ±0.220 ±0.249 ±0.255 ±0.108 ±0.171 1.1 2.343 2.552 3.399 4.126 4.632 3.622 1.356 3.797 ±0.232 ±0.335 ±0.513 ±0.425 ±0.660 ±0.618 ±0.131 ±0.429 1.3 3.272 3.274 3.543 4.813 5.087 5.441 2.87 6.800 ±0.658 ±0.158 ±0.563 ±0.801 ±0.974 ±0.594 ±0.553 ±1.047 124 7 6 5 & 4 3 3 2 1 0 — Subject 1 — • — Subject 2 A Subject 3 —K - Subject 4 — — Subject 5 - o - Subject 6 *— Subject 7 - Subject 8 0.85 0.95 1.05 1.15 Velocity (m/s) 1.25 1.35 Figure 4.17 Variation of WUJU' versus velocity. Table 4.4 Mean and Std. Dev. of WUJII' for the subjects for three velocities. Subject code Velocit i m / s l 1.748 2.233 2.741 2.660 2.684 1.923 0.429 2.265 0.9 ±0.219 ±0.488 ±0.643 ±0.197 ±0.277 ±0.304 ±0.050 ±0.164 1.1 2.637 3.151 3.798 3.696 5.145 4.331 0.645 3.629 ±0.261 ±0.414 ±0.574 ±0.381 ±0.732 ±0.740 ±0.062 ±0.410 1.3 3.682 4.042 3.959 4.311 5.650 6.506 1.326 6.500 ±0.740 ±0.195 ±0.630 ±0.717 ±1.082 ±0.710 ±0.191 ±1.001 125 0.85 0.95 1.05 1.15 Velocity (m/s) 1.25 • Subject 1 — • - Subject 2 • Subject 3 —X - Subject 4 )l( Subject 5 - o -Subject6 —4—* Subject 7 — - Subject 8 1.35 Figure 4.18 Variation of EBI versus velocity. Table 4.5 Mean and Std. Dev. of EBI for the subjects for three velocities Subject code Velocit (m/s) 8 19.152 15.428 20.308 28.194 15.378 18.443 8.016 38.019 0.9 ±1.933 ±1.647 ±3.429 ±1.333 ±1.962 ±0.896 ±0.455 ±2.217 1.1 22.641 14.327 19.731 28.520 24.374 18.157 11.868 40.522 ±1.320 ±2.298 ±2.177 ±2.840 ±2.019 ±4.328 ±0.780 ±0.643 1.3 24.328 16.318 15.967 25.539 20.582 19.176 15.670 39.785 ±3.688 ±1.251 ±3.921 ±1.933 ±2.284 ±1.287 ±0.758 ±1.407 126 4.4.3 Constant Wheelchair Velocity In the second category of the experiments, the tests were performed at three X and two Y settings, and the velocity of 0.9 m/s for all subjects. Five consecutive pushing phases were analyzed for each test. 4.4.3.1 Seat Height Y l Using repeated-measures A N O V A the results showed that the horizontal position of the seat was significantly related to the indices at low seat position Y l (p<0.05). Figures 4.19, 4.20 and 4.21 show the variations of WUJII, WUJII', and EBI against the ratio of X to the arm length (X-ratio) at Y l , respectively. X-ratio was used to normalize the horizontal seat position amongst the subjects. It is seen that WUJII and WUJII' increase by moving the seat forward, except for the subjects 1, 4 and 7 in Figure 4.19 and subjects 1, 4, 6 and 7 in Figure 4.20. Figure 4.21 shows that, except subjects 1 and 4, the other subjects had their minimum values of EBI at most backward seat position, and six subjects had their maximum value of EBI at most forward seat position. Tables 4.6, 4.7 and 4.8 present the mean and Std. Dev. of WUJB, WUJII' and EBI for the subjects at three X-ratios at seat height Y l , respectively. The Std. Dev. of WUJII and WUJE' vary between 0.053-0.783, and 0.025-0.967, respectively, but are predominantly under 0.400. The Std. Dev. of EBI varies between 0.75-3.06 and is mostly below 2.00. The results indicated that the average values of the injury indices and EBI at low seat height Y l , can vary between 5-27.5% and between 3.1-21.1%, respectively. 127 -X o Subject 1 Subject 2 Subject 3 Subject 4 • Subject 5 Subject 6 Subject 7 Subject 8 Seat height Y l - --30 -28 -26 -24 -22 -20 -18 -16 X-ratio* 10~2 r 7 : 6 : 5 s : 4 i 3 1=3 ; 2 \ i : 0 •14 Figure 4.19 Variation of WUJU against X-ratio at Y l . Minimum values encircled. Seat height Y l o Subject 1 1 — • — Subject 2 A Subject 3 I — X - Subject 4 I * Subject 5 - Subject 6 I „ Subject 7 I — - Subject 8 -30 -28 -26 -24 -22 -20 -18 -16 -14 X-ratio* 10"2 Figure 4.20 Variation of WUJU' against X-ratio at Y l . Minimum values encircled. 128 — Subject 1 — • — Subject 2 A Subject 3 — X - Subject 4 - - Subject 6 • Subject 7 — - Subject 8 Seat height Y l 7 ^ - -30 -28 -26 -24 -22 - X-ratio* 10' 20 2 • 18 -16 60 50 - t 40 ff u 30 £Q 20 10 0 ffl •14 Figure 4.21 EBI with respect to the X-ratio at Y l . Maximum values encircled. Table 4.6 Mean and Std. Dev. of WUJII for the subjects at three X-ratios and seat height Y l . Subject Seat^^code X-position 8 1.370 3.414 2.068 2.529 5.708 2.315 0.551 2.734 ±0.099 ±0.738 ±0.361 ±0.612 ±0.568 ±0.154 ±0.053 ±0.245 XI X2 X3 0.934 2.849 1.415 2.317 4.905 1.941 1.085 1.790 ±0.093 ±0.783 ±0.355 ±0.167 ±0.576 ±0.500 ±0.152 ±0.201 1.134 1.566 1.472 2.766 3.034 1.981 0.929 1.589 ±0.114 ±0.308 ±0.074 ±0.383 ±0.261 ±0.346 ±0.110 ±0.114 129 Table 4.7 Mean and Std. Dev. of WUJII' for the subjects at three X-ratios and seat height Y l . Subject Seat^\code 1 2 3 4 5 6 7 8 X - p o s i t i o n \ 1.542 4.214 2.311 2.265 . 6.339 2.768 0.262 2.614 XI ±0.112 ±0.911 ±0.403 ±0.548 ±0.631 ±0.184 ±0.025. ±0.234 1.051 3.517 1.582 2.075 5.448 2.321 0.516 1.711 X2 ±0.104 ±0.967 ±0.397 ±0.149 ±0.640 ±0.598 ±0.072 ±0.192 1.275 1.933 1.644 2.477 3.369 2.368 0.442 1.519 X3 ±0.128 ±0.380 ±0.083 ±0.343 ±0.290 ±0.413 ±0.053 ±0.109 Table 4.8 Mean and Std. Dev. of EBI for the subjects at three X-ratios and seat height Y l . Subject Seat^\code X - p o s i t i o n \ 1 2 3 4 5 6 7 8 XI 24.526 ±0.752 15.953 ±1.518 9.193 ±0.881 30.519 ±2.251 25.884 ±1.461 22.470 ±2.375 12.610 ±0.796 53.123 ±1.430 X2 17,211 ±1.114 10.851 ±1.830 12.539 ±2.661 26.653 ±1.123 25.323 ±1.403 29.675 ±3.057 10.289 ±0.933 41.715 ±2.219 X3 18.511 ±1.166 9.325 ±1.075 8.475 ±0.708 30.333 ±2.424 20.303 ± 0 . 6 9 0 19.556 ±1.569 9:235 ±0.706 34.602 ±1.314 To have a better understanding of the variation of the average values of the indices, Figures 4.22, 4.23 and 4.24 show the maximum and minimum values of WUJII , WUJII', EBI and their Std. Dev. among the subjects with respect to the X-ratio at Y l . 130 Seat height Yl • Subject 1 (mean) • Subject 1 (mean* SD) • Subject 2 (mean) Subject 2 (mean± SD) -30 -28 -26 — ! -24 6 5 4 3 2 1 0 s s H -22 -20 -18 -16 -14 X-ratio* 10 -2 Figure 4.22 Maximum and minimum values of WUJII and its Std. Dev. against X-ratio at Y l , among the subjects. Seat height Yl • Subject 1 (mean) Subject 1 (mean+ SD) • Subject 2 (mean) Subject 2 (mean± SD) -30 -28 -26 -24 -22 -20 X-ratio* 10" •18 •16 -14 Figure 4.23 Maximum and minimum values of WUJII' and its Std. Dev. against X-ratio at Y l , among the subjects. 131 • Subject 8 (mean) Subject 8 (mean± SD) • Subject 2 (mean) Subject 2 (mean + SD) Seat height Y l -30 -28 -26 -24 X-ratio* 10 22 -20 -18 2 •16 60 50 40 30 20 10 0 S CQ W •14 Figure 4.24 Maximum and minimum values of EBI and its Std. Dev. against X-ratio at Y l , among the subjects. The above results show that by decreasing the magnitude of X-ratio or moving the seat forward at low seat height Y l , both the average value of the injury indices and EBI may increase. Overall, the results show that the indices are sensitive to horizontal seat position at seat height Y l . 4.4.3.2 Seat Height Y2 Using repeated-measures ANOVA the results showed that horizontal position of the seat was significantly related to the indices at high seat position Y2 (p<0.05). Figures 4.25, 4.26 and 4.27 show the variation of WUJII, WUJII' and EBI with respect to X- ratio at seat height Y2, respectively. Five subjects showed their highest values of the 132 injury indices at the most forward seat position or highest X-ratio, whereas, subject 4 showed the minimum value at this position and the other two subjects did not show significant change. Five subjects showed that their EBI decreases by increasing X-ratio or moving the seat backward, whereas two subjects had their maximum EBI at X2. EBI had insignificant change with respect to the X-ratio for subjects 3. Tables 4.9, 4.10 and 4.11 present the mean and Std. Dev. of WUJn, WUJlT and EBI for the subjects at three X-ratios and seat height Y2, respectively. The Std. Dev. of WUJII and WUJH" vary between 0.098-0.629, and are mostly under 0.40. The Std. Dev. of EBI varies between 0.46-3.62, and is mostly under 2.00. The results indicated that the average values of the injury indices vary between 5.6-29.9% and the average value of EBI varies between 3.7-26.0%. O— Subject 1 - Subject 2 A Subject 3 -x - Subject 4 -^—Subject 5 • - Subject 6 - Subject 7 • Subject 8 Seat height Y2 X-ratk>*10 Figure 4.25 Variation of WUJII against X-ratio at Y2. Minimum values encircled. 133 Seat height Y2 «— Subject 1 • - Subject 2 *—• Subject 3 - Subject 4 *—Subject 5 • - Subject 6 4~— Subject 7 — Subject 8 © 0- - r^L-^1 a~ -30 -28 -26 -24 -22 -20 -18 -16 -14 X-ratio* 10" Figure 4.26 Variation of WUJU' against X-ratio at Y2. Minimum values encircled. Seat height Y2 •30 -28 -26 -24 -22 X-ratio* 10 -20 -2 a s •18 -16 -14 Figure 4.27 Variation of EBI against X-ratio at Y2. Maximum values encircled. 134 Table 4.9 Mean and Std. Dev. of WUJII for the subjects at three X-ratios and seat height Y2. Subject Seat^\code X-positioif^^ 1 2 3 4 5 6 7 8 XI 1.495 ±0.102 1.917 ±0.573 2.508 ±0 .139 2.503 ±0.364 4.642 ±0.629 2.610 ±0.144 0.782 ±0.098 2.736 ±0.322 X2 1.182 ±0.134 1.836 ±0.392 1.176 ±0.144 2.450 ±0.273 1.352 ±0.231 1.180 ±0.184 0.693 ±0.180 2.188 ±0.194 X3 0.957 ±0.179 2.012 ±0.262 1.468 ±0.273 2.762 ±0.337 2.136 ±0.283 1.338 ±0.254 0.794 ±0.112 1.748 ±0.223 Table 4.10 Mean and Std. Dev. of WUJII' for the subjects at three X-ratios and seat height Y2. .^v . Subject S e a i \ c o d e X - p o s i t i o n \ 1 2 3 4 5 6 7 8 X I 1.682 ±0.115 2.366 ±0.707 2.802 ±0.156 2.242 ±0.326 5.156 ±0.699 3.121 ±0.172 0.372 ±0.046 2.615 ±0.308 X2 1.330 ±6.151 2.266 ±0.484 1.918 ±0.161 2.194 ±0.245 1.502 ±0.257 1.411 ±0.220 0.330 ±0.086 2.092 ±0.186 X3 1.077 ±0.202 2.484 ±0.324 1.640 ±0.305 2.474 ±0.302 ; 2.372 ± 0 . 3 1 4 1.600 ±0.304 0.378 ±0.053 1.671 ±0.213 Figures 4.28, 4.29 and 4.30 illustrate the maximum and minimum values of WUJII, WUJII' and EBI and their Std. Devs. among the subjects with respect to the X - ratio at Y2, respectively. 135 Table 4.11 Mean and Std. Dev. of EBI for the subjects at three X-ratios and seat height Y2. Subject S e a t \ « > d e X - p o s i t i o n ^ \ 1 2 3 4 5 6 7 8 1 26.317 ±2.311 11.931 ±2.104 15.548 ±1.019 24.331 ±1.778 26.337 ±2.200 23.813 ±1.427 15.376 ±0.570 40.157 ±0.907 2 19.175 ±1.038 13.902 ±3.621 15.737 ±1.040 28.015 ±1.347 12.634 ±1.699 22.433 ±0.976 10.293 ±1.117 38.019 ±2.217 3 18.894 ±1.048 13.243 ±1.468 14.359 ±2.950 18.463 ±0.977 16.231 ±0.534 20.358 ±0.531 8.016 ±0.455 31.319 ±1.985 Seat height Y2 • Subject 1 (mean) Subject 1 (mean± SD) • Subject 2 (mean) Subject 2 (mean ± SD) 3.5 3.0 2.5 2.0 £ 1.5 1.0 0.5 0.0 Figure 4.28 Maximum and minimum values of WUJII and its Std. Dev. against X-ratio at Y2, among the subjects. 136 Seat height Y2 • Subject 1 (mean) Subject 1 (mean± SD) • Subject 2 (mean) Subject 2 (mean+ SD) 1 1 1 1 1 — 30 -28 -26 -24 -22 -20 X-ratio* 10"2 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 = p •18 -16 • 14 Figure 4.29 Maximum and minimum values of WUJU' and its Std. Dev. against X-ratio at Y2, among the subjects. Seat height Y2 subject 8 (mean) Subject 8 (mean± SD) • • Subject 2 (mean) Subject 2 (mean± SD) 60 50 40 ¥ £3 30 20 10 0 03 UJ J-30 -28 -26 -24 X-ratio* 10 22 -20 -18 -16 2 •14 Figure 4.30 Maximum and minimum values of EBI and its Std. Dev. against X-ratio at Y2, among the subjects. 137 The above results show that the average values of the injury indices may increase at the most forward seat position at seat height Y2. Also, it can be possible that EBI increase by moving the seat forward. The results show that indices are sensitive to horizontal seat position at seat height Y2. 4.4.3.3 Horizontal Seat Position X I Two tests were performed for all subjects at horizontal seat position XI with two possible vertical seat positions Y l and Y2. To normalize the seat height for the subjects, the ratio of Y to the arm length was defined as Y-ratio. Figures 4.31 and 4.32 show that WUJII and WUJII' decrease by increasing the Y-ratio (or seat height) for four subjects at position XI , whereas they increase for subjects 2 and 8. The average values of the injury indices do not show considerable variation for subjects 3 and 4. Figure 4.33 shows that four subjects have their maximum values of EBI at Y l . Three subjects have their maximum values of EBI at Y2. Subject 1 did not show considerable variation by changing the seat height. Performing repeated-measures A N O V A the results did not show significant relationship between that vertical position of the seat and the indices at horizontal seat position XI . 138 Seat position XI 20 22 24 26 Y-ratio* 10" 28 30 — — Subject 1 —"* - Subject 2 * Subject 3 —O - Subject 4 H Subject 5 - + -Subject 6 —o™— Subject 7 • Subject 8 Figure 4.31 Variation of WUJU against Y-ratio at XI . Seat position XI 20 22 24 26 Y-ratio* 10 28 30 — Subject 1 — Subject 2 Subject 3 — Subject 4 — Subject 5 - Subject 6 »~ Subject 7 - Subject 8 -2 139 Figure 4.32 Variation of WUJII' against Y-ratio at X I . Seat position XI 40 30 i D Q m 10 20 +• — Subject 1 — Subject 2 Subject 3 — Subject 4 Subject 5 - • - Subject 6 ~ H — ~ Subject 7 Subject 8 22 24 Y-ratio* 10 26 28 2 30 Figure 4.33 Variation of EBI against Y-position at X I . 4.4.3.4 Horizontal Seat Position X2 At position X2, two tests were performed for all subjects with seat heights Y l and Y2. Figures 4.34 and 4.35 show WUJII and WUJII' versus Y-ratio. For half of the subjects no specific relationship is observed. Figure 4.36 illustrates that EBI increases for four subjects and decreases for three by increasing Y-ratio. Subject 7 does not show considerable change for EBI against Y - ratio. Overall, using repeated-measures A N O V A the results did not show significant relationships between the average values of the indices and the seat height at position X2. 140 Seat position X2 6 5 4 6 0 „ ^ 3 3 2 1 0 20 22 24 26 Y-ratio* 10" 28 30 — Subject 1 — X - Subject 2 EJ Subject 3 — O - Subject 4 — + . — Subject 5 - - • Subject 6 — Subject 7 - Subject 8 Figure 4.34 Variation of WUJII against Y-ratio at X2. 6 5 ^ 4 Es 3 1 0 20 Seat position X2 22 24 26 Y-ratio* 10" 28 30 Subject 1 — • - Subject 2 — * — Subject 3 —X - Subject 4 Subject 5 - • - Subject 6 Subject 7 — - Subject 8 Figure 4.35 Variation of WUJU' against Y-ratio at X2. 141 Seat position X2 • Subject 1 — • — Subject 2 Subject 3 — X - Subject 4 )|( Subject 5 - • - Subject 6 -"4 •— Subject 7 Subject 8 20 22 24 26 28 30 Y-ratio* 10" Figure 4.36 Variation of EBI against Y-ratio at X2. 4.4.3.5 Horizontal Seat Position X3 Figures 4.37 and 4.38 show that both WUJII and WUJII' increase by increasing Y-ratio for six subjects. An increasing trend for the average values of injury indices against Y-ratio at X3 can be seen. Figure 4.39 shows that EBI increases by increasing Y-ratio for four subjects. EBI decreases for three other subjects. Subject 5 did not show considerable variation for EBI against Y-ratio. Using repeated-measures ANOVA the results did not show significant relationship between the indices and the seat height at horizontal seat position X3. 142 S e a t p o s i t i o n X3 OO ^ ^ 2 1 0 20 —o 22 24 26 Y-ratio* 10 28 30 -2 — Subject 1 - Subject 2 • Subject 3 —o - Subject 4 — Subject 5 am mm - Subject 6 — Subject 7 — - Subject 8 Figure 4.37 Variation of WUJII against Y-ratio at X3. S e a t P o s i t i o n X3 X ~ - — - A — X KJJUPlJ 20 22 24 26 Y-ratio* 10" 28 30 — • — Subject 1 —• - Subject 2 A Subject 3 — X - Subject 4 )K Subject 5 - • - Subject 6 ""I1 Subject 7 Subject 8 Figure 4.38 Variation of WUJJJ' against Y-ratio at X3. 143 Seat at position X 3 20 22 24 26 Y-ratio* 10" 28 30 — Subject 1 — — Subject 2 • Subject 3 - Subject 4 — * • - • - Subject 6 "~™4~™~ Subject 7 - Subject 8 Figure 4.39 Variation of EBI against Y-ratio at X3. 4.4.3.6 Optimum Seat Position To determine the optimum seat position for a user at a propulsion velocity the Bivariate Quadratic Function (BQF) was used. BQF method requires at least nine tests. This method was performed for subjects 7 and 8 that were able to perform nine tests at nine seat positions. The approximate locations of XI to X3 and Y l to Y3 are shown in the X-ratio - Y-ratio plane of the following figures for ease of reference. Figure 4.40 presents a saddle surface and illustrates the lowest WUJII, between Y l and Y2, and close to XI for subject 7. The lowest value of WUJU' is seen in Figure 4.41 almost at the same location as the lowest WUJII. Figure 4.42 shows the response surface for EBI against X and Y-ratios for subject 7. It shows that the maximum EBI appears close to Y2 and X I . 144 Figure 4.40 Variation of WUJII versus seat position, for subject 7. Figure 4.41 Variation of WUJU' versus seat position, for subject 7. Figure 4.42 Variation of EBI versus seat position, for subject 7. Considering the general form of BQF as in Equation 4.12 and by using the MATLAB® software, the coefficients and constants of the response equations for subject 7 were determined (Table 4.12). Table 4.12 The coefficients and constants for the response equations that determine the indices at different seat positions for subject 7. b \ Z>2 63 Z>4 bs b(, EBI 401.785 -365.205 273.914 150.773 -213.573 24.520 WUJH -48.251 200.876 -46.751 -83.883 94.303 6.447 WUJII' -22.929 95.426 -22.234 -39.828 44.870 3.055 ^Coefficients & Constant Index 146 The same procedure was performed for subject 8 and the results are presented in Figures 4.43^4.45. Figure 4.43 shows that the maximum value of WUJII occurs close to Y2 and X I . The maximum value of WUJII' is shown in Figure 4.44 at the same location as the maximum WUJII. Figure 4.45 shows that the maximum value of EBI is at XI and Y l for subject 8. The minimum value appears in the opposite side of the maximum value. 147 Figure 4.44 Variation of WUJII' versus seat position, for subject 8. Figure 4.45 Variation of EBI versus seat position for subject 8. 148 The coefficients and constants of the related response equations for subject 8 have been determined and presented in Table 4.13: Table 4.13 The coefficients and constants for the response equations that determine the indices at different seat positions for subject 8. b\ bi 63 64 bs be EBI -414.777 189.879 488.559 652.596 2079.642 198.779 WUJII 106.198 -718.477 72.073 323.304 -76.75 -27.430 WUJII' 101.662 -686.740 68.995 300.985 -73.546 -26.203 jCoefficients & Constant Index 4.5 Conclusions In this chapter, a new method for determining the optimum seat position for the M W U was introduced. Description of the study population, the demographic and anthropometric data were given. The test protocol and experimental setup were explained. The kinematic and kinetic parameters and values of the proposed indices were calculated for each subject at different seat positions. The optimum positions for the users were determined by using the values of indices at different settings. The results of the experiments answered four research questions. bi this study, because of the small sample size of the subjects we performed the statistical analysis for estimating me Type I or Alfa error. We can decrease the Type II or Beta error by increasing the sample size of the subjects. 149 The results showed that the average values of the injury indices for all subjects increase considerably by increasing the linear wheelchair velocity (p<0.01). This result verifies the direct effect of velocity on the injury indices. Therefore, one may conclude that higher propulsion velocity will increase the risk of injury. Boninger et al. [4,69] reported that the flexion/extension and rotation angles for the shoulder and elbow joint of MWUs, as well as applied radial force, increase with increasing propulsion speeds confirming our results. However, a significant relationship was not observed between the values of EBI and velocity. Efficient propulsion velocity is therefore case dependent, and relates to the physiological, anatomical and technical characteristics of the subjects. Efficient propulsion velocity for one subject would not necessarily be the same for the others, and should be determined individually. This result corroborates the report of Mukherjee et al. [38] that there is no specific relationship between the propulsion speed and efficiency, and that the energy-efficient propulsion speed is related to the user's freely chosen speed as a characteristic of the subjects. Considering the results for the constant speed and fixed seat height experiments, one may say it is possible that the values of EBI increase by moving the seat forward related to the wheel axle (p<0.05). Whereas, the average values of the injury indices may decrease by moving the seat backward (p<0.05). We know of no other research that investigated the variation of the G M E with respect to the horizontal seat position with constant speed of propulsion. However, the report of Cooper [12, page 271] confirms our results for the injury indices. He explained that if the seat is too far forward, the shoulder will be excessively extended and internally rotated, which may lead to rotator cuff injury. 150 Also, the results of Boninger et al. [35] report that more forward seat position can increase median verve injury that compliment above results. Our results indicated that the average values of the injury indices and EBI can be 5.6-29.9% and 5-27.5%, respectively. Lower seat height showed lower variation for the results. The higher variations mostly are related to the subjects whose index values changed significantly with respect to the X and Y-positions. Therefore, the indices appear to be sensitive to the seat position. The response equations were determined for subjects 7 and 8 by using the BQF method. These equations can be used to determine the optimum seat position. The presented 3D-graphs for these two subjects show the optimum seat positions and indicate that the positions determined by using EBI and the average values of injury indices are not necessarily the same. These graphs illustrate the probable average values and variations of the indices at different positions by using the BQF method. Subject 5 had the highest BMI and %BF, and subject 7 had the lowest, at the time of the experiments. They presented the highest and lowest average values of the injury indices for most of the test situations, respectively. This supports the work of Boninger et al. [23] and other researches [70,71] that BMI affects CTS and shoulder injuries. Also, the above figures showed that subjects 2, 3, and 4, who were younger and had less wheelchair experience, had lower EBIs. In the next chapter, a method is introduced to determine the values of the injury indices at the upper limb joints of a wheelchair user. This method helps to determine the optimum wheelchair variables by considering the regarding concerns and priorities. 151 CHAPTER 5 Injury Assessment for the Upper Limb Joints 5.1 Introduction In Chapter 1, the prevalence of pain in the upper limb joints of MWUs was discussed. Previous studies presented methods for measuring pain or injury were explained in Chapter 3. There are very few studies that determine the pain or injury at the upper limb joints. The previous methods have shortcomings as they use questionnaires rather than direct measurements, or focus only on measuring a specific factor. In this chapter, the values of the proposed injury indices are calculated for different joints of the upper body for subjects 7 and 8. To do this, a 3D rigid-body dynamic model for the upper limb is presented, and a method (Method I) for calculating the upper limb joint forces and moments is described. Cooper [12] introduced the 152 structure of this method in 1995, and Vrongistinos [46] presented it with some differences in 2001. This method is reproduced here with some changes to the load calculations. The joint loads are calculated using the new method and are used as part of the required data for determining the values of the injury indices. 5.2 Method I In Chapter 4, the test setup, the model, and the methods were explained. The upper limb segments were assumed as rigid-bodies to be able to use the dynamics of the rigid body. hi this chapter, the focus is on determining the optimum wheelchair variables for each user considering the risk of the injury for the upper limb joints. Subjects 7 and 8 participated in this part of the experiments. To define the optimum position, nine tests at different combinations of three X-positions and three Y-positions for each user were performed at a constant propulsion speed. WUJII and WUJII' using Equations 3.14 and 3.15 were used as criteria to determine the optimum position. The values of the injury indices were determined at shoulder, elbow and wrist joints for each subject. The kinematic data acquired by VICON motion analysis system, the kinetic data measured by the instrumented wheel, and the subject's anthropometric data were used in the model to determine the joint loads as part of the required data to calculate the injury indices. The optimum positions determined minimize the probable injuries at different joints for each subject. 153 Considering the general form of Bivariate Quadratic Function (BQF) and using the MATLAB® software, the coefficients and constants of the related equations were obtained for the subjects. 5.2.1 The Kinematics of the Upper Limb To determine the orientation of each body segment with respect to a fixed coordinate system in a 3D analysis, a frame is attached to the Center Of Mass (COM) of the segment, and then a description of this frame is given relative to the reference system. Figure 5.1 shows local frame B ({B}) attached to C O M of a segment. A description of {B} relative to global frame A ({A}) gives the orientation of the segment. To describe the orientation of {B}, the unit vectors of its three principal axes with respect to {A} are determined. APBORG is the vector that determines the position of the origin of {B} with respect to {A}. XB, YB, and ZB are the unit vectors giving the principal directions of {B}. When written in terms of {A}, they are shown as AXB, AYB, and AZB. If one stacks these three unit vectors together as columns of a 3><3 matrix, a new matrix AR is obtained, which is referred to as the rotation matrix (Equation 5.1) [96]. ^ Figure 5.1 Local and global frames for a rigid body. Segment 154 where, rn_33 are the components of AXB, AYB, and AZB. Figure 5.2 shows a randomly selected point E in {B} and its relationship to {A}. P E represents the position vector of point E with respect to {A}, and P E is the vector that shows the position of point E with respect to {B}. A P E = BR B P E + A P B O R G (5-2) In the case where the local and global coordinate systems are concentric and one needs the information with respect to the global coordinate system, the following equation is used: APE = ABR BPE (5.3) Figure 5.2 General transformation of a vector. 155 5.2.1.1 Velocity of the Segment The linear velocity of a point with respect to {A} is obtained at any instant by using the position vectors as Ay - ± A p y E ( ; + A Q - y E ( Q K B " A ^ b " 1 S J At { 5 A ) where E is a point in {B}, A represent {A}, and P is its position vector, and AV% is the linear velocity of point E with respect to {A} [96]. Euler angles, Bryant angles, and Euler parameter are different methods, which are commonly used to derive the rotation matrix. In this study, three non-collinear markers on each segment, and the Euler angles were used to define the segments in the local coordinate system [12,46]. 5.2.1.2 Z - Y - X Euler Angles One method of describing the orientation of {B} with respect to {A} is as follows. Start with the frame coinciding with known {A}, first rotate {B} about ZB by an angle a to obtain {A1}, then rotate about the new YB by an angle /? to find {A"}, and finally rotate about the last^B by an angle y [96,97]. Frames A' and A" are the intermediate frames for transforming {A} to {B}. These rotations give us BR as BR = ROT(BX,y) R0T(BY,J3) ROT(BZ,a) (5.5) 156 Because"/? =^i?, we can compute BR as R = ROT(BZ,a) ROT(BY,p) ROT(BX,y) R = ca - soc 0 sec ca 0 0 0 1 c/J 0 sp 0 1 0 -sp 0 cP 1 0 0 " 0 cy -sy 0 5 7 ca.cP ca.sp.sy-sa.cy ca.sp.cy+ sa.sy sa.cp sa.sp.sy+ca.cy sa.sPry-ca.sy -sP cp.sy cp.cy (5.6a) (5.6b) (5.6c) where ca = cos(a) and s a = sin(a), etc. g i? is determined by using Equations 5.1 and 5.6c as ru 12 ra ca.cP ca.sp.sy-sa.cy ca.sp.cy+sa.sy A BR = r22 r23 = sa.cp sa.sp.sy+ca.cy sa.sp.cy-ca.sy (5.7) / 3 1 r32 r33_ -sp cp.sy cfi.cy The results for Z - Y - X Euler angles from a known rotation matrix are as follows: a = Atan2 (r2l,rn) P^Atan2(-r3l,±^rx]+r2]) y=Atan2 (rn,r33) (5.8a) (5.8b) (5.8c) Considering the positive square root in the formula for 6, a single solution was computed. The range for R was -90 <= /? <= 90. 157 5.2.1.3 Determining the Directional Cosines In this study, three markers were placed on three non-collinear landmarks to determine the position and orientation of each segment of the upper body of the M W U . The positions of the markers were tracked during the tests using the VICON Motion Analysis System with a sampling frequency of 100 Hz. Points 1, 2, and 3 represent the three markers on a typical segment, and E\, E2 are the position vectors between points 3 and 1, and between points 3 and 2, respectively. Directional cosines (r̂ ) were determined for the rotation matrix, which transforms the coordinates from the local frame to another, with the origin of the local and the orientation of the global coordinate system. {B} is transformed to the center of mass of the segment. {A} and {B} are concentric. Figure 5.3 shows the directional cosines of the x-axis of {B} with respect to the three axes of {A}. Figure 5.3 Directional cosines of rotation matrix for the axes of {B} with respect to {A}. To determine r\j, the unit vectors of the axes of frames {A} and {B} are calculated. The unit vectors of the axes of the global coordinate system {A} are 158 T "0" "0" 1 = 0 , J = 1 , K = 0 0 0 1 (5.9) To determine the unit vectors of the axes of frame {B}, the vectors E\ and E2 are calculated as ~x2 y\ -y3 , E2 — -y3 _ Z 3 . .Z2 _ Z 3 . where J t i , 2 , 3 , 7 1 , 2 , 3 and z i , 2 , 3 are the position components of the points 1, 2 and 3 with respect to the global coordinate system. The unit vectors are now determined as EX=Y£-> , 4 = ] | l ,E3=ExxE2 (5.11) \E\\ 1-̂ 21 The directional cosines are calculated using Equations 5.9 and 5.11 as rn = I • Ex , r]2 = I • E2 , rl3 = I • E3 r2l=J-El , r22=J-E2 , r23=J-E3 (5.12) r3i=K-Ex , r32=K-E2 , r33=K-E3 Linear velocity of a point on a segment is determined as 159 BV _ ± B P _ VE(̂  + AQ-VE(0 dt A / ^ Q Ar (5.13) where BVE and B P E are the velocity and position vector of a selected point E on the segment with respect to frame B. Angular velocity of the segment with respect to the global coordinate system, AQB, can be determined at any instant by using the time derivatives of a, B and y as QB=a Ak + J3 AjA. + y Ai, (5.14) where Ak, AjA, and AiA. are the unit vectors for the z, y and x-axes of the frames {A}, {A'} and {A"} with respect to the frame {A}, respectively [96,97]. The time derivatives of a, B and y are determined as <*t &l^>0 d_ dt Ol A/_>0 a(t + At) -a(t) At Pit + At) -Pit) \ At y{t + At) -yit) At (5.15a) (5.15b) (5.15c) Ak, AjA. and AiA. are calculated by using the following equations: 4k = 0 0 1 (5.16a) 160 ca -sa 0 "0" -sa AJA'= sa ca 0 1 = ca 0 0 1 0 0 (5.16b) ca -sa 0" 0 sP "1" cacP sa ca 0 0 1 0 0 = sacP 0 0 1 -sP 0 cp 0 -sP (5.16c) Substituting Equations 5.16 into Equation 5.14, the relation for AQ.B is determined as "0 -sa cacP a AQB = 0 ca sacP P 1 0 -sp t (5.17) 5.2.1.4 Acceleration of a Segment Linear and angular acceleration of body segment can be determined at any instant by using the linear and angular velocity vectors as _d_sv _ g K E ( f + A Q - V E ( Q at A / - . 0 A? (5.18a) dAr, _ . . AnB(t+&tyAnB(t) B - ^B - lim ai A/->O A? (5.18b) where BVE is the linear velocity of point E in the frame B [96]. 161 Linear acceleration— The linear velocity of the vector P E with respect to frame {A} is given as AVE=AVB0RG +  A BRBVE+AaBxARBPE (5.19) The linear acceleration of the vector APE is determined by calculating the derivative of Equation 5.19 as AVB=AVBORG+BRBVE +2AnBxARBVz+AnBxARBPE+AQB x(AQBxARBPE) (5.20) hi case b P E is constant, Equation 5.20 simplifies to AVE=AVB0RG+AClBxARBPE+AQBx(AQBxARBPE) (5.21) Angular acceleration— Considering three frames {A}, {B} and {C}, if frame {B} rotates relative to {A} with angular velocity AQB, and {C} rotates relative to frame {B} with BQc, then AQc is determined as AQC=AQ.B + ARBQC (5.22) and by differentiating, we obtain A£lc=A£lB+ABRB£lc+AaBxARB£lc (5.23) When BQc is zero, Equation 5.23 simplifies to 162 Anc=Aa, (5.24) 5.2.2 Kinetics of the Upper Limbs MWP produces repetitive stress on the user's joints. Determining the loads that cause this stress can help researchers to better understand the biomechanics of MWP. It is possible to directly measure moments and forces in the joints by surgically implanting transducers! However, this method is used in special circumstances. One case is with the implantable prostheses. Indirect estimation of joints loads can be made from the measured external loads, kinematic data (trajectory points of the upper limb), and anthropometric data. Knowledge of the time profiles of the joint loads is necessary for an understanding of the cause and implications for any movement [12]. In this research, rigid linkage system model was used to calculate net joint action/reaction forces and net muscle moments using inverse solution with the Newton- Euler method. The lengths of the segments are assumed to remain constant during the motion. The free body diagrams for all segments are similar. 5.2.3 Mass Distribution Each segment is assumed as a rigid body, which can move in three dimensions. Inertia tensor is required to describe the moment of the segment. The inertia tensor with respect to {A} is expressed as the 3><3 matrix: 163 -L -I*y -/» (5.25) The elements / « , lyy and lzz are called the mass moments of inertia. The elements with mixed indices are called mass products of inertia. These six independent quantities depend on the position and orientation of the frame in which they are defined. If we consider the axes of calculating the moment of inertia to coincide with the principal axes, the products of inertia will be zero, and the corresponding mass moments will be the principal moments of inertia. To determine the change of inertia tensor under translation of the reference coordinate system, the parallel axes theorem is used, which relates the inertia tensor in a frame with origin at C O M to the inertia tensor with respect to another reference frame. Following equations present this theorem [96]: AI„=CIzz+m(Xc+y2c) (5.26a) 'I^l^+mx^ (5.26b) where xc, yc, and zc are the coordinates of the center of mass with respect to {A}. The remaining moments and products of inertia are computed from permutation of x, y, and z in Equations 5.26. In this study, the shape of the upper arm and forearm were assumed as a frustum of cone, and that of the hand as a rectangular prism. The local frame of each segment is 164 placed at its own center of mass. Figure 5.4 shows a frustum of conic segment and its local frame {C}. H and h are the height of the frustum and its center of mass in the x direction. The inertia tensors with respect to the local frame at the center of mass, which is the principal frame, is determined as 0 0 0 0 yy 0 0 (5.27) Figure 5.4 Frustum of conic rigid body with local frame on its center of mass. where R and ro are the radius of the proximal (larger) and distal (smaller) ends of the frustum, respectively. The position of C O M for the frustum is given by 165 h = H(R2 +2Rr0+3r02) 4(R2+Rr0+r02) (5.28) The inertia tensor for the frustum is determined using Equations 5.29 as CI =CI = / / 2 (2/? 2 +6/?r 0 +12r 0 2 )-3r 0 2 ^ 2 5H2(R2 + 2Rr0 +3r 0 2 ) 2 , „ n 2 , ^ R'+Rr0+r0 4(R 2+Rr0+r02)2 cj Jm(R5-r05) " 10(/? 3 -r 0 3 ) (5.29a) (5.29b) where m is the mass of the segment [98]. Figure 5.5 shows a rectangular prism segment, which represent the rigid body model for the hand. The local frame {C} is located at C O M . Hh, Wh and Lh are the parameters corresponding to the thickness, width and the length of the hand. Figure 5.5 Rectangular prism rigid body with local frame at its center of mass. 166 The components of the inertia tensor for the rectangular prism are determined using Equations 5.30 as :I« =^(K +Hl), % =^iWl +Ll), CIZZ =f2(Hl +Ll) (5.30) 5.2.4 M o d e l i n g In linkage system model, four basic groups of loads act: 1- Gravitational forces (weights), 2- External forces and moments (reactions on the hand of the user), 3- Muscle and ligament forces (net muscle moments and joint forces), 4- Inertial loads. To calculate the net muscle moments and joint forces, three free body diagrams in sagittal (Figure 5.6), frontal (Figure 5.7), and transverse (Figure 5.8) planes, and the following force and moment balance equations are used. 2X=>"a" YaFy=mCXyi HF:=mCl: (5-31a) Z M , = i ^ , 2 X = ^ (5.31b) ^ * dt y dt ^ 2 dt where ax,y<z are the linear acceleration, and cox,yfZ are the angular velocity components of the segment. All parameters are with respect to the global frame {A} [12,46]. 167 168 Figure 5.8 Free body diagram of a segment in transverse plane. The force balance in Equation 5.31a is expressed in the vector notation as ^com "0" Xcom = m y com => Fpy + Ffy -m 8 = m y com _ ̂  com _ F p 2 + F d 2 _ 0 _^ com _ Having the external force (Fd), mass of the segment (ni), gravitational acceleration ig), and linear acceleration of COM (CICOM), one can calculate the unknown force on the proximal end of the segment (Fp). 169 XCOM = m yCOM +s - F, ZCOM (5.33) Also, the moment balance in Equation 5.31b, is expressed in the vector notation as IX IX =Ai coy 0), + d{AI) dt 0)r OJ., CO, (5.34) Using Equations 5.12, and 5.29-30, one can determine / as AI=ARcIAR~l = ARcIART (5.35) where £R is the rotation matrix, which describes {C}in C O M of the segment with respect to the global frame A, GR~l is inverse of £R, ARTis transpose of AR, and CI is the inertia tensor with respect to {C}. Equation 5.34 then becomes ^M=AI-d>+<axAI-a> (5.36) where all of the parameters are with respect to {A}. A cross product between any two vectors (q and e) in 3D space can be written in terms of pure matrix multiplication as the product of a Skew-symmetric matrix and a vector as follows: 170 ' 0 V Qiei ~Q3e2 qxe-Qxe = 0 = Qiex r°2 0 . g 3 . qxe2 -Qiei_ (5.37) where is the Skew-symmetric matrix of q. In the matrix form, Equation 5.36 is expressed as IX" " Aj -A J _A J -xx xy xz "<»/ 0 -OJz eoy ' AI —A I —A I xx xy xz 'Vx IX = _A J Aj _A J yx yy yz + o)z 0 -cox _A j Aj _A J y* yy yz <°y —A I -A I AI zx zy zz A . -CDy 0JX 0 _A J _A J Aj zx zy zz (5.38) Using the free body diagrams (Figures 5.6, 5.7 and 5.8) the equation of the moment balance for a segment is determined: ^M = Td+Tp+Md +Mp=(rd-rC0M)xFd+(rp-rC0M)xFp + Md + Mp (5.39) where Vj and xp are the produced moments due to the external forces at the segment's ends points d and p, respectively. Using Equations 5.36 and 5.39 the unknown moment Mp is determined as Mp=AI-d)+aixAIco-Md-{rp-rCOM)xFp-{rd-rC0M)xFd (5.40) 171 The quantities rCoM , rp, rd, and rpd (rd-rp) are related together [12,46]. Figure 5.9 shows these position vectors. Figure 5.9 Position vectors for rpd, proximal end (p), distal end (d), and COM bf the segment. rcom can be expressed in the following forms: VCOM - r P + r p d ' K fcoM = r d - r P d • ( ! " * ) where k is defined as The distance from COM up to the proximal end Segments length Equation 5.40 is simplified using Equation 5.41 as (5.41a) (5.41b) 172 Mp=AIoj+OJKAI-co-Md+krpdxFp+{k-\)-rpdxFd (5.43) The matrix form of Equation 5.40 is Mpx Al XX M — - A I X py yx Mpz_ - A I zx - Pdz. -AI - A I xy xz AI - A I yy yz -AI AI zy zz + k •Pd 0 ' y pd Xpd 0 -COz coy ' A + az 0 -<»x _A <°z_ ~OJy (Ox 0 _A yPd 0 FPy + (k--1) z pd 0 FP* yPd Ixx - A I - *y •A i xz ty* A I - yy AIyz Izx- - A I zy AK ~zpd yPd ~Fdx~ 0 -XPJ F* Xpd 0 f d z . CO, co„ CO, and with some manipulation (5.44) M nr px M — py M AI - I xx xy _ A T AT _ A yx yy A h I yz zy CO, coy CO, + 0 -coz oo } coz 0 -a 0 -ooy m> I — I xy x - A I AI yx yy A T A yz I AI zy zz cor CO., CO, 0 ~zPd yPd > * ' 0 ~zPd yPd Fpx + Fax Mdy - zpd 0 -Xpd Fdy + k zpd 0 -Xpd Fpy + Fdy -Mdz_ _-yPd Xpd 0 fdz_ _-yPd Xpd 0 FPz (5.45) Using Equation 5.32 an alternative form for expressing Equation 5.45 is 173 MPx AI XX - A I xy MPy = - A I AI yy M P Z - A I zx - A I zy _ A _A A i yz CO, CO,, CO, CO, -OJy CD, 0J2 CO, 0 - 0 y 0)r AI - A I xx xy - A I AI yx yy - A I - A I zx zy yz co„ y 0 y p d ~Fdx~ 0 ~zPd y p d ^com Mdy - 0 ~Xpd Fdy + mk zpd 0 ~Xpd y com & _-yPd 0 fdz. _-yPd xPd 0 ^ com The combined form of the load balance equations is (5.46) L = IT aT + Q r • IT coT + O • Ld (5.47) where the parameters in the above equation are obtained from the following relations and using a recursive matrix back-propagation algorithm the loads at the joints of the other segments are obtained [12]. aT = " V m 0 0 0 0 0 Fpy 0 m 0 0 0 0 Foz 0 0 m 0 0 0 — Pz Mni px (5.48a), IT = 0 ~mkzPd m typd AI XX - A I xy _ A Lz Mpy mkzpd 0 -mkxpd - AIyx AI yy _ A lyz Mp2_ - mkyPd mkxpd 0 AIzx - A I zy Alzz J X "0 0 0 0 0 0 com y com 8 0 0 0 0 0 0 Z 0 0 0 0 0 0 = com (5.48c), Q r = 0 0 0 0 -C02 0)y 0Jy 0 0 0 0 ~<Ox <>>z . 0 0 0 ~(Oy 0 (5.48b) (5.48d) 174 0 0 0 (Ox CO, (5.48e), 0 = -1 0 0 0 0 0 0 - l 0 0 0 0 0 0 -1 0 0 0 0 Zpd -yPd -1 0 0 - z p d 0 XP0 0 -1 0 ypd — Xpd 0 0 0 -1 dx dy dz M M M dx dy dz (5.48g) 5.3 Results The optimum seat position for each user can be determined by considering the joint injury prevention priorities for subject. In this study, analyses have been performed for all upper limb joints. The approximate locations of XI to X3 and Y l to Y3 are shown in the X-ratio - Y-ratio plane of the next figures for ease of reference. Figure 5.10 shows that the minimum WUJU for the wrist joint is close to Y l and XI for subject 7. The highest value is close to the high seat position Y3 and XI . Another method to determine the optimum seat position is by using WUJU'. Figure 5.11 indicates that the minimum WUJU' appears around the same location as the minimum WUJU, but the maximum values of the injury indices are not co-incidental. 175 0.16 Y-ratio 0.2 -0.3 X-ratio 0.4 0.35 ^.3 0.25 0.2 0.1 Figure 5.10 Variation of WUJII versus X and Y-ratios for subject 7 at wrist joint. -0.16 -0.14 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 Y-ratio 0.2 -0.30 X-ratio Figure 5.11 Variation of WUJII' versus X and Y-ratios for subject 7 at wrist joint. 176 Figure 5.12 illustrates the variation of WUJU for elbow joint at different seat positions. The minimum WUJU appears close to X2 and either of the low seat height Y l or high seat Y3 for subject 7. The optimum W U J J T T is determined in Figure 5.13 in the same position forWUJn. A , -0-28 Y-ratio 0.2 -0.3 X-ratio Figure 5.12 Variation of WUJII versus X and Y-ratios for subject 7 at elbow joint. Figure 5.14 and 5.15 show the variation of WUJU and WUJU' against seat position for shoulder joint of subject 7, respectively. The minimum injury indices have been appeared close to the high seat height Y3 and backward seat position X3 with respect to the wheel axle. 177 Figure 5.13 Variation of WUJII' versus X and Y-ratios for subject 7 at elbow joint. Figure 5.14 Variation of WUJII versus X and Y-ratios for subject 7 at shoulder joint. 178 The above results showed that almost the same optimum positions were determined by using the injury indices at each joint of subject 7. The response equations have the general form of Equation 4.12. Tables 5.1 and 5.2 show the coefficients and constants of WUJII and WUJII' response equations, for the upper limb joints of the subject 7, respectively. Figures 5.16-5.21 show the variations of injury indices for upper limb joints of subject 8. Al l of the Figures indicate that the minimum values for injury indices have been appeared close to Y3 and X3. 179 The coefficients and constants of WUJU and WUJU' response equations for the upper limb joints of the subject 8 have been determined and presented in Tables 5.3 and 5.4, respectively. Table 5.1 The coefficients and constants for the response equations that determine WUJU for the upper limb joints at different seat positions for subject 7. ^^^Coefficients & """"^Constant Joint bx b2 b4 b5 h Wrist -20.227 2.468 -22.948 11.763 54.293 -3.908 Elbow 43.625 -72.585 12.435 44.869 25.760 -4.289 Shoulder 53.785 -50.357 10.482 39.081 53.671 -2.869 Table 5.2 The coefficients and constants for the response equations that determine WUJU' for the upper limb joints at different seat positions for subject 7. ^^^Coefficients & ^^^Constant Joint bx b2 h bs h Wrist 2.014 -34.362 -5.712 24.167 23.127 -3.823 Elbow 20.885 -34.562 6.009 21.337 -12.133 -2.029 Shoulder 25.570 -23.682 5.016 18.417 25.385 -1.340 Analyzing the results for these two subjects, at each joint one can see that the magnitude of the calculated values of the injury indices are different for subject 7, 180 whereas they are very close together for subject 8. Actually, subject 7 had the lowest %BF. Therefore, if two people show the same value for WUJII, the one who has less fat will show lower WUJU', which is reasonable. This may suggest WUJU' as a better index to estimate the injury. Y-ratio 0.2 -0.3 X-ratio Figure 5.16 Variation of WUJII versus X and Y-ratios for subject 8 at wrist joint. 181 Figure 5.17 Variation of WUJII' versus X and Y-ratios for subject 8 at wrist joint. Figure 5.18 Variation of WUJII versus X and Y-ratios for subject 8 at elbow joint. 182 -0.16 -0.14 2 1.8 1.6 1.4 1.2 1 0.8 0.6 Y-ratio 0.2 -0.3 -0.28 X-ratio Figure 5.19 Variation of WUJJJ' versus X and Y-ratios for subject 8 at elbow joint. 2.5 -0.16 -0.14 1.5 Y-ratio 0.2 -0.3 -0.28 X-ratio Figure 5.20 Variation of WUJU versus X and Y-ratios for subject 8 at shoulder joint. 183 Figure 5.21 Variation of WUJII' versus X and Y-ratios for subject 8 at shoulder joint. Table 5.3 The coefficients and constants for the response equations that determine WUJII for the upper limb joints at different seat positions for subject 8. Coefficients & ^^"^^Constant Joint ^ ^ ^ ^ h h &3 In h bb Wrist -6.518 -173.804 1.789 87.738 0.790 -9.468 Elbow 39.541 -173.145 47.775 67.026 -81.220 -0.357 Shoulder 67.664 -471.257 78.949 216.618 -107.372 -13.429 184 Table 5.4 The coefficients and constants for the response equations that determine WUJII' for the upper limb joints at different seat positions for subject 8. Coefficients & ^^^Constant Joint — ^ bi b2 bi b4 bs be Wrist -6.184 -166.175 1.689 83.918 0.883 -9.061 Elbow 37.757 -165.625 45.676 64.111 -77.724 -0.346 Shoulder 64.833 -450.541 75.501 207.123 -102.528 -12.841 5.4 Conclusions The joint loads during MWP are generated by muscle action and the interaction of M W U with the environment. These loads are repetitive and can cause RSI. It is necessary to determine the kinetic profile of the MWUs for calculating the injury indices to determine the optimum seat position to prevent injury. In this chapter, a model for the dynamic analysis of the upper limb was introduced. This model is generic and can be used for other parts of the body such as lower limbs. The joint loads of subjects 7 and 8 during the experiments were calculated by using this model, followed by calculation of the injury indices for the upper limb joints of the subjects. The results showed that both injury indices for each joint determine the same optimum position for the users, except the injury indices for the wrist joint of subject 7. Subject 7, who had the lowest %BF showed that his response surfaces for WUJII and WUJII' differ in magnitude and pattern, whereas the response surfaces were almost the same for subject 8, who had a higher %BF. Considering two persons with different 185 %BF, they may have the same value of WUJII but the one with less %BF will appear to have a lower WUJII'. Therefore, one may consider WUJJJ' as a more suitable index to estimate probable injury, as it can evaluate the injuries more realistically. The coefficients and constants of the BQF response equations of the injury indices were determined for subjects 7 and 8. The optimum seat position for subject 7 was different for various joints, but for subject 8 all of the experiments determined a unique optimum position. Comparing these results with the results in Chapter 4 reveals that the optimum seat position can vary depending on the general injury indices or the specific joint used to calculate the injury indices. In the next chapter, a new model is introduced to analyze the dynamics of the upper limb based on the concepts of robotics. This model requires less post-processing, as it uses the data of only two landmarks of the upper body for kinematic analysis. 186 CHAPTER 6 A New method for Dynamic Analysis of the Upper Limb 6.1 Introduction A number of models for the dynamic analysis of the upper limbs have been developed in previous studies but shortcomings and/or oversimplifications of important aspects of MWP are evident in some. Models presented by Cooper [12] and Vrongistinos [46] are among the best and most widely referenced examples. In Chapter 5, a 3D rigid-body model for the dynamic analysis of the upper limbs, similar to those of Cooper and Vrongistinos, but with some difference in the manner in which the loads are calculated was presented. This model needs at least three markers to determine the position and orientation of each segment. For a three-link model and assuming common markers at the two joints, at least seven markers are needed for the 187 d y n a m i c a n a l y s i s o f t he u p p e r l i m b . T o d e t e r m i n e the o r i e n t a t i o n o f t he s e g m e n t s i n a 3D a n a l y s i s , t he a b o v e r e q u i r e m e n t m u s t b e m e t . H e n c e , w e r e f e r to t h i s as " M e t h o d I". I n t h i s c h a p t e r , a n e w m e t h o d i s i n t r o d u c e d , w h i c h w e r e f e r to as " M e t h o d I I " . It u s e s a m o d e l tha t n e e d s d a t a f r o m t w o m a r k e r s o n l y f o r k i n e t i c a n a l y s i s o f t he u p p e r l i m b . U s i n g t h i s m e t h o d , t he o r i e n t a t i o n o f the s e g m e n t s c a n n o t b e d e t e r m i n e d , b u t t he k i n e t i c r e s u l t s c a n b e r e a d i l y c a l c u l a t e d . T h e p o s t - p r o c e s s i n g o f t he e x p e r i m e n t a l d a t a b e c o m e s m u c h fas te r a n d e a s i e r w h e n f e w e r m a r k e r s a re u s e d f o r t he tes ts . T h e m e r i t s o f u s i n g M e t h o d II a re p r e s e n t e d i n t h i s c h a p t e r , f o l l o w e d b y a c o m p a r i s o n o f t he r e s u l t s c a l c u l a t e d b y t h i s m e t h o d w i t h t h o s e c a l c u l a t e d u s i n g the m e t h o d i n t r o d u c e d i n c h a p t e r 5. T h e r e s u l t s c o n s i s t o f t he l o a d p r o f i l e s , o v e r e s t i m a t i o n ra tes o f the c a l c u l a t e d l o a d s , a n d the r e l a t i v e e r ro r s a n d S t d . D e v s . o f t he c a l c u l a t e d m a x i m u m l o a d s f o r e a c h j o i n t o f the s u b j e c t s . 6.2 Method II I n C h a p t e r s 4 a n d 5 t he s p e c i f i c a t i o n s o f the m o d e l w e r e e x p l a i n e d . I n M e t h o d II t he s a m e m o d e l w a s u s e d w i t h t w o m a r k e r s . T h e m o v e m e n t o f the s h o u l d e r as o r i g i n o f t he l i n k a g e s y s t e m , a n d the m o t i o n o f the h a n d w e r e t r a c k e d u s i n g t h e s e m a r k e r s , a n d the V I C O N M o t i o n A n a l y s i s S y s t e m . T h e r e c o r d e d d a t a w e r e u s e d to d e t e r m i n e the p o s i t i o n s a n d o r i e n t a t i o n s o f the u p p e r l i m b . T h e i n v e r s e k i n e m a t i c s m e t h o d , a n d r o b o t i c s c o n c e p t s a n d r e l a t i o n s w e r e e m p l o y e d to c a l c u l a t e the l o c a l a n g l e s , a n g u l a r v e l o c i t i e s a n d a c c e l e r a t i o n s o f the u s e r s ' u p p e r l i m b j o i n t s . 188 6.2.1 Link Parameters A robot can be kinematically described in terms of four parameters for each link. Two of them describe the link itself and the other two describe the connection of one end of the link to its neighboring link. These parameters are referred to as the Denavit- Hartenberg notation [96]. Figure 6.1 Link frames and link parameters. Referring to Figure 6.1 these parameters are described as follows: a,: Distance from Z, to Z,+i measured along Xi Oi: Angle between Z, and Z,+i measured about Xj di: Distance from Xi.\ to Xj measured along Z, Tji: Angle between Xj.\ andX, measured about Z, The coordinate systems are fixed at the joints. Transforming matrix for each link is defined as [96,99,100]: 189 i—\rp COS TJi -s in 77,. 0 a. sin rji • cos or,_! cos rji • cos orM - sin arM - sin • d(. sin J J . • sin or,_, cos rji • sin 0 0 cosor,.., cosor,_,-J, This is referred to as the Denavit-Hartenberg matrix. 6.2.2 Link Parameters of the Model Figure 6.2 shows the model and its local (1 to 8) and global (0 and 9) coordinate systems. Z 4 Y 4 X4 A9 Figure 6.2 Half-body Linkage model for the upper limb with all coordinate reference systems. 190 L i n k p a r a m e t e r s o f t he m o d e l a re g i v e n i n T a b l e 6 . 1 . T h e l e n g t h s o f t he u p p e r a r m , f o r e a r m , a n d h a n d a re s h o w n b y La, Lf, a n d Lh, r e s p e c t i v e l y . T a b l e 6.1 L i n k p a r a m e t e r s o f t he m o d e l . i di 1 0 ° 0 0 2 9 0 ° 0 0 3 - 9 0 ° 0 0 rjs 4 0 ° La 0 5 - 9 0 ° 0 Lf 6 9 0 ° 0 0 m 7 9 0 ° 0 0 T h e r e i s n o j o i n t at the o r i g i n o f f r a m e 8, b u t t h i s f r a m e i s n e e d e d to t r a n s f o r m the r e a c t i o n l o a d s o f the h a n d r i m from the c o n t a c t p o i n t to frame 7. T h e t r a n s f o r m a t i o n m a t r i c e s f o r e a c h r e f e r e n c e frame are d e t e r m i n e d b y u s i n g E q u a t i o n 6.1 a n d T a b l e 6.1 as f o l l o w s : T = \T = c o s 7 , s i n 77, 0 0 COS773 0 - s i n TJ3 0 - s i n ;7, 0 0 " c o s 77, 0 0 0 1 0 0 0 1 -sin773 0 0 0 1 0 -cos773 0 0 0 0 1 ( 6 . 2 a ) , ( 6 . 2 c ) , \T = COS772 - s i n 772 0 0 0 0 - 1 0 s i n TJ2 c o s / 7 2 0 0 0 0 0 1 c o s / 7 4 - s i n 7 7 4 0 La s in77 4 C0S77 4 0 0 0 0 1 0 0 0 0 1 ( 6 . 2 b ) ( 6 . 2 d ) 191 \T = COS77 5 0 - sin TJ5 0 -sin TJ5 0 0 1 L COS / 7 5 0 C 0 0 0 1 (6.2e), \T = COST], 0 sin/76 0 -singes 0 COSTJ6 0 0 0 -1 0 0 0 0 1 (6.2f) 6nn 7 J COS TJ7 0 sin TJ1 0 - sin TJ7 0 COS J]1 0 0 0 -1 0 0 0 0 1 (6-2g), \T = 0 -1 0 Lh 0 0 1 0 -1 0 0 0 0 0 0 1 (6.2h) 6.2.3 Calculating the Joints Angles The joints angles were calculated by using the inverse kinematics method, and the positions of two markers on the shoulder and wrist. Considering the limitation of this method because of using minimal dynamic data and the general motion of the propulsion two assumptions were made. An abduction angle of 20° was considered at shoulder joint for rj\. Also, the orientation of the hand was considered to remain vertical during the propulsion and while in grabbing contact with the handrim. However, these assumptions can be modified. Thus, the position and orientation of frame 7 are known as components of the following matrix. 12 ri3 p • wx 0 -1 0 p wx oT = r22 r23 P wy 1 0 0 p wy 1 R31 r33 P wz 0 0 1 Pwz 0 0 0 1 0 0 0 1 (6.3) where Pwx,wy,wz and n i_ 3 3 are the components of the wrist position and frame 7 orientation, respectively. 192 Considering Figure 6.2 and the fact that the orientation of frame 7 was assumed to remain fixed during the propulsion, one can determine 7R as 0 n _ fo Y O y O y 1_ 0 - 1 0 1 0 0 0 0 1 Sequential transformation matrices are related as follows: Orji (jrp - Irji 7.rp ^'J1 ^JT (6.4) (6.5) Pre-multiplying both sides of Equation 6.5 by 20T, one obtains: 2ijl Orp 2rp 3rp 4IJI 5rp (sr£ C\C2 S\C2 s2 0 — C , 5 2 — sxs2 c2 0 0 0 0 0 0 1 0 - 1 0 P., 1 0 0 P wy 0 0 1 Py 0 0 0 1 (6.6a) (6.6b) where c, is cos(77,) and Si is sin(/7,), and i'=l to 7 is the reference frame number. Since robot mechanisms are uniquely defined by the transformation matrices, there is a one-to-one equivalency between the matrix elements on the left and the right side of the equations derived here. We use this property to determine certain unknowns through the following calculations. Multiplying the matrices in Equation 6.6b one has: 193 f S\C2 C | C 2 s2 — sxs2 cxs2 c2 ~cl 0 0 0 0 L\2 Ln Ll4 L2X L12 L23 L24 L3\ L32 L* L34 L„ L<2 L« L„ (6.7a) Lxx — c34(c5c6c7 + s5s7) —s34s6c7 ; LX2 =c34(—c5c6s7 + s5c7) +s34s6s7 L\3 = C 3 4 C 5 C 6 + S34C6 > Lx4 = S34Lj- + C3LQ L2X =—s5c6c7 + c5s7 ; L22 = s5c6s7 + c5c7 ; L23=—s5s6 , L24=0 L3X =—s34(c5c6c7+s5s7) — c34s6c7 ; L32 = — s34(—c5c6s7 +s5c7) + c34s6s7 L33 = —s34c5c6 +c34c6 ; L34 = — c34L^ —s3La L4X=0 ; L42=0 ; L43=0 ; L„=l (6.7b) where S34=sm(7j3+7]4), 034=008(773+774), and L\ 1^4 are lumped parameters. Now, by equating the element (2,4) of both sides of the Equation 6.7a we obtain ~cxs2Pwx s ^ P ^ + c ^ = 0 (6.8a) c 2 P R A - 5 2 ( c 1 P R A + 5 1 P M y ) = 0 (6.8b) Converting to polar coordinate system the following relations can be written p^=ps<Po (6.9a) Cxpwx+sxPwy=p-c% (6.9b) P ^ H c ^ + s ^ ) 2 ) - 1 ' 2 (6.9c) % = Atan2(Pm,cxPm +sxP^) (6.9d) 194 where (p0 and p are the polar coordinate angle and radius, respectively. Substituting these in Equation 6.8b, TJ2 is determined as c2-s<p0-s2-c(p0 =0 (6.10a) sin(^70 -TJ2) = 0 => cos(^0 -rj2) = ±l (6.1 Ob) %-rj2= Atan2(0,±\) => t]2=(p0- Atan2{0,±\) (6.10c) TJ2 = Atan2{Pwz,cxPwx + s,Pw)-Atan2(0,±l) (6.10d) Therefore, there are two answers for TJ2. Equating elements (1,4) and (3,4) from both sides of Equation 6.7a and using Equation 6.7b, one obtains Equations 6.1 la and 6.1 lb, respectively, and using Equations 6.11 774 is calculated. ^c2Pm + 5 , ^ +s2Pm = -si4Lf +c,La (6.11a) sxPwx ~ c\p*y = ~CML2 ~ s,La (6.1 lb) ^ 1 = ( c 1 C 2 P R A + 5 1 C 2 J P H Y + 5 2 J P T O ) 2 (6.11C) K2=(slPwx-clPwy)2 (6.11d) KX+K2=L/ +La2-2LaLfs4 (6.11e) h / + h a 2 - ( K l + K 2 ) 2hfha c4=±J\^J4~ (6.11g) 7]4= Atan2(s4,c4) (6.1 lh) where K\ and K2 are lumped parameters. To find the other angles, A0T is pre-multiplied to both sides of the Equation 6.5 as 195 4rp Orp 4rp 5 rrt ()rp <r i1 ~ 51 61 i1 (6.12a) C,C 2 C 3 4 — 5[5 3 4 S\C2C34 "'"^ 1̂ 34 •^34 " 4 ^ 4 — C , C 2 S 3 4 — S \ C 3 4 — 5 , C 2 5 3 4 + C , C 3 4 — ,S2'S34 4 * 4 — cis2 — 5,5 2 c 2 0 0 0 0 1 Orp 4rp I1 7 (6.12b) With some manipulation another form of Equation 6.12b is given by K12 *>3 K K2l K22 A:23 K Ki\ K32 ^33 K K4l K42 ^43 K c5c6c7 + s5s7 — s5c6c7 + c5s7 C 5 C 6 S 1 S 5 C 7 '5^7 C 5 S 6 0 ~C6 h ~ S 5 S 6 0 0 1 (6.13a) — S \ C 2 C i A + Cj5 3 4 , KX2 = —c,c2c34 + s,s34 K„ = 52C34 > K\4 = (c,c 2c 3 4 — s^s34)Pm + (s,c 2c 3 4 + cls34)Pwy +s2c34Pwz —Lac4 K2] 34 + C1C34 , K22 — C,C 2 5 3 4 + 5jC 3 4 K23 = —^2*34 > ^24 = (-c,c 25 3 4 -sxc34)Pm + (stc2s34 + ^ , 0 3 4 ) / ^ -s2s34Pm +LaS4 = — sxs2 ; ^ 3 2 = -cxs2 ; K33 = c2 ; K34 = —c]s2Pwx —sls2Pwy +c2Pm = 0; ; ^42=0 ; K43 — 0 ; = 1 (6.13b) where K\ 1-44 are lumped parameters. Equating elements (1,4) and (2,4) from both sides of the Equation 6.13a and using Equations 6.13b, one obtains Equations 6.14a and 6.14b, respectively. 196 CiWuP** -*i*34P»* + + c^P^ + s2c,4Pm - Lac4 = 0 (6.14a) - C l < V 3 4 ^ « -S&AKX - * l C 2 * 3 4 ^ y + C . C 3 4 ^ - * 2 * 3 4 ^ v z + L a S 4 = L f (6-14b) First, solve for 534 and C34: (Las4 -Lf)(cxc2Pm +sxc2P^ +s2Pm)-Lac4(slPwx - c .P^) ( * i ^ -cf^YHcfrPn +s2Pm)2 C34 — ' (Las4 -Lf)(SlPm -c.P^ + L^c^P^ + 5 , c 2 P +s2Pm) (s,Pm - c . P ^ ) 2 + (clc2Pwt +sic2Pwv +s2Pm) (6.15a) (6.15b) Then, 773 is calculated as 7 / 3 4 = Atan2 (sM,cu) r?3=r/i4-T]4 (6.15c) (6.15d) Now, elements (1,3) and (3,3) of both sides of Equation 6.13a and Equations 6.13b are equated to determine 775 as r\3C\C2C34 r i 3 * l *34 r 2 3 * l C 2 C 3 4 ~*~ '*23C1*34 ~*~'33*2C34 ~ S5C6 — r i 3 C j 5 2 — 7*23*1*2 ~^~r33C2 = ~ S 5 S 6 ^3 ~ 13*1*2 '23*1*2 — r33C2 K4 = C34{rl3CxC2 +'*23*1C2 3̂3*2 ) *34 ('*33C1 — l 3 * l ) s6 * 0 => 7]5 = Atan2(K3,K4) (6.16a) (6.16b) (6.16c) (6.16d) (6.16e) where K3 and K4 are lumped parameters. Then, both sides of the Equation 6.5 are pre-multiplied by 50T as 197 Equating elements (1,3) and (3,3) from both sides of the Equation 6.17, s6 and C(, are obtained. Therefore, % is determined as Tj6=Atan2(s6,c6) (6.18) Also, equating elements (2,1) and (2,2) from both sides of the Equation 6.17, one has 5 7 and ci, and 777 is obtained as TJ7 = Atan2(s7,c1) (6.19) The local joint angles of the model for subjects 7 and 8 during the tests were determined using the above relations, the positions of markers on the wrist and shoulder joints, and the subjects' anthropometric data. The linear and angular velocities and accelerations of the links of the model were calculated using outward iteration, in which / varies from 0 to 6. Velocity propagation from link to link is obtained by [96] 'a^=f^MMMZM (6.20a) V,+ 1='K i+'<»,x'P / +i ( 6 2 0 b ) +1^+1='+;/?'^+/7,+1'+1Z,.+1 (6.20c) *VM ='+;/?C Vt + '' a>,x'PM) (6.20d) C6C1 5 6 C 7 c6s7 - e , 0 -s6s7 -c6 0 0 0 0 0 -c6 0 1 (6.17) 198 where T,+i and 'coi+\ are linear and angular velocities of link i+l with respect to frame /, lPi+\ is the position of the origin of frame /+1 with respect to frame i, and771+1 is the joint angular velocity of frame /+1. Acceleration propagation is given by "ton^R'^R'ta, xtiMMZM +ifMMZM (6.21a) MVM = »}R [iojixipM+'coix(iojixipM)+iVi] (6.21b) 'VCi ^oo^pCj +'<y» x(oi^pCi)+% (6.2 lc) Where 'V. and 'Vc are linear accelerations of origin of frame i and C O M of link i with respect to frame /, '<i>, is the angular acceleration of link i with respect to frame /, and is the joint angular acceleration of frame H-l. The subscript C j stands for the frame {Cj}, which has the same orientation as link frame i, and its origin is located at C O M of the link*. 6.2.4 Kinetics of Wheelchair Propulsion The net forces and moments in the upper limb joints of the users are calculated by using the inverse dynamics method. Figure 6.3 shows a generic link for modeling the limbs. The variables fi, F„ and Nt represents the force exerted on link / by link the moment exerted on link i by link the inertial force, and the moment acting at C O M , respectively. 199 Figure 6.3 Forces, moments and inertial loads on a generic link /. To calculate the net forces and moments in the upper limb joints, the applied forces and moments on the user's hand during MWP are required. These loads were measured by using the instrumented wheel in the tests. The forces and moments acting at C O M of each link were calculated using Newton's and Euler's equations. 'F.=m.% (6.22a) W,=c'7,. ld)l+,a)lxClIly!o)l (6.22b) where ' F „ 'TV,, 'cot, and are force, moment, angular velocity, and angular acceleration vectors of link / with respect to frame /. The variable m is mass of the link, ' v c is linear acceleration vector of C O M , and CiI. is the moment of inertia of the link / with respect to { Q } . The net forces and moment at joints are computed using inward iteration, in which i varies from 7 to 1: 'fr^fn+'F, (6.23a) 200 \=%+jRMmM+%xiFi+iPMxjR"fM (6.23b) where W , and '«, are moment vectors, 'F, and % are force vectors and 'Pa is the position vector of the COM with respect to the frame i. 6.3 Comparison of Methods I and II The net loads at the upper limb joints of subjects 7 and 8 were calculated using Methods I and II. The results were compared to determine the utility and reliability of Method II. The profiles of the applied force and moment on the wrist, elbow and shoulder joints are compared between the two methods in Figures 6.4 and 6.5, Figures 6.6 and 6.7, and Figures 6.8 and 6.9, respectively. 201 Figure 6.5 Total applied moment on the wrist joint. Figure 6.6 Total applied force on the elbow joint. 202 - - - MethodI Method II 0 1 2 3 4 5 6 7 8 9 10 Time (s) Figure 6.7 Total applied moment on the elbow joint. Figure 6.8 Total applied force on the shoulder joint. 203 Figure 6.9 Total applied moment on the shoulder joint. Comparing the profiles in the preceding figures indicates that the values calculated by Method II are over-estimated. The average degree of over-estimation of the loads over 5 consecutive cycles is determined according to Equations 6.24. 5 F '=' rny Joint force over estimation = — (6.24a) n 5 M y mnj Joint moment over estimation = — (6.24b) n 204 where F/,y and MUJ are maximum joint force and moment of propulsion cycle / for subject j calculated using Method I, FUij and M//,y are maximum joint force and moment of propulsion cycle i for subject j calculated using Method II, and n is the number of the subjects. The average rate of over-estimation for joint loads are shown in Table 6.2. Table 6.2 Average rates of over-estimation for upper limb joint loads. Upper limbs' Average rate of joint load over-estimation Force at wrist 1.056 Force at elbow 1.209 Force at shoulder 1.321 Moment at wrist 1.499 Moment at elbow 1.936 Moment at shoulder 1.416 The calculated maximum loads using Method II were then corrected by multiplying them by the inverse of the over-estimation rate for the joint load. The relative errors for the corrected joint load were determined with respect to the loads obtained from Method I. Table 6.3 shows the mean and Std. Dev. of the relative error of the maximum calculated load at upper limb joint using Method II. The forces showed lower mean error and Std. Dev. than the moments. 205 Table 6.3 Mean and Std. Dev. of the relative error (%) for upper limb joint loads. Upper limbs' joint load Mean relative error (%) Std. Dev. (%) Force at wrist 2.886 1.456 Force at elbow 9.758 3.302 Force at shoulder 7.518 2.788 Moment at wrist 6.848 2.329 Moment at elbow 13.759 6.500 Moment at shoulder 11.870 5.603 6.4 Conclusions In this chapter, a new method was developed to analyze the dynamics of the upper limb joints and to calculate the forces and moments during MWP. A robotic model was constructed using the inverse dynamic method. The local joint angles of the model were determined by using the inverse kinematic method. Three-dimensional net joint loads were calculated from kinetic, kinematic, and anthropometric data by using an inverse solution and the Newton-Euler method. The advantage of this method, which we refer to as Method II, is that one can perform inverse dynamic analysis using the kinematic data of only two markers on the arm. The results calculated using Method II were compared with the results of Method I. The results showed an over-estimation for the calculated loads using the new method. The rates of the over-estimation were determined for the loads at the upper limb joints. As one investigates the over-estimated values from the wrist joint towards the shoulder 206 joint they increase because of accumulation of the kinematics deviations. However, the mean relative error was calculated as between 2.9 and 9.8 % for the maximum joint forces and between 6.9 and 11.9 % for the maximum joint moments, which appears to be acceptable for many studies. Considering the ease of application of this method, it can be used in studies that are more related to the kinetics of motion of the similar models. One may decrease the relative errors by adjusting and modifying the assumptions for this model with more realistic ones. In any case, the overestimation can be considered as a conservative measure, which provides a further level of protection in any calculation of wheelchair- related parameters for manual wheelchair users. 207 CHAPTER 7 Conclusions 7.1 Introduction This chapter summarizes the work performed in this dissertation and overall conclusions emerging from the research conducted are presented. The particular contributions relating to the fabricated instrumented wheel, proposed injury and efficiency indices, optimum seat position, and a new model for the analysis of the dynamics of the upper limb, are outlined. To motivate other interested researchers, possible future research directions and their scopes are proposed. 7.2 Conclusions We hypothesized that an instrumented wheel fabricated by using a PY6 load sensor would prove to be a reliable and valid instrument for measuring 3D loads at the hub of a wheelchair during MWP, and that changing the seat position of the wheelchair 208 would change G M E and upper limb joint loads of MWUs. Therefore, an instrumented wheel system was developed, fabricated and validated, and a method for determining the optimum wheelchair seat position for MWUs was determined. To open the discussion about this research, the importance of the problems such as injury and pain associated with MWP for the users was emphasized, and the anatomy of the corresponding joints of the upper limbs was reviewed. The dynamic concepts of the MWP and the conflict concerning the direction of the applied load were explained, and the effects of the seat position on MWP factors were highlighted. The feasibility of using the heart rate instead of oxygen consumption to estimate M E E was investigated. The significance of using an instrumented wheel system developed in-house was emphasized. A literature review of previous work on the above topics was also presented. 7.2.2 Research Questions and Answers The work carried out in this dissertation can be summarized by answering the following research questions. • Is the P Y 6 load transducer a suitable and sufficiently accurate measuring device for determining 3D forces and moments at the handrim of a wheelchair during propulsion? The P Y 6 load transducer was used in the fabricated instrumented wheel system. General uncertainty analysis as an analytical method was performed to verify the instrumented wheel. The results were compared with the reported results for the Smartw h e e l, an instrumented wheel that is frequently referred in the literature. The results indicated that for our fabricated instrumented wheel, the uncertainty values for the 209 important load components, namely the planar forces and the axial moment, are low. The absolute error for hand-contact position was determined as ±3° or ±1.5 cm along the rim, which is promising for a method that does not use cameras to calculate this angle. The specifications of the instrumented wheel were determined using an experimental technique performed under different static and dynamic conditions. Both qualitative and quantitative analyses were performed. The tests showed high linearity with r above 0.9, Std. Dev. mostly close to zero, and overall mean coefficient of variation less than 4% for measured loads. These results indicated high repeatability, and a mean error of mostly less than 5% for all loads. The resultant specifications showed high linearity, high repeatability and a low percentage of errors. The overall results ensured the reliability of the system. • How can the optimum seat position with respect to the wheel axle be determined for each wheelchair user? To determine the optimum seat position a new method was introduced, and the test protocol and experimental setup were explained. In this method, the optimum seat position was determined by using the values of one of the three new indices proposed for efficiency and injury assessment. EBI was proposed as a new index for efficiency assessment. This index was considered as a good alternative to estimate the G M E of MWP because it uses the heart rate of the user to estimate the variation of M E E . As injury prevention is very important for the MWUs, two indices were proposed to measure possible injuries. The important factors that can affect the MWP are included in these indices. The indices can be used for injury assessment for a specific upper limb joint. One can compare the effects of BMI 210 and %BF in probable injuries using these indices. The values of the indices were calculated for each of the test subjects at different seat positions. By using these values, the optimum position for each individual was determined. • Can one propose some generic rules to estimate the optimum seat position for various users? To answer this question, a set of constant speed experiments was designed and performed at different seat positions for all subjects. The results of the fixed seat height experiments showed that EBI may increase by moving the seat forward (p<0.05). The average value of the injury indices may decrease by moving the seat backward (p<0.05). The statistical analysis estimated the Type I or Alfa error because of the small sample size of the subjects. Previous studies [12,35] confirm the finding for the injury indices. We were not able to find a similar case to compare the results for efficiency evaluation. One should consider the point that MWP is a combination of a human body and a device. There is no report that indicates the most efficient seat position should be necessarily the safest with less possibility of the injury. Therefore, it is not surprising that the optimum positions, which determined by using the efficiency and injury indices were different. These results indicated that the average values of the injury indices and EBI can vary between 5.6-29.9% and between 5-27.5%, respectively. The higher variations mostly belong to the subjects whose index values changed significantly with respect to different seat positions, which indicates that the indices are indeed sensitive to seat position. However, to determine the optimum seat position for each individual, the 3D response surfaces were determined for two subjects by using the BQF method. The 211 results indicated that the positions determined by using the efficiency and injury indices can be different. The subjects with highest and lowest BMI and %BF at the time of experiments showed the maximum and minimum values, respectively, for injury indices for most of the propulsion phase. Therefore, one may conclude that BMI and %BF have significant effects on the probable injuries due to MWP that confirm the findings of the previous studies [23,70,71]. Also, the subjects with less wheelchair experience showed lower EBI. • Is there a relationship between the velocity and user injury? To respond to this question, another set of experiments was designed and performed at a fixed seat position and three propulsion velocities. The results obtained by the average of primary relations for the injury indices and performing the repeated- measures A N O V A indicated that higher propulsion velocity will increase the risk of injury for all subjects significantly (p<0.001). As this proved the direct effect of velocity on the injury indices, the equations of the injury indices were further modified to include Vj as one of their parameters. This refinement allows each of the injury indices to be a promising stand-alone measure of wheelchair user joint injury. • Is there a relationship between velocity and the propulsion efficiency of the manual wheelchair user? The results from repeated-measures A N O V A on a group of experiments at a fixed seat position and three different propulsion velocities indicated that there was no significant relationship between EBI and velocity. These results emphasize that each user 212 has his own efficient propulsion velocity, which is related to the physiological, anatomical and technical characteristics and limitations of his body. Different subjects can have different efficient propulsion velocity that should be determined individually. The results of this study compliment the report of Mukherjee et al. [38]. • How can one estimate the probable injuries to upper limb joints? To answer this question, a generic model for dynamic analysis of the limbs was introduced to determine the joint loads, which we referred to as Method I. The injury indices for the upper limb joints of two subjects were calculated using the modified equations for the joints. The results showed that both injury indices determine almost the same optimum position for each joint of the user. The subject with the lowest %BF showed that his response surfaces for WUJII and WUJU' are different in magnitude and pattern for each joint, whereas the response surfaces were almost the same for the subject who had a higher %BF. It could be concluded that two persons with different %BF may have the same values of WUJII but the one with less %BF appears to have lower WUJU'. This implies that WUJU' may be a more suitable index to estimate probable injury than WUJU, as it can evaluate the injury more realistically. The results indicated that the optimum seat position can vary depending on the general injury indices or specific joint used to calculate the injury indices. • To what extent will a 3D simulation of the upper limb joints be reliable, if only two markers are used for the kinematic tracking and analysis? 213 Using concept drawn from robotics and inverse dynamics, a new method was developed to calculate the joint loads during MWP, which we call Method II. The inverse solution and Newton-Euler method were used to calculate the local joint angles, and the 3D net joint loads of the model. This method performs inverse dynamics by having the kinematic data of only two markers during the experiments as part of the required data. Method II over estimates the results, therefore the rates of over-estimations were determined to correct the calculated loads. The mean relative errors for the maximum joint forces and moments were determined to be between 2.9 and 9.8 % and between 6.9 and 11.9 %, respectively. One can shorten the test procedure and the post-processing time by using Method II, which can be used in similar kinetic studies. Although overestimation of the joint loads increases the protection level, the relative errors may decrease by adjusting the assumptions in this method. 7.3 Limitations of the Study With considerations given to natural limits on time and resources, and practical aspects of achieving results in reasonable time, this study had some limitations as follows: • Small sample size of the subjects was considered because of the considerable exclusion criteria of this study. Eight subjects were recruited over about a year. More subjects can improve the level of statistical significance. • In this study, male subjects with Spinal Cord Injury (SCI) and lesion level below T5 were used; therefore the results cannot be generalized for all MWUs. 214 • The subjects used the test wheelchair not their own because of the fixed instrumentation. The effects of the rolling friction on front wheels due to the changing the center of gravity does not exist in our tests. This can alter the natural performance of the subjects. • One instrumented wheel was fabricated in this study; therefore we focused on analyzing the dominant hand. Using two instrumented wheel may provided more reliable results analyzing both arms of the user. • Accurate measurement of the heart rate was challenging. During some of the tests there was no record for part of the test period that made us to perform the tests again. • The propulsion techniques were not necessarily the same for all of the subjects. • Seat position had limited range. Wider range may provide more significant relations between the indices and the seat position. • Except the wheelchair user himself there was not any other control system to keep the speed at the determined value. • Percentage of body fat was not determined by using the best methods like D E X A . 7.4 Contributions The contributions of this study are as follows: • Development and fabrication of a reliable instrumented wheel for MWP analysis, presenting significant specifications. This system is one of the most essential equipment for kinetic analysis of the MWP. 215 Introducing theoretical and experimental methods for determining the uncertainties and specifications of an instrumented wheel. Validation and specification of the system are vital to ensure reliable data can be acquired during the tests. Development of a kinetic method to reliably determine the hand-contact angular position without the use of expensive cameras. The hand-contact angle can be used to calculate some of the important factors for the analysis of the dynamics of MWP. Proposing a new index for efficiency assessment during MWP that is sensitive to wheelchair seat position and velocity variation. An alternative method can help the probable studies that have limitation for measuring oxygen consumption. Proposing two new indices for injury assessment during MWP that are sensitive to wheelchair seat position and velocity changes. To our knowledge, this is the first time that all known parameters that affect the injury of the subject during the propulsion are considered for the injury assessment. These indices provided a new vision for MWP injury assessment and/or prevention. Introducing a novel method of determining the optimum seat position for MWUs, to reduce injury and/or increase GME. This method can be used for both rehabilitation and sport purposes. Establishing a novel method to prescribe the manual wheelchair seat position for a user that may decrease the probable injury in a specific upper limb joint during the propulsion. To our knowledge, this is the first time that such a specific procedure is used to prescribe the optimum seat position for each individual. 216 • Initiating a method that needs the kinematic data of only two markers on the arm of the user as part of the data required for analyzing the kinetics of the upper limb during MWP by using the inverse solution. 7.5 Future Research Directions In this study, a novel methodology was developed for prescribing the optimum seat position for the M W U on the basis of the values of the proposed indices. Although, the indices proved to be practical, the injury indices could be modified to include the effect of muscle activities and the range of motion of the joint angles as factors to cover fatigue and R O M effects. Also, one may wish to consider a weight coefficient for the factors in the equation of the injury indices to scale their effects. The analysis of the propulsion frequency versus the applied loads on the handrim during MWP will be very helpful for improving the proposed indices and injury assessment. The method proposed in this study can be improved if the anthropometric information and the kinetic and kinematic data from both upper limbs of the user during propulsion are obtained and used in the analysis. Providing two instrumented wheels can eliminate probable asymmetries because of differences in the wheelchair's wheels and improve the propulsion of the users. Although there are a number of obstacles to overcome, shortening the test procedure duration and increasing the number of the seat positions for the tests can lead to a more reliable response surfaces. To improve the results of the generic rules about the optimum seat position, increasing the number of subjects can provide data that is statistically more significant. As an extension of this study, one may consider the muscle forces in the dynamic 217 analysis to calculate joints contact loads instead of the net joint forces and moments to yield a better estimation of probable injuries. Also, the maximum and minimum of the internal/external rotation angles of the joints during MWP can be determined to analyze their relationship to the seat position. Potential opportunities for the extension of the application of the proposed indices to other areas do exist. In addition to rehabilitation wheelchairs, one may continue exploring the possible application of the indices for sports wheelchairs to improve the efficiency and productivity of disabled athletes. This method can be used to improve the design of the wheelchairs, as well. Another possible extension of this research is the application of the proposed methodologies, Method I, and Method II to the kinetic and kinematic analysis of the upper or lower limbs of able-bodied subjects during different activities such as particular motions during sport or work, and also to clinical aspects such as gait analysis. In this work, we collaborated with different departments at UBC and benefited from accessing their research laboratory equipment for data collection. Similar collaborations with other research teams can be considered in the future, which can lead to multi-disciplinary research projects in different aspects of manual wheelchair use such as rehabilitation or sport. A team composed of an orthopedist or an occupational therapist and a biomechanical engineer could be a good combination for the studies that deals with both clinical and engineering issues. 2 1 8 References 1. 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