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A functional task analysis and motion simulation for the development of a powered upper-limb orthosis Anglin, Carolyn 1993

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A FUNCTIONAL TASK ANALYSIS AND MOTION SIMULATIONFOR THE DEVELOPMENT OFA POWERED UPPER-LIMB ORTHOSISbyCAROLYN ANGLINB.A.Sc., University of Waterloo, 1989A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment of Mechanical EngineeringWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIASeptember 1993© Carolyn Anglin, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature) Department of ME CA-1-4,0 t CA-L Ee1Q,.JaThe University of British ColumbiaVancouver, CanadaDate oc--11:1.%€R-, 14, i°1413DE-6 (2/88)ABSTRACT The objective of this thesis is to determine an optimal configuration of a powered upper-limborthosis. The criterion is to minimize the complexity, defined as the number of degrees offreedom of the orthosis, while maintaining the ability to perform specific tasks. This goalwas realized in three stages of research. In the first stage, potential users were interviewed todetermine their task priorities. In the second stage, the natural arm motions of able-bodiedindividuals performing the tasks identified as high priority were profiled with a video trackingsystem. Finally, a kinematic simulation algorithm was developed to evaluate whether a givenorthosis configuration is able to perform the identified high-priority tasks.It was found that the task functionality was overly compromised for any configuration withless than five degrees of freedom. Two different configurations with five degrees of freedomare recommended. The recommendations are: (1) to power all but the motions of elevationand wrist yaw, or (2) to power all but wrist flexion and wrist yaw.TABLE OF CONTENTS Abstract ^^Table of Contents ^List of Tables List of Figures ^  viAcknowledgements CHAPTER 1: INTRODUCTION ^  1CHAPTER 2: LITERATURE REVIEW  42.1 Powered Upper-Limb Orthoses ^  42.1.1^Summary ^  112.2 Task Priority Surveys  122.2.1^Summary  162.3 Motion Analyses ^  172.3.1^Summary  212.4 Kinematic Evaluations and Results ^  212.4.1^Summary ^  222.5 Summary  23CHAPTER 3:POTENTIAL USERS OF A POWERED UPPER-LIMB ORTHOSISAND THEIR TASK PRIORITIES ^ 243.1^Introduction ^  243.2 Characteristic Description of the User ^  253.3 Medical Classifications ^  263.4 Interviews Conducted with Potential Users  28CHAPTER 4: MOTION ANALYSIS ^  344.1^Introduction ^  344.2 Method  344.2.1^Test Setup ^  344.2.2^Subjects  374.2.3^Procedure  374.2.4^Tasks ^  384.3 Motion Analysis Software ^  424.3.1^Joint Angle Definitions ^  434.3.2^Joint Angle Calculations  454.4 Accuracy of the System ^  544.5 Results  544.5.1^Single Subject/ Single Trial ^  544.5.2^Single Subject/ Multiple Trials  584.5.3^All Subjects / Single Trial Comparisons ^ 584.5.4^Comparisons with Previous Work  614.5.5^Implications for Orthosis Design  68CHAPTER 5: ORTHOSIS SIMULATION ^  755.1^Introduction ^5.2 Kinematic Formulation ^  765.3 Cost Function  815.4 Minimization Procedure & Program Design ^  845.5 Comparison of Simulated Fixed Elbow to Braced Elbow ^ 845.6 Results ^  875.6.1^Preliminary Evaluation ^  875.6.2^Analysis of Individual Subjects ^  985.7 Implications for Orthosis Design  995.8 Conclusion  101CHAPTER 6: CONCLUSIONS AND RECOMMENDATIONS ^ 1026.1^Introduction ^  1026.2 Task Definition and Priorities ^  1026.3 Motion Analysis  1046.4 Orthosis Simulation ^  1056.5 Orthosis Design  1076.4 Recommendations for Future Work ^  108REFERENCES ^  110Appendix A: A Brief Medical Description of the Disability Categories ^ 120Appendix B: Task Priority Questionnaire ^  121Appendix C: Subject Task Priorities  128Appendix D: Equipment Specifications  130Appendix E: 3D Coordinate Calculations ^  131Appendix F: Euler Angle Joint Angle Calculations ^  134Appendix G: Derivation of Location of P2 for Roll & Elbow Flexion Calculations^137Appendix H: Angle-Time Graphs from the Motion Analysis Study ^ 139Appendix I: Summary Table of Motion Analysis Results, All Subjects ^ 150Appendix J: Conversion of Shoulder Joint Angles from UM to UBC  152Appendix K: Simulation Values ^  155ivLIST OF TABLES Table 2-1: Relative Frequency of Joint Rotations ^  18Table 3-1: Diseases and Injuries Causing Upper Limb Weakness ^ 27Table 3-2: Task Priorities from Potential-User Interviews  31Table 4-1: Single Subject Motion Analysis Results  59Table 4-2: Summary of Motion Analysis Results, All Subjects ^ 60Table 5-1: Denavit-Hartenberg Parameters ^  78Table 5-2: Success Criteria ^  86Table 5-3: Initial Test Positions  88Table 5-4: Coupled Degrees of Freedom Results  96Table 5-5: Single Fixed Degree of Freedom Results ^  91Table 5-6: Coupled plus Single Fixed DOF Results  92Table 5-7: Two Fixed Degrees of Freedom Results  93Table 5-8: Three Fixed Degrees of Freedom Results  95Table 5-9: Maximum Required Torque for Each Joint ^  96Table 5-10: Advantages and Disadvantages of Preliminary Alternatives ^ 97Table 5-11: Unsuccessful Tasks for Final Alternatives  99Table I-1: Motion Analysis Results, All Subjects  151Table K-1: Joint Limit Values ^  151Table K-2: Initial Joint Estimates  156Table K-3: Desired Endpoint Positions  157Table K-4: Desired Orientation Vectors and Weighting ^  158Table K-5: Actual vs. Desired Values for Fixed Elevation and Wrist Yaw ^ 159Table K-6: Resulting Joint Angles for Fixed Elevation and Wrist Yaw  160Table K-7: Actual vs. Desired Values for Fixed Wrist Flexion and Wrist Yaw ^ 161Table K-8: Resulting Joint Angles for Fixed Wrist Flexion and Wrist Yaw ^ 162VLIST  OF FIGURES Figure 2-1:^Rancho Los Amigos Orthosis ^  5Figure 2-2:^Case Western Reserve University Orthosis ^  6Figure 2-3:^Texas Institute of Rehabilitation Research Orthosis ^ 7Figure 2-4:^Institute of Rehabilitation Medicine Orthosis  8Figure 2-5a: Hugh MacMillan Rehabilitation Centre Orthosis: Lateral View ^ 9Figure 2-5b: Hugh MacMillan Rehabilitation Centre Orthosis: Medial View  9Figure 2-6a: UBC-Enhanced HMRC Orthosis: Lateral View ^ 19Figure 2-6b: UBC-Enhanced HMRC Orthosis: Medial View  10Figure 2-7:^University of Toronto Orthosis ^  11Figure 4-1:^Subject Performing Task  35Figure 4-2:^Test Setup ^  36Figure 4-3:^Calibration Frame  36Figure 4-4:^Carrying Angle  37Figure 4-5a: Hand Positions  39Figure 4-5b: Web-of-Thumb Grasp ^  40Figure 4-6:^Test Setup Dimensions  41Figure 4-7:^Carrying Angle Bone Configuration ^  44Figure 4-8:^Azimuth Angle Definition  45Figure 4-9:^Elevation Angle Definition ^  46Figure 4-10a: Roll Anatomical Definition, Upper Arm Horizontal ^ 47Figure 4-10b: Roll Anatomical Definition, Upper Arm Vertical  47Figure 4-11: Elbow Flexion Anatomical Definition ^  48Figure 4-12 Roll and Flexion Angle Definitions  48Figure 4-13: Traditional Forearm Rotation Anatomical Definition ^ 50Figure 4-14: Forearm Rotation Angle Definition  50Figure 4-15: Wrist Flexion Anatomical Definition ^  51Figure 4-16: Wrist Flexion and Wrist Yaw Angle Definitions ^ 52Figure 4-17: Wrist Yaw Anatomical Definition  52Figure 4-18: Angle-Time Graph for Eating with the Hands  56Figure 4-19: Angle-Time Graph for Brushing the Teeth  56Figure 4-20: Comparison of Motion Studies for Elbow Flexion ^ 62Figure 4-21: Comparison of Motion Studies for Forearm Rotation  62Figure 4-22: Comparison of Motion Studies for Wrist Flexion  64Figure 4-23: Comparison of Motion Studies for Wrist Yaw ^  65Figure 4-24: Comparison of Motion Studies for Azimuth  66Figure 4-25: Comparison of Motion Studies for Elevation  67Figure 4-26: Comparison of Motion Studies for Roll  67Figure 4-27: Azimuth: Average Min/Max & Extremes for All Subjects ^ 69Figure 4-28: Elevation: Average Min/Max & Extremes for All Subjects  69Figure 4-29: Roll: Average Min/Max & Extremes for All Subjects  70Figure 4-30: Elbow Flexion: Average Min/Max & Extremes for All Subjects ^ 71Figure 4-31: Forearm Rotation: Average Min/Max & Extremes for All Subjects ^ 71Figure 4-32: Wrist Flexion: Average Min/Max & Extremes for All Subjects  73viFigure 4-33:Figure 5-1:Figure 5-2:Figure 5-3:Figure G-1:Figure H-1:Figure H-2:Figure H-3:Figure H-4:Figure H-5:Figure H-6:Figure H-7:Figure H-8:Figure H-9:Figure H-10:Figure H-11:Figure H-12:Figure H-13:Figure H-14:Figure H-15:Figure H-16:Figure H-17:Figure H-18:Figure H-19:Figure H-20:Figure H-21:Figure H-22:Wrist Yaw: Average Min/Max & Extremes for All Subjects ^ 73Kinematic Formulation Axis Deli nitions ^  77Roll vs. Elbow Flexion Coupling Function  89Wrist Flexion vs. Elbow Flexion Coupling Function ^ 90Diagram for Finding Point P2  ^ 137Eating with the Hands  139Eating with a Fork  139Eating with a Spoon  ^ 140Drinking from a Cup  140Reaching to Position 1, Cylinder Vertical ^  141Reaching to Position 2, Cylinder Vertical  141Reaching to Position 3, Cylinder Vertical  142Reaching to Position 1, Cylinder Horizontal ^  142Reaching to Position 2, Cylinder Horizontal  143Reaching to Position 3 Cylinder Horizontal  143Pouring from a Pitcher  ^ 144Reaching for and Rotating a Door Lever ^  144Reaching for and Rotating a Door Knob  145Turning a Tap Lever  ^ 145Flipping a Light Switch  146Pointing to a Button  146Turning a Page  ^ 147Lifting a Phone Receiver 147Reaching to the Lap  148Washing the Face  ^ 148Brushing the Teeth 149Combing the Hair  149viiACKNOWLEDGEMENTS I would like to thank the BC Health Research Foundation and NSERC for providing thefunding for this project. In addition, I would like to thank Dr. Doug Romilly and Dr. RayGosine for their continuing efforts and guidance. Thank you also to Silvia Raschke forsharing her practical knowledge of orthoses and Gerry Rohling for his assistance indeveloping the motion analysis software. And special thanks to my husband Eric for hispatience, love and helpful ideas.viiiCHAPTER  1: INTRODUCTION A powered upper-limb orthosis is an exoskeleton worn on one arm by a person with flailarms, that is, having severe muscle weakness or paralysis in the arms. This is in contrast to aprosthesis, which replaces an amputated limb, or a robotic assistive device, which operatesseparately from the user. By activating controls, the orthosis user directs the supported arm toperform various tasks such as reaching for objects, washing the face or eating. By regainingsome function in the assisted limb, the user achieves a higher degree of independence.The typical user has a neuromuscular disease such as poliomyelitis [40], muscular dystrophy[108] or amyotrophic lateral sclerosis (called ALS or Lou Gehrig's disease) [111], with twoflail arms but full sensation. Because the user has two flail arms, the powered orthosis isused to perform the entire task instead of acting as a secondary support. Full sensation oftemperature, pressure and texture is important both for safety reasons and because this makesit worthwhile to move the user's own arm. Otherwise, a robotic device may be more suitable.Achieving the functionality, strength and aesthetics of the human arm in a practical andaffordable orthosis is currently infeasible. Thus, design compromises are necessary. Themost significant compromise is in the choice of degrees of freedom provided by the orthosis.It may be possible to reduce the degrees of freedom while the functionality of the device,defined as the ability to perform the most important tasks, remains acceptable. A simplerdevice is normally less expensive, less bulky and less prone to break down. It is the goal ofthis work to discover an optimal compromise with regards to the necessary degrees offreedom in a user-acceptable orthosis design.1The following objectives were set out for the research outlined in this thesis:1) To research the needs and wants of potential users of a powered upper-limb orthosis;2) To establish the priority of various daily-living tasks;3) To record the motions of able-bodied people performing the identified high-prioritytasks;4) To analyse these motions in terms of the joint rotation angles, hand orientations andpaths taken during each task;5) To develop a kinematic simulation program to evaluate possible configurations of apowered upper-limb orthosis; and,6) To use this simulation program to determine the simplest orthosis configuration that isstill capable of performing the highest priority tasks.These objectives were achieved in three stages: a task analysis, a motion analysis and akinematic simulation. The literature review (Chapter 2) gives a background to these threeareas and to powered upper-limb orthoses. In the first stage, interviews were conducted withpotential users to establish the high-priority tasks (Chapter 3). In the second stage, these andother tasks were profiled as performed by able-bodied subjects (Chapter 4). In the thirdstage, the motion analysis data were used as inputs to a simulation program to find acceptableorthosis configurations (Chapter 5).Control strategies were not examined in detail as they were beyond the scope of this thesis.No powered upper-limb orthosis has yet been made which is acceptable to users and can bemanufactured at a reasonable cost and skill level. Although other researchers have proposeddesigns based on a ranking of joint rotations or on tests with mechanical models, the uniquecontribution of this research is the use of an orthosis simulation to test functionality.Furthermore, the number of functional tasks analysed for whole arm motion exceeds that ofprevious researchers. The analysis of motion provided an extensive set of data for the2kinematic simulations as well as providing a detailed characterization of human armmovement.A prototype orthosis will be built at the University of British Columbia using therecommendations of this thesis.3CHAPTER 2: LITERATURE  REVIEWA review of the literature provided background information for the proposed research work aswell as direction for further research. For clarity this literature review is divided into fourcategories corresponding to the different aspects of the project: 1) previously developedpowered upper-limb orthoses, 2) potential users and their task priorities, 3) motion analyses,and 4) kinematic analyses.2.1 Powered  Upper-Limb  OrthosesAn orthosis supports or controls deformities in an intact limb. Externally powered orthosesrepresent only a subset of these. Many unpowered static, spring-operated or ratchet-operatedhand and arm orthoses have been developed [117] but will not be discussed because they donot address as severe a problem as the bilateral flail arm user. Similarly, those powering onlythe elbow [51,109] or only the hand [26,27,49,81,82] will not be included in the discussionbelow. Robotic manipulators will not be described because the design and purpose ofautonomous manipulators are different from that of an exoskeletal device moving the user'sown arm.The development of powered upper-limb orthoses began in the 1960s as a result of the polioepidemic, the thalidomide tragedy and a growing number of surviving quadriplegics, all ofwhich generated interest in restoring function to the upper limb. In the following two decadessuch work was almost nonexistent. Recently, further research towards improving poweredupper-limb orthoses has been conducted.4Figure 2-1: Rancho Los AmigosOrthosis (After [28])The human arm has seven degrees of freedom, excluding finger motion and complex shouldermotion. This includes three degrees of freedom at the shoulder plus elbow flexion, forearmrotation and two degrees of freedom at the wrist. Each of the orthoses discussed below has adifferent set of powered degrees of freedom, including variations in the sequence of shoulderrotation axes.The first attempt at developing a powered orthosis was the Rancho Los Amigos Hospitalwheelchair-mounted electrically-powered arm orthosis developed in the 1960s by Nickel et al.[28,49,81,82,89,90,116]. Having six degrees of freedom plus grasp the orthosis was capableof all of the basic motions of the human arm exceptwrist yaw (radial/ulnar deviation) (see Figure 2-1).The Rancho orthosis was developed as a clinicaldevice "to provide severely paralysed patients with thebest voluntary arm motions possible" [49].Each joint rotation was controlled by a separatebidirectional tongue switch, making it slow anddemanding to control properly. (Even "one of thebest performers, a polio patient, used 150 motions totake five bites of food and 45 motions to pick up a cupand drink from it" [90].) There were "successful fittings leading to measurable functionalindependence" [28]. However, patient rejection was high [37]. The device was cumbersomeand costly. Its major problem was the frequency of breakdown [53]. Safety was also aconcern because of the lack of sensory feedback among most of the quadriplegic users.5Figure 2-2: Case Western ReserveUniversity Orthosis (After [98])In the latter half of the 1960s, Case Western Reserve University and the Case Institute ofTechnology conducted a research program into 'cybernetic systems for the disabled'. Incombination with related developments, Casedesigned and built a floor-mountedpneumatically-powered Case Research Arm Aid(see Figure 2-2) [4,48,52,56,98,116]. Althoughthe arrangement of shoulder rotations wasdifferent than for the Rancho orthosis, the Caseorthosis also powered all of the degrees offreedom except wrist yaw. The arm aid wasused exclusively for research, in combinationwith a programmable, real-time CyberneticOrthotic/Prosthetic Simulator that was designedprimarily to test control strategies, includingendpoint control. While the ideas were impractical to implement in a clinical device at thetime, it is possible that they could be implemented using the significantly smaller and morepowerful microcomputers available today.Another development in the 1960s, by Engen and Spencer at the Texas Institute forRehabilitation Research (TIRR), was a pneumatically-powered arm orthosis, as shown inFigure 2-3 [26,27,65,97]. The power actuator was a helical-wound bladder that contractswhen pressurized, called a McKibben muscle substitute. The two degree of freedomwheelchair-mounted arm orthosis used one actuator to flex the elbow and simultaneouslyrotate the forearm and the other actuator to elevate the arm using a parallelogram elevation6Figure 2-3: Texas Institute ofRehabilitation Research Orthosis (After[25])mechanism. These could be controlled separately or in combination. Both the position offorearm rotation (pronation/supination) and the desired degree of coupling could be preset.Alternatively, if the user retained the ability to pro/supinate, the action was not restricted.Grasp was optionally powered [27,85]. Azimuth rotation, occurring about a vertical axisthrough the shoulder, was unpowered but couldbe moved under the user's own power. Frictionwas reduced to a negligible amount with ballbearings so that azimuth movement could beeffected with weak but functioning muscles.The pivoting of the TIRR orthosis is similar tothe unpowered mobile arm support (MAS) whichis commonly used by people with weak butfunctioning muscles [49,65,97]; the poweredorthosis addressed the needs of those with armstoo weak or paralysed even for the MAS. The1IRR orthosis represents a good compromise between simplicity and functionality. It alsoutilized the remaining abilities of the user. Virtually all (90%) of those who received aprototype version of the device are still using it, as of 1992. However, the orthosis requiredsuch precision machining and specialized training that it was not commercialized [29].An electrically-powered clinical orthosis was also developed in the 1960s by Lehneis at theInstitute of Rehabilitation Medicine in New York [59,60]. It, too, was based on the pivotingdesign of the unpowered mobile arm support orthosis (see Figure 2-4). Elevation, elbow7Figure 2-4: Institute of Rehabilitationflexion, forearm rotation and grasp were powered. As with the TIRR orthosis, horizontalmovement (azimuth) was permitted but unpowered since the users had sufficient residualshoulder control once the effects of gravity were eliminated. A friction-controlled wrist jointallowed the user to preset wrist flexion. Thus,all of the degrees of freedom except wrist yawwere accounted for, with azimuth unpowered,wrist flexion passive and the remaining degreesof freedom powered. The design used flexibleBowden cables to locate the drive mechanismsremote from the arm. No further mention ismade of this orthosis, so it was presumablyunsuccessful.Medicine Orthosis (After [571)Because of the lack of success of these early attempts as well as lack of funding, no furtherattempts were made until the 1980s when efforts were put into robotic manipulators ([801,[100]). Robotic manipulators address the needs of those with quadriplegia but make no useof weak but sensate arms. This realization in combination with advances in computers andother technology favoured a renewed investigation of powered upper-limb orthoses.In 1987, the Hugh MacMillan Rehabilitation Centre (HMRC) in Toronto developed a onedegree of freedom plus grasp portable powered orthosis (see Figure 2-5a,b). It was designedprimarily to allow a person with severe upper arm weakness to eat [34,35,106]. Until thistime, there had been little success in developing powered upper-limb orthoses for ambulatoryusers mostly due to the weight of the actuators and power source that had to be carried on the8person. Thus, most powered orthoses were developed for wheelchair users. The HMRC'starget was people with ALS, a disease that leads to rapid progressive muscle weakness.Those with ALS are normally ambulatory at the initial stages only requiring a wheelchair atlater stages of the disease progression. Figure 2-5b: Hugh MacMillanRehabilitation Centre Orthosis:Medial ViewFigure 2-5a: Hugh MacMillanRehabilitation Centre Orthosis:Lateral ViewThe HMRC orthosis flexes the elbow while simultaneously rotating the forearm in order toput the hand in a suitable position when at table level and when at the mouth. The couplingis accomplished by a cable crossing over the arm. A linear actuator powers the grasp. Apowered winch unit drives the elbow motion with a timing belt [34].The first user was very successful: using the orthosis to access the keyboard, he wrote a book,graduated from university and held a part-time job. Encouraged by this success the HMRCbuilt five more prototypes but none were as successful as the first for varying reasons [35].In reality, the first user primarily utilized the orthosis to hold his arm in a useful position9Figure 2-6a: UBC-Enhanced HMRC Orthosis:Lateral View(rather than hanging by his side) then used his trunk to move the endpoint. The controlsystem, myoelectric control with the forehead frontalis muscles alternately activating the handor the arm, is a major handicap in dynamic use of the orthosis because the system is difficultand tiring to use reliably.Upon further evaluation of the HMRC design at the University of British Columbia (UBC), aproject of which this thesis forms a part, many possibilities for improvements were noted[44]. Modifications were made to the HMRC orthosis to make it lighter (by 28%), easier tofabricate and easier to repair. The modifications also included improved cosmesis and a morefunctional hand position (see Figures 2-6a,b) [95]. However, due to the pre-defined scope ofthe modifications, the actuators were kept the same. Thus, while the UBC-enhanced orthosishas many improvements over the original HMRC version, the device functionality is still toolimited to make its use widespread.Figure 2-6b: UBC-Enhanced HMRCOrthosis: Medial View10The newest multi-degree of freedom endeavour, developed by From at the University ofToronto [32], is a wheelchair-mounted, voice-controlled orthosis incorporating all of thedegrees of freedom up to but not including thewrist, as shown in Figure 2-7. It was designed asa research tool, "to evaluate the functionality andacceptability of a voice-controlled exoskeletalpowered upper-extremity orthosis" [32]. Theintention is to add a shape-memory-alloy orthosis[25] or to use functional neuromuscularstimulation [88] to control grasping. The targetpopulation is those with high-level quadriplegia•..•:: .^...Figure 2-7: University of Torontodue to spinal cord injury. Borrowing from theOrthosis (After [32])rehabilitation robotics field, the orthosis includesmany new orthosis concepts including endpoint control and several layers of mechanical,electrical and operational safety. This orthosis has been laboratory tested but has not yet beenclinically tested.2.1.1^Summary Although not discussed here, single joints, specifically the hand and the elbow, have beensuccessfully powered [27,49,51,85,109]. The above review has demonstrated, however, thatorthoses that powered almost all of the degrees of freedom of the arm were too complex to besuccessful. Despite the need for a powered upper-limb orthosis by a wide variety of users, anacceptable one has yet to be developed.112.2 Task  Priority SurveysThe functionality of an orthosis is established by the tasks that can be performed with it andthe ease with which these tasks can be performed. Both the number of tasks and the priorityof those tasks are of interest. Since the priority of tasks affects both the design and itsultimate success, it was an important first step in this research to discover task priorities frompotential users.Previous researchers have surveyed potential users and their task priorities but none of thesurveys were intended for use in designing a powered orthosis. While it was necessary toperform our own interviews because of this difference, the results from other surveys are ofinterest and, for the most part, are applicable to users of a powered orthosis.The first reported classification of task priorities was performed by McWilliam in 1970 [70].Seventeen able-bodied people recorded and rated their activities-of-daily-living; the mostessential tasks formed the basis for the design of a prosthesis. Paid work and recreationaltasks were not included. The tasks that were rated essential by all subjects (listed in noparticular order) were:• brushing the teeth• loading a spoon from a plate• unloading food into the mouth• public transport• lifting and tilting either a cup or tumbler• stirring with a spoon• toileting• turning pages• writingIt will be seen that the priorities set by people with disabilities are moderately different fromthose set by able-bodied people.12In the last decade, several rehabilitation robots have been developed. Just as with poweredorthoses the priority of various tasks is a primary issue if the design is to be tailored to theneeds and wants of the users. The Neil Squire Foundation conducted interviews with fivepotential robotic arm users, all of whom had quadriplegia, prior to and following their firstcontact with the prototype vocational robot [39]. It was found that user expectations were insome cases unrealistically high prior to contact due to the fictional depictions of robots inmovies. After exposure to the robot the desired tasks, in response to an open-ended question,were defined (listed in no particular order) as:• turning pages• loading cassettes and compact discs• opening drawers & closets for clothes• changing volume & station on stereo• performing personal hygiene tasks(brushing teeth, washing face, shaving)• repositioning hands on the armrests• picking up books & papers• serving drinks• manipulating floppy disks• brushing debris from the eyes• fetching manualsWhile this "wish list" was compiled for a robotic manipulator, the results are applicable to anorthosis because the individuals wished to regain these tasks, however that may be achieved.Further interviews were conducted during clinical trials of the robot [9] which had greateremphasis on vocational activities.Despite the desire for the daily-living activities outlined in the Neil Squire task list, theresulting robot is essentially restricted to vocational tasks. Vocational tasks can be performedin a structured environment, they encourage the integration of disabled people into theworkplace and they are safer because the robot usually operates out of range of the user. Incontrast, activities-of-daily-living require a more versatile device and more intimate human-device interaction.13An individual's current abilities, pastimes and living situation may also affect the design. Toexamine these areas as well as task priorities, the Bath Institute of Medical Engineering(BIME) interviewed 42 potential users of a robotic manipulator [45]. Twenty-five hadmultiple sclerosis, ten were spinal cord injured and the others had miscellaneous diseasescausing upper-limb weakness. The most common suggestions for robot use in answer to anopen question (the frequency of suggestion is given in brackets) were:• making a hot drink (18)• feeding (4); picking items up from the floor (4); kitchen use (4)• loading a cassette-tape (3).The emphasis on making a hot drink may have occurred because the interviewer used makinga cup of tea as an example of a task that the robot could perform or because the majority ofsubjects had multiple sclerosis with which hand tremors are common. Although the subjectswere shown a conceptual drawing of the robot, several remarked that they would need to usethe system before being able to determine more uses for it, making the design process and thetask list iterative. After progressing through three basic systems with continued userfeedback, the result has been a robotic workstation capable of loading a floppy disk into acomputer, retrieving books from a shelf and operating a cassette recorder/radio, among othertasks. Feeding was not considered a desirable activity by the users since it would reducesocial interaction.Building upon the Bath survey, Middlesex Polytechnic conducted a survey of 50 potentialusers of an electric-wheelchair-mounted robotic arm [94]. Of the 17 different disabilitiesrepresented, the most common were spinal cord injury (11 subjects) and multiple sclerosis (8subjects). Although not wishing to influence the subjects' answers, a computer simulationvideo was shown to the subjects before filling in the questionnaire to give them some concept14of what the robot could do. The top five tasks in answer to "what would you most like to dobut cannot?" were:• reaching, stretching, gripping (22)• gardening (13)• reaching to the floor (12)• cooking (10)• eating (9)Others listed were:• lifting large objects (6); dressing (6)• drinking (5); driving (5)• standing / walking (4); getting in & out of the wheelchair (4)• do-it-yourself (3); getting tight grip on lids (3); washing/bathing (3);playing sports (3); emptying bladder(3); and cleaning/wiping (3).Reaching to pick up objects has the highest priority, especially from the floor, as mentionedin the Bath results. Cooking and eating also have a high rating, confirming the Bath results,but without the emphasis on preparing hot drinks.The Arbutus Society for Children also developed a questionnaire for electric wheelchair users.They have not analysed the task priorities, but noted that "certain tasks are identified clearlyas being performed with difficulty, e.g. picking and placing objects" [42]. This againconfirms the importance of reaching tasks.In an evaluation following development of the Stanford/VA Desktop Vocational AssistantRobotic Workstation (DeVAR), the tasks that the 24 high-level quadriplegic users "wouldmost like to have the robot do" were [41];• performing hygiene tasks, e.g. brushing teeth, shaving and washing (9)• preparing a meal and feeding (6); getting a drink of water (6)• fetching and carrying objects (4); operating environmental appliances,e.g. phone, TV, stereo (4)15• setting up a splint for feeding/writing (2); performing tasks at bedside (2)• turning book pages (1); writing letters (1); and lighting a cigarette (1).This list puts a greater emphasis on personal hygiene tasks than the previous surveys. Sincethe accent was on activities-of-daily-living (ADL) the first three versions of the robotemphasized ADL, recreational and personal clerical tasks. The fourth version is configuredfor vocational tasks as well. The robot is reported to be preferred to an attendant or familymember because the robot performs tasks according to the user's own schedule.An extensive evaluation of the MANUS robotic manipulator was performed in ADL,vocational and school settings [72]. The tasks that received the highest number of ratings inthe "want to do" category were:• picking up a book (13); placing a book on a shelf (13)• pouring liquid (12); fetching objects from shelves (12)• turning knobs (10)• drinking from a cup or glass (9); using standard fork, knife and spoon (9);opening cupboard door (9); retrieving books (9); operating wall switches (9); and,grasping and releasing (9).Once again, the emphasis is on picking and placing objects. This is in contrast to the taskpriorities compiled by the able-bodied subjects earlier. Both, however, consider eating anddrinking important.2.2,1^summary The literature indicates the importance of contacting potential users directly before developinga new device. In response to task priorities, potential users of a robotic device indicated theimportance of reaching and picking up objects. Cooking and eating also had a high priorityalthough some people were concerned about losing the social contact that occurs at mealtimes.16The importance of personal hygiene varied from survey to survey but is among the highestpriority tasks. Other factors, such as living at home or an institution will also affect thepriority of tasks and thus the design of the device. The next chapter discusses the interviewsperformed for this research with potential users of a powered upper-limb orthosis.2.3 Motion A nalysesIn order to determine the motions associated with the higher priority tasks defined above, amotion analysis was performed. This analysis recorded the free movements of a subjectperforming the higher priority tasks, then calculated the associated joint movements. Whilethe majority of this work is original, the development of the system used for this purposebenefitted from previous work in the area, as described below.The functional movement of the entire upper limb has only been recorded previously by a fewresearchers. Single joints have been studied more thoroughly, but this provides little insighttowards the simultaneous movement of all joints. Most human motion studies haveconcentrated on gait analysis, which until recently has largely been done in two dimensions,whereas the study of upper-limb movement requires three. Many techniques have been usedfor gait analysis and single arm joint recordings including LED infrared markers [73,83],reflective markers [8,71,75,87], electrogoniometers [13,15,52,74,83,101], optical scanners withprismatic markers [76], electromagnetic sensors [2,67] and laser scanners with photodetectors[63].17In 1947, Keller et al. conducted studies of able-bodied subjects to determine the functionalrequirements of hand and arm prostheses [50, 66]. The most common motion, based on 51activities-of-daily-living, was found to be elbow flexion, which represented 16.5 percent of allmotion. Table 2-1 shows the relative frequencies of each joint rotation. Shoulderflexion/extension refers to movement of the arm forward and back; shoulder abduction refersto movement of the arm to the side.Joint Rotation Frequency (%)Elbow Flexion 16.5Shoulder Flexion/Extension 15.1Grasp 14.1Upper Arm Roll 12.9Forearm Rotation 12.8Wrist Flexion/Extension 12.7Shoulder Abduction 9.3Wrist Yaw 6.6Table 2-1: Relative Frequency of Joint RotationsThis shows that elbow flexion is critical while wrist yaw is relatively insignificant. In fact,Keller concluded that wrist yaw can be eliminated entirely without important functional loss.Many of the other joint rotations are quite similar in frequency and may vary with a differentselection of tasks.The first motion analysis of the entire upper limb was performed by Engen in the late 1960s[27]. Using mirrors mounted above and to the side of the subject he was able to capture allthree views on one image. Five activities were studied: diagonal reaching, writing, page18turning, hair combing and eating. Each activity was performed with and without anunpowered orthosis. The images were hand digitized to create stick-figure diagramsrepresenting the movement in all three views. However, although the stick figure diagramsdo provide visualization of common daily-living tasks, the data is difficult to adapt to otherpurposes since there is no explicit data concerning joint angles and the images obtained aredistorted by the mirror angles. The current research updates and expands upon aspects ofEngen's work.Engen's results highlighted the importance of providing shoulder movement as the primarypositioning mechanism. He postulated that a prosthetic elbow could be fixed at a givenlocation for a particular activity without losing the ability to perform that task. It was alsonoted that forearm rotation and wrist flexion/extension should be powered to allow for moreprecise movements.Also in the 1960s, Lake at Case Western Reserve University studied whole arm motion usinga seven-axis exoskeletal goniometer [52,56,98]. Nine daily-living tasks were studied: drinkingfrom a cup, eating with a spoon, eating a hamburger (finger food), transferring a block fromone position on the lapboard to another, transferring a book from a shelf to a lapboard, slidingan object across the lapboard, drawing with a pencil, operating a push-button phone andscratching the face. However, details of the results are not available. The primary purposeof the recordings was to be able to replay the actions rather than to determine joint anglepriorities.19In 1981, Langrana used side and overhead videocameras to record diagonal reaching with andwithout an unpowered orthosis [54]. Three-dimensional axis markers were placed at theelbow and the wrist while two position markers were placed at the shoulder. Euler angleswere used to describe the rigid body motion. This was the first example of calculating jointangles from motion data. Only the shoulder and elbow were analysed, thus no informationconcerning the orientation of the hand or the wrist is available. The results were therefore ofno further use to this project.While other researchers, such as Maulucci [67] and LipitIcas [62], have studied reaching, thiswork either did not deal with the entire arm or was not analysed for functional tasks.Therefore the results are not suitable for comparison to results in this research or as input tothe simulation program.An analysis relevant to this research was performed by Safaee-Rad et al. at the University ofManitoba who recorded the motion associated with three eating tasks using a video-basedsystem [102,103,104]. The three tasks were eating with a fork, eating with a spoon anddrinking from a cup. In this work, seven markers were attached to the subject, three at theshoulder, one at the elbow, two at the wrist and one on the hand. Two videocameras weredirected horizontally towards the subject, separated by an angle of 40°. Further details aregiven in Section 4.5.4. The relative importance of the joint rotations for the feeding tasks,based on the arc of motion, was found to be: forearm rotation (100°), elbow flexion (600),shoulder flexion (40°), wrist flexion (35°), shoulder abduction (25°), roll (20°) and wrist yaw(20°). This highlights the importance of forearm rotation and elbow flexion during eatingtasks.2013,1^Summary The literature review revealed that few researchers have studied whole-arm motion. Giventhat technology is improving and there are many applications for these results, these studiesshould become more common. For the purposes of this research, a new motion analysis studywas needed to gather quantitative joint and path data for a large number of high-priorityfunctional tasks to be used as input to the simulation program.IA Kinematic Evaluations  and  ResultsThe human arm was simulated kinematically for this research to investigate how an orthosisdesign can be simplified without sacrificing too much functionality. Other researchers haveattempted to evaluate simplified prostheses by mechanical means; the techniques and resultsare described below. The difference in this research is that the investigation is performednumerically, allowing many options to be examined.The complex three degree of freedom shoulder motion was studied by Enger in the 1960swith the objective of compressing the required motion into a single turn axis for the design ofa prosthesis [30]. Using geometric relationships, stereometry and a specially-designedmechanical device to simulate the arm, his team determined that a 45° turn axis would bringthe arm from the side "table" position to the front "mouth" position. All of the remainingdegrees of freedom were powered independently in the prosthesis except wrist yaw, whichwas coupled to elbow flexion. This simplified the shoulder mechanism and control, but onlyallowed for eating-like activities.21By recording and rating the everyday activities of 17 able-bodied subjects, McWilliamidentified 180 tasks as the most important for daily living, as described in Section 2.2 [70].The endpoints of each action and any essential paths were noted through observation, leadingto a non-quantitative characterization of the task movements [68]. Since dressing tasks wereincluded, the requirements were different than for this project. A mechanical model was builtto evaluate various selections and combinations of axes against the task requirements. The`.resulting minimum requirements were found to be: shoulder flexion/extension, roll coupledwith shoulder abduction, elbow flexion, forearm rotation, wrist flexion and grasp, therebyeliminating one degree of freedom through coupling and one by fixing wrist yaw altogether.Whereas the above two researchers examined motions for the purposes of design, Reddingrecently developed a diagnostic tool for visualizing the resulting workspace volume of aselected prosthesis [96]. The purpose was to alleviate the time-consuming process ofchoosing appropriate prosthesis components for an individual amputee. After selecting andjoining predefined prosthesis components, all of the reachable points are displayed on thecomputer screen. Contact points, such as against the body or a table are shown in order todetermine how functional the setup is for performing daily-living tasks. Although thisprovides an effective diagnostic tool, it cannot be used to analytically determine the optimalconfiguration.2.4.1^Summary The literature review demonstrates that a new kinematic analysis is required. No definitiveanswer exists concerning the optimal set of degrees of freedom for a powered upper-limborthosis. Since task priorities have now been defined by potential users (as opposed to the22able-bodied subjects in the McWilliam study), the results will more likely lead to anacceptable orthosis. Also, joint angle data is now available in a form suitable for thesimulation program because of the motion analysis performed in this research.Zif summary This literature review has covered past work on powered upper-limb orthoses, task priorities,motion analyses and kinematic analyses. In each case there is a clear lack that needsaddressing. In the following chapters, interviews with potential users are discussed, themotion analysis of the important tasks arising from the interviews is described and thekinematic simulation program, which uses the data from the motion analysis results todetermine an optimal set of degrees of freedom for a powered upper-limb orthosis, isreported.23CHAPTER  11POTENTIAL  USERS  OF  A POWERED UPPER-LIMB ORTHOSIS AND  THEIR TASK PRIORITIES 3.1 Introduction In this chapter, the characteristic user for this study is defined, relevant medical details aregiven and the interviews conducted with potential users to obtain information on taskpriorities are described.While market surveys are common in the development of products in other fields, they arerelatively new in the rehabilitation field. Rehabilitation products have often failed in the pastbecause the assumptions of researchers and designers were incorrect. In recognition of this, ithas now become common to survey potential users before developing a product so thatfeedback and ideas can be incorporated into the design [10,84].Early feedback is especially important in the design of a powered upper-limb orthosis. Iffunction is to be compromised in a powered orthosis for the sake of simplicity, betterreliability and reduced cost, the defined priority of tasks will have a major impact on thedesign. Furthermore, the high cost of design and manufacturing and the small populationprovide few opportunities for experimentation.The task priorities defined here formed the basis of the tasks selected for the motion analysisstudy. Those tasks were, in turn, used to test the simulated orthosis. The tasks will alsoserve to evaluate the prototype orthosis.243.2 Characteristic Description  of the  User The objective is to design and build an orthosis which allows a person with severe upper-limbweakness to perform daily-living activities. The variety of disabilities, however, necessitatedthat a user be characterized for the design purposes of this study. The characteristics, for thisstudy only, are:1) two completely flail arms,2) intact sensation (temperature, pressure, texture),3) no spasticity,4) a full range-of-motion of the joints,5) full cognitive abilities and,6) adult-sized.The reasons for these criteria are outlined below. A person with two completely flail arms isuncommon but poses the most severe requirements in terms of the level of assistance to beprovided in the design. If the user still has some abilities, such as hand function, the orthosisshould allow the user to utilize that remaining function. If a function is retained, that degreeof freedom can be left unpowered, thus simplifying the design.At least partial sensation is required since artificial sensors are unlikely to be built into anorthosis. This criterion is justified because sensation is unaffected in the first three medicalcategories listed below and in some individuals of the other categories (see Section 3.3). Ifthere is no sensation, then for reasons of both safety and versatility the person should beencouraged to consider using a robotic arm instead. However, if the individual retainssensation there is a strong incentive to move the user's own arm.25The uncontrollable contractions associated with spasticity can overpower an orthosis, posing asafety hazard to the user and possibly damaging the power actuators. Similarly, if the userdoes not have a full range of movement, which is common due to lack of regular movement,the orthosis cannot operate beyond the limited range of motion. Full cognitive abilities arerequired as the user must be able to learn how to control the orthosis. Since virtually all ofthe people affected by the diseases and injuries listed are adults, it is justified to make theorthosis adult-sized at this stage of the work.The importance of user selection has been mentioned by previous researchers [27,35,49,90].The individual must be highly motivated and must receive good training in the control andoperation of the orthosis. It is also advantageous for the user to be introduced to the deviceas soon as possible after injury or the onset of the disease. Deformities must not beexcessive, and good head and trunk stability are required so that the arms are not needed forsupport [90].3.3 Medical  ClassificationsKnowledge of the medical background and consequences of the diseases and injuries causingdisability is a prerequisite to understanding the difficulties faced by potential users of apowered orthosis. Certain characteristics make an upper-limb orthosis more suitable for anindividual while other characteristics make its use impossible.The diseases and injuries under consideration are poliomyelitis [40], amyotrophic lateralsclerosis (also called Lou Gehrig's disease) [12,111], muscular dystrophy [12,108], spinal cord26injury (also called quadriplegia) [65,117], multiple sclerosis [57], brachial plexus injury [58],stroke (also called hemiplegia) [23,105] and Charcot-Marie-Tooth disease [22]. See AppendixA for a brief medical description of each one.Table 3-1 gives the extent and form of upper-limb weakness commonly found in eachcategory.Disease/InjuryDescription of Upper-Limb WeaknessP Polio causes muscle weakness. Although the weakness plateaued decades ago formost victims, new symptoms are now appearing, a syndrome referred to as post-polio. The legs are usually affected before the arms. Sensation is not affected andthere is no spasticity.ALS Because of the continuing progressive dysfunction related to ALS, flail arms willalways result. The weakness starts at the extremities and works upwards. Armweakness usually occurs later in the disease. Sensation remains and there is noassociated spasticity.MD With muscular dystrophy, the upper limb is affected most by reduced shoulder andgrip strength.^Sensation is not affected and there is no associated spasticity.SCI Injury to the spinal cord is named according to where the injury occurs, withparalysis below that point. A C4 injury involves paralysis below the 4th cervicalvertebra leaving only shoulder shrug and head movement. With a C5 injury, handand wrist function, pronation and elbow extension are lost, but shoulder function isretained. In a C6 injury, only hand function is lost. Sensation may be full, partialor nonexistent. Spasticity is commonMS Multiple sclerosis results in overwhelming fatigue and poor motor coordination.Sensation is usually affected. Spasticity is common.BPI Brachial plexus injury is a sudden severing of the nerves of one arm, mostcommonly due to motorcycle accidents. The arm may be totally flail if all of thenerves are affected. Sensation may or may not be affected. The arm is oftenamputated and a prosthesis worn to provide the individual with more function [77].Sir Stroke affects one side only. Recovery varies widely but half of those survivingcontinue to need special services [105]. Spasticity is common and sensation isaffected.CMT The greatest impact of Charcot-Marie-Tooth disease, in terms of the upper limb, is areduction in grip strength. Loss of strength in the entire arm is uncommon but doesoccur.Table 3-1: Diseases and Injuries Causing Upper-Limb Weakness27As seen from the above summary, a tremendous variety of upper-limb disabilities exist. Thefirst three (P, ALS and MD) are the focus for our initial users because sensation is unaffectedand spasticity does not result. Individuals from the other categories may also be suitable forthe orthosis but will only be considered after the development of a working prototype.3.4 Interviews  Conducted  with  Potential UsersAlthough the surveys outlined in the literature review contribute to our knowledge of potentialusers, this project is concerned with potential users of a powered orthosis, not a robotic arm.An orthosis user may not be in a wheelchair and the disabilities differ. More importantly,regaining function of one's own arm using an orthosis differs from having an independentrobotic manipulator performing the tasks. Interviews were therefore conducted in order todetermine task priorities directly from potential users, to understand how people deal withtheir disabilities, to gather early feedback concerning the development of a powered upper-limb orthosis and to survey potential users of a powered orthosis rather than of a roboticmanipulator.An abstract describing the project and its objective was distributed at two post-polio supportgroup meetings and through the ALS and muscular dystrophy newsletters, but unfortunatelyproduced no response. The best response was obtained from the Limb Girdle MuscularDystrophy (LGMD) group whose leader sent the abstract to each member of the group.The questionnaire, included in Appendix B, was based on both the Arbutus and Middlesexsurveys [42,94]. However, there were several differences from these previous surveys.28People were asked first which tasks they would most like to regain so as not to bias them tothose included in the questionnaire; they were asked at the end to name the five mostimportant tasks. Subjects were asked to rank criteria concerning acceptance of the orthosis,such as cost or cosmesis, and they were questioned about their use of daily-living aids.Personal questions were moved to the end of the survey so as to be less intrusive and to putmore emphasis on task abilities and priorities.Seven women and four men were interviewed, for a total of 11 subjects. One had post-polio,two had Kugelberg-Welander disease (a mixture of ALS and MD), one had C5/6 spinal cordinjury and the remaining seven had limb-girdle muscular dystrophy (LGMD). In all but onecase, which was conducted in person, the interviews were conducted by telephone.The average age of the subjects interviewed was 44, with a range from 27 to 65. This issimilar to the average age of 45 for the Bath survey and 40 for the Middlesex survey. Thelength of time since diagnosis ranged from 4 to 39 years, with an average of 18 years, so allwere accustomed to their disability. With four single, one divorced and six married subjectsthere were a greater proportion of married people than in previous surveys. All lived at homealthough three lived in modified homes. Four had full-time jobs, one was a homemaker,another retired; the other five had no employment. The lesser degree of disability of many ofthe subjects in this survey as compared with other surveys likely contributed to the greaterpercentage of full-time workers. Pastimes included TV, reading, travel, painting, visiting,sports and computers among many others. Several watched more television than29desired because they were unable to do what they wished to do. All of the subjects indicatedthat they would consider buying a device that could perform some of their tasks, dependingon the price, and all were willing to be contacted for clinical trials of the orthosis.The above data was not expected to be statistically representative of the population ofpotential users because of the low number of subjects, the greater number with LGMD andthe fact that many were not disabled enough to require the whole orthosis.All of the subjects felt that it would be easier to see the device in order to understand what itcould do (hence the simulation in the Middlesex study and the conceptual drawings in theBath study). Although the responses may be more reasonable, demonstrating a device maymake respondents tailor their wishes to the capabilities of that particular device. In general,the expectations of the respondents were realistic.Daily-living aids were reported as rarely used by the subjects. Most people seem unaware ofcommercially available aids or the cost was deemed prohibitive. The aids that are used arehomemade, such as a back-scratcher or BBQ tongs used as a reacher.The respondents were asked about their ability to perform a variety of specific personalhygiene, domestic, recreational and work- or school-related tasks. Of most interest, however,were the responses to the "top five tasks that you would most like to do but cannot". Table3-2 summarizes the responses for the 11 subjects; details are given in Appendix C.30TASK FREQUENCYReaching / Picking up Objects 9Personal Hygiene 7Hobbies / Crafts 7Eating / Drinking 6Housework 4Dressing 4Strengthening Grip 4Cooking 2Toileting / Transferring 2Reading 1Using Computer 1Table 3-2: Task Priorities from Potential-User InterviewsReaching has the highest priority because it is integral to many activities. This concurs withthe task listings cited in the literature review, all of which gave reaching and picking upobjects a high priority. 'Personal hygiene' includes brushing the teeth, washing the face,combing the hair, applying makeup, shaving, scratching and blowing the nose. Personalhygiene, eating and drinking ranked consistently high among the task priorities noted in theliterature review. The desire for regaining creativity is strong, including such tasks aspainting, crafts, baking, woodworking and other hobbies. This was not demonstrated in theinterviews with potential users of the robotic manipulators, likely because it would be anindependent assistive device performing the actions which is less personal and moreintimidating than performing them oneself.31Although the ability to dress and toilet contributes to greater independence, both were deemedoutside the realm of a practical orthosis and were therefore not included in the motionanalysis. Both actions involve parts of the body other than the arm; transference to the toiletrequires greater strength than would be designed into a practical orthosis; and dressingnormally occurs only twice a day when a helper would normally be available. Vocational,educational and recreational activities have not been directly included but many of the actionsare similar to those in the daily-living tasks listed.Another use for an orthosis is to hold the arm in a single position, such as for keyboarding,using a TV remote, telephone or environmental controls, painting or for performing many ofthe personal hygiene tasks. The ability to hold the arm in a given position reduces fatigue instill-functioning muscles, controls shakiness, allows pages to be held down and permits two-handed actions if only one side is affected.Respondents were also asked to rate the importance of various criteria towards making theorthosis acceptable. The list was derived from Batavia and Hammer's compilation ofconsumer-based criteria [6]. Cosmesis was identified as a very important factor towards theacceptance of the orthosis since the respondents did not wish to look disabled or attractattention. Others, however, indicated that the importance of regaining the function wasgreater than the importance of cosmesis ("they already stare anyway").Affordability was considered critical to the acceptance of the orthosis. The price people arewilling to pay is largely dependent on the independence that would be gained, although nodollar figures were given. Robustness and portability were also considered essential. The32importance of water-resistance was noted by several of the respondents to allow for washing,spilling drinks and possibly for bathing and showering. They also emphasized that theorthosis must be designed to avoid fatiguing the shoulder. There was some concern beforethe interviews that potential users may be uneasy with technology; based on the results of theinterviews, this concern was not warranted.While the initial impetus for performing the interviews was to establish a set of task priorities'for use in design and development, a useful outcome was the personal contact with peoplehaving severe disabilities. Further association will be ongoing during the design phase andthrough clinical trials of the prototype orthosis.33CHAPTER 4: MOTION ANALYSIS4.1 Introduction Functional arm movements have rarely been studied, as shown in the literature review, yetthey are the most relevant for clinical applications. The analysis of functional arm movementachieved two goals: 1) it provided insight and data on how the arm moves while performingfunctional tasks, beyond what other researchers have provided and 2) it provided data withwhich to evaluate whether a simulated powered orthosis with limited degrees of freedomcould perform the functional tasks chosen. The selection of tasks was based on the prioritiesdefined from the interviews with potential users. The data from the motion analysis wasessential for the orthosis simulations, to provide the desired positions, orientations and intialestimates of joint angles.4.2 Method The natural motions of able-bodied subjects performing specific functional tasks wererecorded with two video cameras. The two sets of images were analysed with customizedmarker tracking software to determine the joint angle rotations and marker paths. Details areprovided below.4.2.1^Test  S etup Wearing a dark turtleneck and thin gloves, the subject was positioned in an armless chair at aspecified location, with the distance from the table determined by placing the subject's elbow34comfortably at the edge. The subject was then strapped to a post behind the shoulders suchthat the trunk would not move forward while performing the tasks (see Figure 4-1). This wasnecessary as the expected orthosis user is not able to bend forward.In order to follow the joint locations and to define rotations, five markers were attached to theright arm of the subject: one at the shoulder, one at the elbow, one at the wrist, another on anextension from the wrist, and one on the hand at the second knuckle, MCP 3, as shown inFigure 4-1. The markers, 25 mm diameter white styrofoam spheres, were attached withdouble-sided adhesive. The backdrop and all of the objects used in the tasks were covered inblack in order to increase the contrast of the markers.Figure 4-1: Subject Performing TaskTwo video cameras mounted on tripods approximately 50 degrees apart, as shown in Figure4-2, were used to record each task. Appendix D lists the hardware used. The cameras werecalibrated using a rigid three-dimensional frame with ten markers positioned at known35Camera &Videotape *1 Task Setup Table500Camera tVideotape 112ProgramMonitor ImageMonitorTVVCR^ComputerFigure 4-2: Test Setupcoordinates (see Figure 4-3).The frame provides a referencefor the two-dimensional imageplanes of both cameras to becorrelated to three-dimensionalspace coordinates. A squarewhite reference marker wasincluded within the image fieldto adjust for movements of thecamera image. Using the ten calibration markers (only six are needed) to produce 20 linearequations, the eleven calibration parameters are solved for using a least-squares fit. Theknown image coordinates from each camera together with the calibration parameters can thenbe used to solve for the unknown three-dimensional coordinates. Known as the Direct LinearTransformation method, developed by Abdel-Aziz and Karara [1], the details of thecalibration and three-dimensional coordinate calculations are given in Appendix E.Figure 4-3: Calibration Frame36^4.2.2^SubjectsIn total six able-bodied subjects, ranging in age from 22 to 44 and in height from 5'-2" to 6'-1/2" participated in the study. Three were female, three male. All were right-hand dominant.^4.2.3^Procedure Before beginning the tasks, the subject assumed a "standard position" with all joint angles atzero degrees except the elbow, which is bent at 90 degrees, i.e. with the upper arm straightdown, the elbow flexed to 90 degrees and the hand flat with the thumb up. Safaee-Rad [102]and Maulucci [67] used this position to correct the calculated joint angle values. This was notdone in this research because it was determined that the inaccuracy of positioning the subjectin the standard position was greater than the inaccuracy of positioning the markers (elevationin the standard position was as much as 13° due to body geometry, whereas marker positionaccuracy is within 4°). It was useful however to have one known position when examiningthe results of the tests.The distance between the marker centroid and the jointcentre was measured for each joint. This was used laterto translate the markers from the outside of the arm tothe joint centres. See Section 4.3.2 for further details.The carrying angle, shown in Figure 4-4, was alsomeasured for each subject. The value of the carryingangle is used in the joint angle calculations (see Section4.3.2).Figure 4-4: Carrying Angle(After [471)374.2.4^Tasks Twenty-two standardized daily-living tasks were performed. Before each trial the subjectactivated a camera flash in order to synchronize the two camera images to the same frameduring analysis. A starting position was defined for all of the tasks; starting from thisposition the subject completed a single task, then returned to the starting position. All but onesubject executed each task four times with only one trial chosen for analysis. Normally thelast trial was chosen for analysis, since unfamiliar tasks became more natural, but another trialwas selected if the camera flash occurred on a frame boundary or the trial was performedincorrectly. One subject performed each task eight times, with four trials being analysed toexamine the variability for a single individual.The 22 tasks were classified into several categories:Eating and Drinking:1. Eating with the Hands2. Eating with a Fork3. Eating with a Spoon4. Drinking from a CupReaching:5. Reaching to Position 1, Cylinder Vertical6. Reaching to Position 2, Cylinder Vertical7. Reaching to Position 3, Cylinder Vertical8. Reaching to Position 1, Cylinder Horizontal9. Reaching to Position 2, Cylinder Horizontal10. Reaching to Position 3, Cylinder HorizontalDaily-Living:11. Pouring from a Pitcher12. Reaching for and Rotating a Door Lever13. Reaching for and Rotating a Door Knob14. Turning a Tap Lever15. Flipping a Light Switch3816. Pointing to a Button17. Turning a Page18. Lifting a Phone Receiver19. Reaching to the LapPersonal Hygiene:20. Washing the Face21. Brushing the Teeth22. Combing the HairSince it would be impractical to design more than one grasp type into the orthosis (Figure 4-shows various possibilities), the tasks were always performed using the overhand cylindricalor palmar grasp. The palmar grasp is normally used about 50% of the time for pickingobjects up and about 88% of the time when holding objects for use [114] and is therefore themost likely to be designed into an orthosis. The cylindrical grasp accommodates holdingutensils with a cylindrical handle or in a palm cuff. This grasp contrasts with other motionanalysis researchers who have used the more traditional 'web of thumb' grasp for eating tasks(see Figure 4-5b).Figure 4-5a: Hand Positions (After [66])394,1111:\Figure 4-5b: Web-of-Thumb Grasp(After [112])During the tests, the utensils were covered with a cylindrical foam handle (a commonly-useddaily-living aid) and a stopper piece to keep the fingers in the proper grasp. In all other waysthe subject was instructed to perform the tasks as naturally as possible. Muffin pieces orraisins were used for eating with the hands and with a fork, yoghurt was used for eating witha spoon, and water was used for drinking from a cup. A daily-living-aid cup having a lid andspout but no handle was used in the testing. For the reaching tasks, the subject began at thestarting position with a 37 mm diameter by 90 mm long foam cylinder at a defined orientation(vertical or horizontal), carried the cylinder to the desired position and then returned to theinitial position. Position 1 was at the far right of a normal working area, based on theaverage for men and women as reported by Pheasant [91] (see Figure 4-6 for the tabletoppositions); position 2 was directly in front of the right shoulder for an average person; andposition 3 was directly in front of the left shoulder for an average person. The second set ofreaching tasks was to the same positions, but with the hand in the second orientation. Thesepositions incorporate the area that would be needed when using a keyboard.A gardening pitcher was used to study pouring since many of those surveyed expressed aninterest in gardening. This is comparable, however, to pouring from either a kettle or apitcher used for refreshments.40Figure 4-6: Test Setup DimensionsThe door knob and door lever tasks used a mockup door resting on the table, with the heightof the handles from the ground being equivalent to that of a full-sized door (96 cm).Similarly, the light switch was set at the same height as a normal light switch (134 cm); itwas flipped using the left side of the index finger. The "button" task involved pointing to thelight switch, making it identical to the light switch task except for the hand being rotateddownwards (pronated). The tap lever was pulled towards the subject.A rubber page turner was fixed to the end of a straight handle for the page turning task. Thisis the most likely way a person wearing an orthosis would perform this task, and it is asimple daily-living aid to construct.To 'wash' the face, a washcloth was passed over the left cheek, the right cheek and thenreturned to the starting position. To 'brush' the teeth, a toothbrush was held at the front teeth,the left teeth and then the right teeth. Since it was assumed that the orthosis user would usean electric toothbrush, the up and down motions were not required. To comb the hair, eachsubject performed his or her choice of five strokes.41For reaching into the lap, a television remote control was placed on the legs, just in front ofthe knees. Starting with the hand relaxed on the leg, the subject reached forward to theremote then returned to a relaxed position. The inclusion of this task allows the user to reachobjects in the lap (a common place to put things), scratch a knee (a common aggravation) andhave a more relaxed, less obtrusive arm position. All other tasks were performed on thetabletop.4.3 Motion Analysis  SoftwareIn order to analyse the tasks, software was developed [99] to:1. Control the VCR,2. Load and manipulate the video image,3. Track the markers,4. Solve for the three-dimensional coordinates of each marker,5. Display stick figure diagrams of the movement and,6. Calculate the joint angles.Although software was originally obtained from the University of Manitoba to perform thesefunctions [64, 102], the incompatibilities between frame grabbers and VCRs, as well asdiscrepancies in the choice of marker positions and method of calculating the joint anglesnecessitated developing a completely new program. The hardware used in the system is listedin Appendix D.424.3.1^Joint  Angle  Definitions Shoulder DefinitionsThe human arm can be approximated by seven degrees of freedom modelled as sequence-dependent rotations. In anatomy, "abduction" describes lifting the arm up to the side while"flexion" describes lifting the arm forward. There is no definition for any position betweenthese two. If abduction follows flexion, however, the axis of abduction changes. Abductionfollowed by flexion is therefore different from flexion followed by abduction. Both Safaee-Rad [102] and Lipitkas [62] used "flexion", "abduction" and "inward/outward rotation" todescribe the shoulder joint. This is a common definition for other joints as well, such as thehip and wrist [38,110]. Another approach, by An et al. [2], was to use "latitude", "longitude",and "axial rotation" to define the motions. This research instead defines the shoulder rotationsas "azimuth", "elevation" and "roll", definitions that have only been used recently, by From[32] and Maulucci [67]. These rotations are defined in Section 4.3.2.There are two major advantages to using azimuth, elevation and roll. The first is that theorthosis design and control is more likely to correspond to this coordinate system. Thesecond is that, since both azimuth and elevation occur about fixed axes, the coordinates areeasier to visualize.Eukrian vs. Direct CalculationsThe analysis performed here differs from previous studies in that joint angles are solved fordirectly, based on a model of the human arm. Although not as general as the Eulerianapproach, the results are more consistent. In the Eulerian method used by Safaee-Rad [102],43Langrana [54] and Lipitkas [62], marker locations are used to define a set of axes at eachjoint. A transformation matrix is then determined between each set of axes. The numericalvalues of this matrix are equated with the theoretical Euler matrix of three successiverotations to determine the joint rotations. (See Appendix F for a sample calculation.)Because of inaccuracies in the definition of the axes based on the marker locations, thesolution for the three rotations can be inconsistent. Since the calculation of the endpointposition using the resulting joint angle values is therefore also inconsistent, it was decided tocalculate the joint angles directly.Carrying AngleA necessary assumption of the direct method was to defineplane of elbow flexion. The carrying angle is defined withangle between the forearm and the extension of the upperarm. The angle results from the geometry of the bones atthe elbow joint, as shown in Figure 4-7. There arevariations, however, in the reported values. While Bermereports that men typically have a carrying angle from 10to 15 degrees and women have a carrying angle from 20to 25 degrees [7], Hoppenfield reports that 5 degrees isnormal for males and that women normally vary between10 to 15 degrees [47]. The carrying angle measured forhow the carrying angle affects thethe arm fully extended as theFigure 4-7: Carrying AngleBone Configuration (After [471)the three males in this study were 10, 13 and 14 while the females had carrying angles of 10,14 and 19.44For the purposes of this research the carrying angle is considered constant, describing aconstant tilt in the plane of elbow flexion. This is supported by Chao and Money [15,74]and Youm et al. [118] in their studies of elbow motions (although the defined order ofrotations is switched). Both studies demonstrated that forearm rotation does not significantlyaffect the carrying angle. Chao and Money recorded a constant carrying angle throughoutelbow flexion while Youm et al. recorded deviations in the carrying angle and a zero degreecarrying angle past 90 degrees of elbow flexion. Because of the discrepancy, because thedifference does not have a large effect, and for the sake of simplicity, a constant carryingangle was used in this research.In summary, there are three ways in which this analysis differs from previous work:1. A clearer definition of shoulder joint rotations is used, which is more suited toorthosis design.2. Each joint angle is calculated directly, based on a model of the arm, instead ofsolving for the three Euler rotations simultaneously at each joint.3.^A passive carrying angle is defined which rotates the plane of elbow flexion.4.3.2^Joint Angle  CalculationsThe azimuth angle is the rotation about a vertical axisthrough the shoulder joint (see Figure 4-8). Zerodegrees is defined as the upper arm directed towards theside. The following calculations are valid for the rightarm only.Figure 4-8: Azimuth AngleDefinition 45Let p, be the projection of r„ onto the horizontal plane XY (defined by the normal vectorZ), where the vector r„ is defined as the vector from marker 1 to marker 2. This conventionis used throughout the calculations.Then,and,(riz • Z)p1 = ri2 -1212Z^(4 - 1)Oa = azimuth = arccos (4-2)Elevation is the angle of rotation up from a vertical position, about a horizontal axis throughthe shoulder joint (see Figure 4-9). Zero degrees of elevation is defined as the upper armpointed straight down.Figure 4-9: Elevation AngleDefinition46Thus,--- elevation arccos (r12^• (-2))1r121(4 -3)Although carrying angle and roll are sequence independent, the coordinates are dependent andare not uniquely determined by the positions of the markers. The subject's measured carryingangle is therefore input into the program in order to calculate a value for roll. For thepurposes of the following calculations, let thecarrying angle = 0, (measured)^(4 -4)Roll occurs about the axis of the upper arm (see Figure 4-10a,b). Elbow flexion is defined tobe zero with the arm fully extended (see Figure 4-11).Figure 4-10a: Roll Anatomical^Figure 4-10b: Roll AnatomicalDefinition, Upper Ann Horizontal (After^Definition, Upper Arm Vertical (After[1021)^ [1021)47Figure 4-11: Elbow Flexion Anatomical Definition (After [102])Vector n, in Figure 4-12 is normal to the upper arm, facing forward when the azimuth iszero. Plane A in Figure 4-12 isdefined by the upper arm and by theforearm with the elbow flexed at 90degrees. That is, plane A consists ofthe upper arm and the vector n2,which is rotated from n, by the upperarm roll. Plane B is the plane inwhich the forearm moves. Plane B isrotated from plane A by the carryingangle, O.Figure 4-12: Roll and Elbow Flexion AngleDefinitions4804. = elbow flexion =&mos ( T23"^)jfir2311r2p21(r21,2 • ru.) 0 (flexion <(4-8) —11)27C - arccos ( 1rr23 • r2p2 ) if 0.4,22311r2p21^• r12) <0 (flexion > —II )2Thus,ni = Z x ri2^(4-5)n2 = r21 x r2p2 (4-6)= roll = 1 + =COS- atCZOS x rt.2) • r21 s 0 (inward rotation)x n.2) r2i > 0 (outward rotation) (4-7) ■The position of point p2, the projection of point 3 (the wrist) onto the line of the forearm infull extension, is derived in Appendix G.Forearm rotation is defined as rotation about the axis of the forearm. At zero degrees, thewrist extension is perpendicular to plane B, the plane of forearm movement. Zero rotationhas conventionally been defined as the thumb facing up when the elbow is flexed by 90degrees (see Figure 4-13). There is no definition at any other position. In this study, theneutral position is rotated inward by the carrying angle because of the tilt in the plane of49elbow flexion. Pronation, or inward rotation, is defined here as positive while supination, oroutward rotation, is defined here as negative.Figure 4-13: Traditional Forearm Rotation AnatomicalDefinition (After [161)Figure 4-14: Forearm Rotation AngleDefinitionThe calculation of forearm rotation assumes that the wrist extension is perpendicular to theforearm axis. To ensure that this is the case, rm is projected onto the plane defined by r23.This projection is referred to as r34'.r(r34 • „)rm = T34^ir- 4'7 113d(4-9)50e = forearm rotation = maxisf^1r341 • n4  j144 11n41 (4-11)Let n, be the vector normal to plane B, as shown in Figure 4-14:114 = r2p2 X T 23 (4-10)Then,For wrist flexion, a positive angle refers to bending the hand down (flexion), a negative angleto bending the hand up (extension), as shown in Figure 4-15. Referring to Figure 4-16, let p,be the projection of r35 onto the plane of the forearm defined by n,, where:/115^M= r x r 32 (4 - 12)(ras • n.P4 = r35 -^'1115 1 2 1 n^(4 - 13)5Figure 4-15: Wrist Flexion AnatomicalDefinition (After [102])51Figure 4-16: Wrist Flexion and WristYaw Angle DefinitionsFigure 4-17: Wrist Yaw AnatomicalDefinition (After [102])So that,+^(p4 • 7.23 )arCCOS jf p4 • r34 s 0^(flexion)1114iir231)0ye = wrist flexion = I (4-14)(P4 • rn )_ if p4 • r ^0^(extension)&CCM [P4 HT23 I)Positive wrist yaw refers to moving the right hand to the left (radial deviation) while negativewrist yaw refers to moving the hand to the right (ulnar deviation), as shown in Figure 4-17.0 = wrist yawwy = I rss • p4)^(^+ arccos if rss • ns s 0 (radial deviation)Ir3511P41ras • p4)- = (^cos ^ff r35 • n5 > 0 (ulnar deviation)Iras I 041(4-15)52The above equations provide the initial calculations for the joint angles. Adjustments aremade to consider quadrant indeterminacy and to move the markers to the joint centres. Dueto the quadrant indeterminacy of arccosine, the solution for azimuth is in the first quadrantwhen the arm is in the fourth. Also, occasionally when the arm is close to vertical, themarkers will indicate that the arm is in the third quadrant (behind the back) when in fact it isin the first. The following corrections are therefore included:if (pi • Y) < 0^(4 - 16)if (pi^< 0azimuth = it - azimuthelevation = - elevationroll = it - rollforearm rotation: choose the alternate 112 & recalculateif (pi^> 0azimuth = - azimuthAnother consideration is that an error is introduced into the above joint angle calculationsbecause the markers are on the outside of the arm. Past studies have accepted thisapproximation. In this study the distance between the marker centroid and the joint centre wasmeasured for each joint. The markers are then translated mathematically to the joint centresfor a better estimate of the joint angles. The greatest difference in joint angle values occursbecause of the apparent movement of the wrist when the forearm rotates. For example, thewrist marker rotates at a radius of 35 mm, on average, from the centre of the wrist. Bothelbow flexion and roll then appear to change by approximately 8 degrees, whereas at most theinaccuracy of defining the distance between the centres would lead to an error of 2 degrees.53The vectors are first calculated as described above. The markers are then translated along theappropriate vector, from the marker to the joint centre, by the distance measured on thesubject.i)^The shoulder marker (marker 1) is moved along vector r„ x n2 (refer toFigure 4-12).The elbow marker (marker 2) is also moved along vector r„ x n2 (refer toFigure 4-12).iii) The wrist marker (marker 3) is moved along vector r43', down the adjustedwrist extension (see Figure 4-14). The adjusted marker 4 remains in the sameposition.iv) The hand marker (marker 5) is moved along vector r35 x p, if (r35 X P4)•r34' <0 (i.e. the vector is pointing into the knuckle) and in the opposite directionotherwise (see Figure 4-16).The joint angle results shown below are based on the adjusted marker positions.4.4 Accuracy of the System The static accuracy of the system was tested using stationary markers with known positions.Errors in the static accuracy may be due to inaccuracies in the camera calibrations,nonuniform lighting causing noncircular images of the spheres, noise in the image analysissystem or lens distortion. The static accuracy of this system was found to be ± 1 pixel = ± 3mm ± 0.3% based on the field of view. This is an improvement over that of the Universityof Manitoba system (0.8%) [102] and the Langrana system (1.8%) [54] due to differences inthe size of the field of view, and significantly better than the 4% in Shapiro's system [107].For dynamic accuracy, the known distance between the wrist marker and its extension wastracked as the arm moved. This gave a dynamic accuracy of ± 4 mm. The possible causes of54dynamic inaccuracies are changes in the illumination of the markers, elongation of the markerimages during quick movements and the inexact synchronization between cameras.Inaccuracies in the joint angle values due to the imaging system inaccuracy are greatest at thewrist (± 3 degrees) because the markers are closest together in this region. In addition,although the marker positions are well defined at the wrist and on the hand, the short distancebetween markers causes joint angle inaccuracies of ± 3 degrees related to errors in positioningthe markers. Positioning of the shoulder marker has the most variability but the length of theupper arm limits the region of error to only ± 2 degrees in the resulting joint angles.Overall, the coordinates accuracy is ± 5 mm and the joint angles accuracy is ± 4 degrees,which is sufficient for the purposes of this study.4.5^Results4,5,1^Single  Subject/  single Each of the 22 tasks is distinctive, both in terms of the range of motion required for eachjoint and in terms of the path taken to perform the task. It is clear, for example, that Eatingwith the Hands and Brushing the Teeth involve quite different motions despite both bringingthe hand to the mouth. Figures 4-18 and 4-19 show the raw data angle-time graphs for thetwo tasks, with each line representing a different joint angle. Representative angle-timegraphs for all of the tasks are included in Appendix H.55N AZIMUTHI> ELEVATNO ROLLx ELBOW/ FOREARM+ WRISFLEXO WRISTYAWAZIMUTHELEVATNROLLELBOWFOREARMWRISFLEXWRIST YAWFigure 4-18: Angle-Time Graph for Eating with the HandsFigure 4-19: Angle-Time Graph for Brushing the TeethThe tasks can be roughly linked together in terms of the path taken by the endpoint (althoughthe orientations may be different) as follows:1.^The 6 Reaching tasks^(Across the table, parallel to the body)Page Turning562. Eating with the Hands (Towards the face or head, from below)Eating with a ForkDrinking from a CupLifting a Phone ReceiverWashing the FaceBrushing the Teeth3. Flipping the Light Switch (Up and out)Pointing to the Button4. Door Lever (Out, perpendicular to the body)Door KnobTurning the TapThe remaining tasks, Eating with a Spoon, Combing the Hair, Pouring from a Pitcher andReaching to the Lap, have distinct paths and endpoints. Eating with a spoon differssignificantly from either of the other two eating tasks because of the need to keep the spoonlevel, needing greater elevation, roll and wrist flexion. The results show that eating with aspoon and combing the hair place complex demands on the orthosis design.Before this motion analysis study, one possibility for orthosis control was to program"component movements" into the orthosis. Upon examining the results, however, there arenot sufficient similarities between tasks, in both position and orientation, to support thisapproach.The flexibility of the subjects' fingers added movement beyond the basic seven degrees offreedom. While lifting the cup to the lips, for instance, the thumb often rotated down tocause the cup to rotate. Not having this flexibility, the orthosis would have to compensatewith greater forearm rotation.57^4.5.2^Single Subject/  Multiple  Trials For one subject, four trials of each task were analysed to quantify the variability for a singleindividual. Table 4-1 tabulates the results. The sample standard deviation is used because ofthe low number of samples.The table shows that the results are repeatable with elevation being the most consistent andwrist flexion the least. Based on these tests, the average joint angle standard deviation wasfound to be 3.0 degrees. Washing the Face, Combing the Hair and the starting position ofReaching to the Lap were the most variable.^4.5.3^All  subjects  LSingle  Trial Comparisons The average minimums and maximums for each joint angle were calculated for each task forthe six subjects. Table 4-2 summarizes the results; the full table is included in Appendix I.58 AZIMUTH I ELEVATION 1^ROLL E-FLEX^F-ROTN W-FLEX^W-YAWAvgMinStddevAvgMax DevStd-AvgMinStddevAvgMaxStdDevAvgMinStddevAvgMaxStdDev..AvgMinStddevAvgMax DevStd-AvgMinStddevAvgMaxStdDev.AvgMinStddevAvgMaxStdDevAvgMinStddevAvgMaxStdDev'HANDS 332.5 60 3.8 30 1.4 49 5.3 -53 7.1 7.268 1.9 134 4.9 - 8.2 52 0.9-16 2.9 217.1 -156.1 103.0FORK 23 -2. 39 3.0 34 0.3 61 2.0 -28 3.3 10 2.9 80 0.8 136 3.3 -32 3.0 75 4.7 3 5.5 47 13. -21 8.4 12 3.4SPOON 20 1.1 44 2.2 31 0.3 74 5.6 -60 5.5 5 2.9 84 1.4 132 8.8 -9 6.6 77 5.8 -2 2.9 41 4.1 -16 6.2 18 2.2CUP 22 13 45 3.9 29 1.7 68 2.6 -65 2.4 2.2 75 1.1 142 2.4 8 25 51 25 -31 4.7 21 4.6 -19 2.9 4 3.4RCH1A 13 2.5 47 3.6 30 1.3 35 1.5 -50 3.5 ' -31 3.3 69 1.3 85 3.0 -16 3.8 2 2.0 -30 2.6 -5 2.8 -16 3.9 2 3.5RCH2A 40 1.6 76 11. 31 2.5 43 2.9 -37 1.5 -23 5.3 3.5 2.4 -19 6.4 2.1 -31 6.3 -16 5.1 -10 4.3 -2 1.5RCH3A 38 1.0 111 0.9 32 0.4 44 0.9 -40 3.0 -22 1.6 54 1.5 82 1.5 -18 3.2 -2 3.4 -31 1.7 -9 4.5 -10 3.9 -0 1.2RCH1B 11 0.6 43 1.1 35 0.3 40 1.3 -32 0.6 -18 1.0 68 1.2 79 1.4 48 3.4 58 2.2 -19 0.3 -6 1.0 -7 3.2 3 3.2RCH2B 39 2.1 79 1.7 35 1.1 44 1.8 -31 1.7 -20 15 60 1.4 77 1.6 47 2.1 57 0.9 -17 2.1 -6 3.5 -8 0.6 1 2.0RCH3B 41 0.7 109 1.1 34 0.9 46 1.2 -32 3.2 -19 3.0 51 1.3 78 1.3 45 3.2 59 2.6 -18 2.4 -7 43 -7 2.0 2 1.5POUR 34 2.7 73 3.4 33 13 87 4.4 -45 5.4 -17 42 57 35 84 4.2 -46- 4.6 47 2.7 -31 6.5 -1 6.4 -18 2.8 -2 3.0DOOR 39 1.8 71 0.5 34 1.1 57 2.4 -47 1.0 -18 1.3 58 3.4 84 1.9 4 11. 59 1.3 -26 2.8 -2 1.3 -9 1.5 6 1.9KNOB 36 2.6 64 15 38 1.1 65 '0.9 -38 3.3 -10 1.4 42 1.7 81 1.9 11 7.6 62 3.0 -40 5.1 -6 4.7 -13 4.0 3 2.6TAP 37 3.3 66 2.4 34 1.2 63 2.3 -51- 6.0 -24 3.2 59 2.2 74 1.5 25 12. 61 1.2 -15 2.1 26 1.1 -39 2.5 6 2.6LIGHT 40 3.8 73 1.8 33 1.0 94 3.2 -64 6.3 -27 3.6 43 1.7 85 10. -40 6.4 56 4.3 -21 0.8 6 55 -26 4.4 -5 2.2BTTN 44 2.7 68 2.5 33 1.4 85 2.6 -63 1.8 -27 5.1 56 1.4 85 6.6 24 4.5 53 1.8 5.0 5 7.0 -13 3.9 -3 23PAGE 6 1.4 66 3.9 27 15 43 3.4 -24 1.7 -5 2.9 84 1.7 97 1.7 53 2.7 70 1.7 -21 3.4 21 1.4 -20 3.5 10 2.1PHONE 36 1.7 71 4.3 36 0.8 65 3.1 -87 4.8 -29 2.1 74 0.7 153 1.1 -20 3.4 57 1.2 -28 6.3 2 4.6 -20 2.4 8 1.6LAP 4 8.6 83 1.9 9 0.2 32 0.7 -33 1.4 30 6.8 56 2.0 84 1.5 52 2.5 66 2.9 -28 53 23 2.2 -13 3.3 4 1.2WASH 30 5.6 99 3.0 21 1.5 55 0.9 -87 3.4 -23 3.4 76 1.5 150 2.2 -93 2.3 56 2.5 -43 5.1 10 4.8 -28 0.4 4 2.0BRUSH 28 1.0 59 2.9 35 1.1 86 2.8 -83 4.1 -20 2.9 76 1.1 143 4.8 -30 8.1 48 3.1 -19 52 41 13. -23 4.8 15 3.6COMB 29 2.3 97 2.4 32 1.2 82 1.0 -103 5.9 -26 2.6 75 1.4 156 1.7 -26 2.5 55 1.0 -40 4.4 27 7.9 -22 5.2 20 1.7EXTREM. 4 111 9 94 -103 10 42 156 -93 77 -43 47 -39 20AVG SD 2.2 2.8 1.0 2.4 3.5 3.0 1.7 3.2 5.0 2.4 3.8 5.0 3.6 2.4Table 4 -1: Motion Analysis Results, Single SubjectLeastAvg. Min.(degrees)TaskWhere L.A.M.OccursGreatestAvg.Max.(degrees)TaskWhere G.A.M.OccursAverageRange(degrees)Azimuth 7 Page^(sd 6)ReachlA (10)ReachlB^(7)Lap^(23)108 Reach3A (sd 5)Reach3B (sd 7)40Elevation 15 Lap^(sd 3) 96 Light^(sd 6) 26Roll -85 Comb (sd 12) 20 Lap^(sd 25) 34E-Flex 42 Knob^(sd 4) 151 Phone^(sd 15) 39F-Rotn -86 Wash (sd 18) 61 Page^(sd 6) 52W-Flex -42 Wash (sd 10) 53 Spoon^(sd 16) 33W-Yaw -39 Tap^(sd 6) 24 Comb^(sd 10) 21Table 4-2: Summary of Motion Analysis Results, All SubjectsThe standard deviation for the average minimum and maximum joint angles for these testswas found to be 8.0 degrees.A comparison of the plots for the path of the hand for each task showed that the personalhygiene tasks, Washing the Face, Brushing the Teeth and Combing the Hair were the mostvariable from person to person. All of the others were quite similar, although the headposition varied between individuals for the eating tasks.There were no identifiable differences between the male and female subjects except withelbow flexion in which subjects with longer arms did not have to extend the arm as much toreach the same position.604.5,4^Comparisons  with  Previous  Work Figures 4-20 to 4-26 compare the results from this study to previous ones with each jointbeing compared individually. The abscissa range shows the approximate joint limits for eachjoint angle [11]. Since more researchers have studied elbow and wrist motion than shouldermotion, these will be discussed first. In each case, the leftmost end of each horizontal linerepresents the average minimum for that task, the rightmost end the average maximum.When the standard deviation for the average maximum or minimum was given, vertical lineswere included to indicate ± one standard deviation about the minimum or maximum, thus68% of the population would fall within these limits.Two previous researchers have quantified elbow flexion and forearm rotation for functionaltasks: Safaee-Rad et al. [103] and Morrey, Chao et al. [15,74]. The former used a video-based motion analysis system to examine the whole-arm movement in performing Eating witha Fork, Eating with a Spoon and Drinking from a Cup; the latter used a triaxialelectrogoniometer to study elbow motion exclusively. The Safaee-Rad study included tenmale subjects while the Money study included 15 male and 18 female subjects. Nosignificant difference was found between the male and female subjects.In general, the results of the present study (marked UBC) shown in Figures 4-20 and 4-21compare well with the previous studies. The layout of the objects on the table, which wasdifferent between studies, affects how far the subject must reach and thus the minimum elbowextension. Also, trunk movement was not restricted in the other studies. Differences in theamount of elbow flexion are therefore to be expected.61}OM UBCPORI: [102(JOEL [74]SPOON: UBCSPOON: [102]CUR UBCCUR DOMCUP: [74]POUR UBCPOUR: [74]11:NOR UBCINOlt [74]PAGE: UBCPAM: [74]PHONE: UBCPRIME: [74]-75 -50 -25^0^25^50^75Forearm Rotation Angle (Degrees)KAM: UBCPORI: [1021PORX.: 1741SPOON: IRICSPOON: [102]CUP: UDCant [1M]CUP [741-__-_-_-_i _-----^___-__-POUR UBC-I-POUR: (74]-- ^-XT4Oft 1JBC-_INOlk [74]-- ^-PAOR UBCPAGB: [741- ^- --PHONE: UBC_-PBC0411: [74]-1 I I0^40^80^120^160Elbow Flexion Angle (Degrees)Figure 4-20: Comparison of Motion Studies for Elbow FlexionFigure 4-21: Comparison of Motion Studies for Forearm Rotation62There are several explanations for the differences in forearm rotation. The subjects in thisstudy used an overhand cylindrical grasp to hold onto the fork and spoon whereas subjects inthe other studies used the more traditional underhand web-of-thumb grasp. While morepractical for an orthosis, the overhand grasp requires more pronation (positive forearmrotation). The type of pitcher used, a gardening pitcher for this study, a beverage jug for theMorrey study, may account for the differences in pouring. In the "Knob" task, "Opening aDoor" [74] was compared to "Turning a Door Knob while seated at a table" (UBC): theseated subjects reached for the doorknob in a more pronated orientation whereas those whowere standing chose a more supinated orientation; opening the door itself would also requiremore supination. Similarly "Page Turning" for the UBC study used a handled page turner,causing the hand to be more pronated than for "Reading a Newspaper" in the Money study.The definitions of forearm rotation also vary, as outlined in Section 4.3.2 and Appendix F.Three researchers have studied functional wrist motion: Safaee-Rad et al., as mentionedabove, Ryu et al. [101] and Brumfield & Champoux [13]. Ryu studied 40 subjects (20women, 20 men) with a biaxial wrist electrogoniometer while Brumfield and Champoux useda uniaxial electrogoniometer to examine just the wrist flexion of 19 subjects (7 women, 12men). Palmer et al. [86] studied functional wrist motion, but only reported the centroid ofeach joint angle rather than the extremes so the results are not shown here.The graph comparing wrist flexion (Figure 4-22) shows the effect of the overhand grasp oneating with a fork, eating with a spoon and page turning even more dramatically than forforearm rotation. It was clearly more awkward for the subjects to get the food onto the forkor spoon and to keep the spoon level as it was raised. The wrist flexion used to "Turn a Tap"63(UBC) versus "Opening and Closing a Faucet Handle" [101] depends both on the shape andthe height of the tap, which was not documented. All of the other task motions are quitesimilar. The comparisons of wrist yaw (Figure 4-23) show similar results to those for wristflexion.Figure 4-22: Comparison of Motion Studies for Wrist Flexion64Wrist Yew Angle (Degees)10 20 30COM UDCCOM pai)-60 -40 -30 -20 -10 0/POOR UDCWOO* (102)POOR; MCPOOL poiTAT UDCTAT poi)a. imant TECIL 'MOT pal---Figure 4-23: Comparison of Motion Studies for Wrist YawOnly one researcher, Safaee-Rad, has documented shoulder motion while performingfunctional tasks, although others, such as Lipitkas [62] and Maulucci [67], have studiedreaching to specific locations. The rotation axes chosen were "flexion" followed by"abduction" followed by inward/outward "rotation". The results were translated to azimuth,elevation and roll for comparison with this study. Appendix J gives the details of thistranslation.Safaee-Rad reported two sets of results: the original, or initial, joint angles calculated (I) andthe joint angles shifted by an initial deviation (D), based on the subject's standard position.However, the standard position was established only by visual inspection, which Safaee-Radnoted to be inaccurate. Both results are presented here.65TIOM UDCPam perzi IADM [1M] DSPOON: UDCSPOON: PM] ISPOON: [102] DCUP: UDCCUP: [102] ICUP: D-45^15^75^135Azimuth Are (Degrees)Figures 4-24 to 4-26 show a wide variation between Safaee-Rad's original results and theresults with the initial deviation taken into account. In general, the original calculations are inbetter agreement with the current study. The ranges of roll and azimuth are greater becausethe current study includes picking up the fork and spoon as part of the task; the Safaee-Radstudy only considers the task between the point of loading the food to unloading it into themouth. In addition, eating with a spoon requires both greater elevation and greater rollbecause of the grasp type used in the current study, as mentioned previously. Eating with afork shows greater roll in the UBC study because of the grasp position. Drinking from a cuprequired more roll, the amount of roll being largely dependent on the amount of liquid in thecup, which was two-thirds full in this study; the spouted no-spill cup also required the cup tobe rotated slightly more. The wide variation in azimuth demonstrates the variety of techniquesused by the individual subjects to drink.Figure 4-24: Comparison of Motion Studies for Azimuth66__PORK: UBCFORM [102] IPORI: [KM DSPOOK lUBCSPOON: (1Q2]1SPOON: [102] DCUP: UBCCUP: [102] ICUP: [102] D-100 -75 -50 -25 o^25 50 75Roll Angie (Degrees)FORM UBCPORI: [102] IFORM [102] DSPOON: UDCSPOON: [102] 1SPOON: [102] DCUP: UBCCUP: [102] 1CUP: [102] D__ ----- _- _-I^1^I^I0 40^80^120^160Elevation Angle (Degrees)Figure 4-25: Comparison of Motion Studies for ElevationFigure 4-26: Comparison of Motion Studies for Roll674.5.5^Implications  for  Orthosis  Design For each joint, the average minimums, average maximums and extremes of all subjects wereplotted for each task. This gave insight into the possibilities for fixing or otherwisesimplifying each joint. The rightmost point of each solid line is the average maximum forthat task, while the leftmost point is the average minimum for that task. The dashes are thehighest and lowest individual joint angle values for that task. As with the graphs comparingmotion studies, the abscissa axis represents the approximate joint limits.Two ways to simplify the degrees of freedom are to:1) fix a joint rotation, or2) couple two or more joint rotations together.One other possibility is to fix a joint rotation but have more than one predetermined positionsuch that an attendant could change the orthosis from one mode to another. This wasconsidered but was not found to be desirable because there was no clear division of tasks,such as eating, when an attendant would be present to change the mode.Shoulder Motion - Azimuth, Elevation and RollFigures 4-27 to 4-29 show that all three joint rotations of the shoulder vary considerably fromtask to task. A wide range of azimuth and roll is required in order to reach the variouspositions on the table. A low elevation is required to reach to the lap, a high elevation toreach the light switch and so on. It is therefore not immediately obvious which one(s) can befixed or should be fixed. Specific tasks would be sacrificed if any of the shoulder rotationswere entirely fixed. The decision concerning which to fix and which to power will be basedon the results of the simulations and the priority of the tasks as identified in the interviews.68EATING - HANDSEATING - FORKEATING - SPOONDRINKING - CUPREACHING - IAREACHING - 2AREACHING - 3AREACHING - IBREACHING - 2BREACHING - 3BPOURINGT. DOOR LEVERT. DOOR KNOBTURNING TAPSW. LIGHTPT, BUTTONTURNING PAGELIFTING PHONEREACHING - LAPWASHING FACEBRUSH. TEETHCOMBING HAIRo^40^80^120^160Elevation Angle (Degrees)EATING - HANDSEATING - FORKEATING - SPOONDRINKING - CUPREACHING - IAREACHING - 2AREACHING - 3AREACHING- IBREACHING - 2BREACHING - 3BPOURINGT. DOOR LEVERT. DOOR KNOBTURNING TAPSW. LIGHTPT. BUTTONTURNING PAGELIFTING PHONEREACHING - LAPWASHING FACEBRUSH. TEE I HCOMBING HAIR-45^0^45^90^135Azimuth Angie (Degrees)Figure 4-27: Azimuth: Average Min/Max & Extremes for All SubjectsFigure 4-28: Elevation: Average Min/Max & Extremes for AllSubjects69EATING - HANDSEATING - FORKEATING - SPOONDRINKING - CUPREACHING- IAREACHING - 2AREACHING - 3AREACHING - IBREACHING - 2BREACHING - 3BPOURINGT. DOOR LEVERT. DOOR KNOBTURNING TAPSW. LIGHTPT. BITITONTURNING PAGELIFTING PHONEREACHING - LAPWASHING FACEBRUSH, TEETHCOMBING HAIR-100 -75^-50^-25^0^25^50^75Roll Angle (Degrees)Figure 4-29: Roll: Average Min/Max & Extremes for All SubjectsElbow Flexion and Forearm RotationElbow flexion must be powered because elbow flexion alone defines the distance from theshoulder to the wrist. Figure 4-30 shows the range of elbow flexion from the averageminimum to the average maximum for each task. All of the tasks, except the reach tasks,vary considerably in forearm rotation, as shown in Figure 4-31. In addition, most involveboth pronation and supination (positive and negative forearm rotation), especially the eatingand personal hygiene tnsks since a utensil must first be picked up and then pointed towardsthe face. Forearm rotation must therefore either be powered independently or coupled withelbow flexion.70EATING - HANDSEATING - FORKEATING - SPOONDRINKING - CUPREACHING- IAREACHING - 2AREACHING - 3AREACHING - IBREACHING -28REACHING - 3BPOURINGT. DOOR LEVERT. DOOR KNOBTURNING TAPSW. LIGHTVT. BUTTONTURNING PAGELIFTING PHONEREACHING - LAPWASHING FACEBRUSH. TEETHCOMBING HAIR-75^-50^-25^0^25^50^75Forearm Rotation Angle (Degrees)EATING - HANDSEATING - FORKEATING - SPOONDRINKING - CUPREACHING - 1AREACHING - 2AREACHING - 3AREACHING - 1BREACHING -28REACHING - 3BPOURINGT. DOOR LEVERT. DOOR KNOBTURNING TAPSW. LIGHTVT. BUTTONTURNING PAGELIFTING PHONEREACHING - LAPWASHING FACEBRUSH. TEETHCOMBING HAIR40^80^120^160Elbow Flexion Angle (Degrees)Figure 4-30: Elbow Flexion: Average Min/Max & Extremes for AllSubjectsFigure 4-31: Forearm Rotation: Average Min/Max & Extremes for AllSubjects71The Hugh MacMillan orthosis uses the second option, coupling forearm rotation and roll toelbow flexion, but this makes the orthosis extremely limited. Because of the defined forearmrotation, the user cannot drink from a cup or reach for any object with the hand upright. Theuser also cannot eat with a spoon, brush the teeth, comb the hair, wash the face, pour from apitcher or switch a light, which are most of the tasks under consideration. In fact, otherresearchers studying functional arm movement have mentioned the priority of forearm rotation[27,50,1031 The motion analysis results therefore indicate that forearm rotation should beindependently powered.Wrist Flexion and Wrist YawFigure 4-32 shows that the required wrist flexion covers a smaller percentage of the total jointlimit range than for most of the other joints. It is also quite variable between individuals,indicating that more options are possible. If wrist flexion is fixed, the ability to preciselyorient the hand will be lost. However, orientation is not critical for most of the tasks,allowing them to be done differently by an orthosis wearer than by an able-bodied person.Problems with keeping a spoon level, brushing the teeth or combing the hair may beovercome using special handles. Therefore, there is a potential for reducing orthosiscomplexity without a major sacrifice in task performance by fixing wrist flexion.The total joint limit range of yaw motion is quite small, as shown in Figure 4-33.Furthermore, both wrist flexion and wrist yaw are at the end of the kinematic chain so that nofurther joints are affected. Consequently, there is also potential for reducing orthosiscomplexity without significantly reducing functionality by fixing wrist yaw.72EATING - HANDSEATING - FORKEATING - SPOONDRINKING - CUPREACHING - lAREACHING - 2AREACHING - 3AREACHING - IBREACHING -28REACHING - 3BPOURINGT. DOOR LEVERT. DOOR KNOBTURNING TAPSW. LIGHTPT. BUTTONTURNING PAGELIFIING PHONEREACHING - LAPWASHING FACEBRUSH. TEETHCOMBING HAIR-50 -40 -30 -20 -10^0^10^20^30Wrist Yaw Angle (Degrees)EATING - HANDSEATING - FORKEATING - SPOONDRINKING - CUPREACHING- 1AREACHING - 2AREACHING - 3AREACHING - 1BREACHING -28REACHING - 3BPOURINGT. DOOR LEVERT. DOOR KNOBTURNING TAPSW. UGHTPT. BUTTONTURNING PAGELIFIING PHONEREACHING - LAPWASHING FACEBRUSH. 1E11 HCOMBING HAIR-75^-50^-25^0^25^50^75Wrist Flexion Angle (Degrees)Figure 4-32: Wrist Flexion: Average Min/Max & Extremes for AllSubjectsFigure 4-33: Wrist Yaw: Average Min/Max & Extremes for AllSubjects73Fixing both wrist rotations hampers the flexibility of orientation, forcing tasks to be donedifferently or to use the head or trunk to compensate. The simulation results willdemonstrate whether the ability to orient the hand without the wrist rotations is sufficient forthese tasks.SummaryBased on the results of the motion analysis, the following design should be investigated withthe simulation program:Power:^Two of the three shoulder degrees of freedomElbow FlexionForearm RotationFix:^One shoulder degree of freedomWrist FlexionWrist YawPerforming this motion analysis provided data concerning how the arm moves whileperforming daily-living tasks. This allowed some hypotheses to be developed concerning thedesign of a powered upper-limb orthosis. The simulation program described in the nextchapter uses the data to test these hypotheses.74CHAPTER 5: ORTHOSIS  SIMULATION 5.1^Introduction The final two research objectives are to develop a kinematic simulation program to testpossible configurations of a powered upper-limb orthosis and to use this simulation programto determine the simplest orthosis configuration that is still capable of performing the highest'priority tasks. Although other researchers have studied the problem qualitatively, anexamination of required degrees of freedom has never been quantified before. Thequantitative evaluation allowed design options to be examined for a wide variety of tasks andindividuals before building a prototype.The kinematic simulation algorithm determines whether a possible orthosis configuration canachieve a given position and orientation. For example, if a degree of freedom is fixed thealgorithm determines whether the remaining degrees of freedom are able to compensate inorder to still achieve the functional points required for the task. The functional points, i.e. thecritical positions and orientations, are derived from the motion analysis results. The numberof achievable and unachievable tasks is determined for each alternative configuration. Thischapter discusses the calculation procedures employed in the simulation program and theresults of the simulations. In the end, two orthosis configurations are recommended.755,2 Kinematic  Formulation The developed software minimizes a cost function to bring a simulated orthosis as close aspossible to a desired position and orientation while remaining within anatomical joint limits.It employs a forward kinematic solution procedure, calculating the endpoint position fromgiven rotations and link lengths.In robotic analysis, the more common method for finding the joint angles corresponding to adesired position and orientation is the pseudoinverse or generalized least-squares method [79].While the author was not aware of this method until after development of the optimizationapproach, further study in this area should consider this approach as it may be more efficient.The method iteratively calculates the pseudoinverse of the Jacobian of the position function todetermine the direction and magnitude of each step to be taken towards the target position.Weighting constants can be incorporated. Singularities (where no solution exists) present thegreatest difficulty; however several techniques have been developed to deal with this problem[17117811115]. There is no provision for requiring that the solution fall within joint limits.The method used in this research handles singularities, weightings and joint limit penaltiessimply.The software examines the ability to reach particular points rather than follow paths forseveral reasons. First, by dealing with just the functional points, such as loading the foodonto a fork and unloading it into the mouth, the orthosis is not constrained to follow the pathtaken by the able-bodied subjects. Second, it is more straightforward to define a point than apath and consequently it is easier to define whether a simulated orthosis can match a point76rather than match a path. Since a path is a sequence of points, it is possible, in practice, toevaluate a path by evaluating a finite sequence of points. Up to eight functional points weretested for each task. Most importantly, given two achievable points, some path can be foundbetween them unless a constraint is imposed, such as keeping a cup level.In this formulation, the arm is modelled by a sequence of one-dimensional rotations connectedby rigid link segments. Multi-dimensional joints such as the shoulder are created by joiningone-dimensional rotations with zero-length links. The sequence of rotations, in order of effecton the end position, is: azimuth, elevation, roll, carrying angle, elbow flexion, forearmrotation, wrist flexion and wrist yaw. There are three rotations at the shoulder, three at theelbow and two at the wrist. The formulation uses the Denavit-Hartenberg (D-H) method,commonly used in the robotics field, for setting up the axes and calculating the transformationmatrices [33]. Figure 5-1 shows the axis definitions.Figure 5-1: Kinematic Formulation Axis Definitions77The Denavit-Hartenberg parameters are given in Table 5-1.Joint Name 0, a, ai d,^.1 Azimuth 0 90 0 02 Elevation 90 -90 0 03 Roll 0 90 0 - upperarm4 Carrying Angle 90 90 0 05 Elbow Flexion 0 -90 0 06 Forearm Rotation -90 -90 0 - forearm7 Wrist Flexion 90 90 0 08 Wrist Yaw 0 -90 hand 0Table 5-1: Den avit-Hartenberg Parameterswhere,01•^the joint angle from the x1 axis to the xi axis about the z ^usingthe right-hand rule;a;^^the offset angle from the z axis to the zi axis about the xi axis usingthe right-hand rule;• the offset distance from the intersection of the 41 axis with the x, axisto the origin of the 1th frame along the xi axis (or the shortest distancebetween the zo and z, axes); and,di the distance from the origin of the (i-1)th coordinate frame to theintersection of the 41 axis with the x, axis, along the z1_1 axis.The general D-H homogeneous transformation matrix for adjacent coordinate frames i and i-/is given by:78PpuPi,1 cos 01 -cos atsin 01 sin aisinei aicos 0isin.0, cos I:tit:0s 01 -sin aims 01 a/sin 010^sin al^cos a0^0^0^1(5-1)where {P., p,, Pz) is an arbitrary point in the (i-1)th frame and {P., Py, Pz} is the correspondingpoint in the ith coordinate frame. In reduced form this gives:Puvw^[11(1-1, I)] Pzyz^(5-2)The top left 3x3 gives the rotation matrix from one frame of reference to the next; the right3x1 gives the translation vector. The columns of the rotation matrix define the x, y and z unitvectors of the ith set of axes, expressed in the coordinates of the (i-1)th set of axes. The fixedframe of reference (subscript 0) is defined by the identity matrix. The transformation matricesfor each joint, with C1= cos°, and S, = sin0,, are as follows:Azimuth: H01 =C1 0 S1 0SI 0 -C1 001000001(5-3)Elevation: Hu =C2 0 -S2 0S2 0 C2 00 -1 0 00 0 0 1(5-4)79C3 0^53 053 0 -C3 0Roll: H0^1^0 -uPPerarm000 ^1(5-5)Carrying Angle: H34 =-C4 0 54 6S4 0 -C4 001000 0 0 1_(5-6)Elbow Flexion:1145=C5 0 -S5 055 0 C5 00 -1 0 00001(5-7) C6 0 -; 0^-S6 0 C6 0Forearm Rotation: H56= (5-8)0 - 1 0 -forearm000 1C7 0 S7 0S7 0 -C7 00 00 1000 1•Wrist Flexion: H (5 -9)80C8 0 -S8 hand.C8Se 0 C8 hand.S8Wrist Yaw: H (5 - 10)0-10 0000 1The position of the hand relative to the shoulder is defined by the fourth column of H08,where H08 = H011-112". H78. The 'forward' orientation of the hand, corresponding to r35 asdefined in Chapter 4 for the motion analysis, is defmed by x8, the first column of H08. (Referto Figure 5-1 for the orientation axes.) The 'palm' orientation, corresponding to r43 is definedby y8, the second column of H08. The 'up' orientation, corresponding to r34 x r35 in the motionanalysis, is defined by z8, the third column of H.5,3 Cost Function The cost function upon which the optimization is evaluated involves five components:1) the squared distance between the actual and desired endpoint positions,2) the squared angle between the actual and desired 'forward' orientation vectorstimes a weighting factor,3) the squared angle between the actual and desired 'palm' orientation vectorstimes a weighting factor,4) the squared angle between the actual and desired 'up' orientation vectors times aweighting factor and5)^a penalty function for approaching or exceeding a joint limit.The components are effectively normalized by a proper choice of the weighting factors.81Orientation is included in the cost function for two reasons. The first is to ensure that theendpoint orientation is correct in order for the task function to be achieved. For example, thedirection of the fork during an eating task should be similar to that used by the able-bodiedsubjects since it is not only important that the hand reach the destination but also that the forkis facing in the proper direction. The secondary reason is that without the constraint oforientation the solution, if found, will not be unique; the arm could be rotated at any angleabout the line connecting the shoulder and wrist, as long as it is within the joint limits.Constraining the orientation to be close to that of the able-bodied subjects produces a resultthat is more natural. The weighting factor defines the relative importance of eachorientation. In general, for a particular tisk, one orientation is most important and is thereforemore heavily weighted.The penalty function, based on the penalty function proposed by Buchal and Cherchas [14],keeps the simulated arm within the natural limits of the arm. It is defined as:penalty function = E penaltyi • (el -^(5-11)where,and,penaltyi 1 0^if (01)l- eta^ei^(e,),.- etak^otherwise (5-12)_J (e)r.th+ etaega^el (0,) ^etaif 0, k (0) ^eta (5-13)82The constant k is made large enough to produce a cost function value that indicates anunsuccessful configuration even if the desired position and orientation are achieved since theconfiguration cannot be accepted with joint limits exceeded. Instead, the minimization routinecontinues to search for solutions within the joint limits. While an exponential function wouldproduce a more realistic representation, the step function is reasonable because the arm iscomfortable throughout the joint range, until very close to the joint limit.The cost function is therefore:ce) =(Ir rI)2wt • (fonv - fonvd.)2law^actWtpaius • (Pact — palMder? +Wtup • (UPact UPdta)2E [penaltyi (et - ea](5-14) where the 'act' and 'des' subscripts refer to the actual and desired values respectively, 'r' is thevector to the endpoint, 'forw', 'palm' and 'up' refer to the orientation angles and 'wt' is theweighting given to each orientation.The weighting values were typically 0.10 for the most important orientation vector (such asin the 'up' direction - along the fork - for eating with a fork) and 0.05 for the others (since,for example, rotation about the fork is less important). The rationale for these numbers isgiven in Section 5.4. The value for Ou was set to one degree. For the penalty function, kwas set to 0.5 so that the function tolerance of 6.0 was exceeded even if the position andorientation criteria were met. A maximum number of iterations of 10 was enough to find the83minimal solution in almost all cases yet halted the search for configurations that could notachieve the desired position and orientation. Appendix K gives the desired positions,orientations and initial joint angle estimates used in the simulations.5,4 Minimization  Procedure  &Program  Design The minimization procedure was adopted from Numerical Recipes in C, Chapter 10 [93]. Asexplained below, a one-dimensional line minimization is imbedded into the multi-dimensionalminimization. Brent's method with the use of first derivatives was chosen as an efficient butrobust method. For the multi-dimensional minimization the conjugate (or noninterfering)gradient method was used. The Polak-Ribiere variant was selected because of its smoothertransition to further iterations. In both the multi-dimensional method and the imbedded one-dimensional method the Jacobian is calculated analytically to improve the computationalefficiency.In the simulation program, the following steps are taken to minimize the cost function:1) A scalar function f(c) is constructed having the value of the cost function alongthe line passing through the current point and in the direction of the gradient ofao^atz)^at,ito =^— 1-41) e, + c . , e, C—,. ", e,(vvi^ae2 aeg (5 - 15)2) Three points are found which bracket the minimum of f(c) to ensure that aminimum exists. The direction of search depends on the function values attwo given abscissa; the third point is then chosen by taking steps until thefunction value increases again.843) A parabola is fit to the three points and the minimum of the parabola is foundby formula. If the parabolic step falls within the bounding interval (a,b) foundin step #2, and implies a movement from the best current value that is less thanhalf the movement of the step before last then this minimum point isexchanged with the point having the greatest function value. Otherwise theinterval is bisected, with the segment chosen by the sign of the derivative.This procedure is repeated until the value of c is not changing by greater than atolerance, the minimum step in the downhill direction takes the function valueuphill, or the maximum number of iterations is exceeded.4) The new point of interest is thenvi = v, C—ae, (5 - 16).New gradients are calculated and the procedure is repeated from step #2.5)^The procedure is stopped when either the cost function value is less than atolerance or the maximum number of iterations is exceeded.This routine finds only a local minimum. The original estimate of the joint angles musttherefore be reasonable for the global minimum to be found. The motion analysis resultsprovided this initial estimate.Upon completion of the minimization procedure the results are classified as successful, close-to-successful or unsuccessful. The criteria, based on the distance between the actual anddesired endpoint positions and the angles between the desired and actual orientations, aregiven in Table 5-2.85Distance 'Up'Angle'Forward'Angle'Palm'AngleWithinJoint LimitsSuccessful <3.0 cm < 10° < 10° < 10° YesClose <3.0 cm <20° <20° <20° YesUnsuccessful > 3.0 cm or , > 20° or > 20° or > 20° or NoTable 5-2: Success CriteriaThe criteria for success are approximately equal to the position and orientation standarddeviations for all of the tasks and all of the subjects. The close-to-successful category wasincluded because often the orientation is not as critical for performing the tasks as distance.In some cases a task may even be adequately achieved while differing from the average able-bodied orientation by more than 20 degrees, but these need closer examination.Given the criteria for success, the rationale for the weighting values can now be given. If thesolution is within the joint limits and matches the success criteria, the value of the costfunction is:(I) (0) = (3)2 + 0.10 (10)2 + 0.05 (10)2 + 0.05 (10)2= 9 + 10 + 5 + 5Thus, the contribution of distance to the cost function value is comparable to the contributionof the most important orientation. Although the two orientations of lesser importance areweighted half as much, they contribute the same amount to the cost function at 14 degrees asthe first orientation does for ten degrees. They, too, must therefore be matched closely.865.5 Comparison  of_Simulated  Fixed Elbow  to_Braced Elbow The human arm has not previously been simulated with variable reduced degrees of freedom.Motion analyses have been performed, however, with the subject's elbow physically braced ata specific angle. Maulucci [67] studied subjects performing reaching tasks with and without abraced elbow, but the results have not yet been analysed. Cooper et al. [20] studied eatingwith a fork, eating with a spoon, and drinking from a cup with and without a braced elbow,however these results cannot be used for comparison for several reasons. First, although theelbow was braced, there was still movement of up to 15 degrees. This is not comparable tothe rigidly fixed degree of freedom employed in the simulation. Secondly, the subjects wereable to move their trunks to compensate for the fixed elbow, a movement not accounted for orpermitted in the simulation. Thirdly, different hand grasps were used for the eating tasks, asexplained in Chapter 4.5.6^Results5.6.1^Preliminary  Evaluation For an initial evaluation, the positions and orientations at the extremes of each task wereanalysed. The desired positions and orientations, provided in Appendix K, were determinedby averaging the data for each subject from the motion analysis. Table 5-3 lists the 34 initialpositions chosen.87Position#Abbreviation Task Position1 H1 Eating with the Hands Picking up the Food2 H2 At the Mouth3 Fl Eating with a Fork Picking up the Food4 F2 At the Mouth5 Si Eating with a Spoon Picking up the Food6 S2 At the Mouth7 Cul Drinking from a Cup Before Tilting8 Cu2 After Tilting9 R1A Reaching, Position lA Final Position10 R2A Reaching, Position 2A Final Position11 R3A Reaching, Position 3A Final Position12 R1B Reaching, Position 1B Final Position13 R2B Reaching, Position 2B Final Position14 R3B Reaching, Position 3B Final Position15 Po Pouring from a Pitcher Fully Tilted16 D1 Door Lever Before Rotating17 D2 Fully Rotated18 K1 Door Knob Before Rotating19 K2 Fully Rotated20 Ti Tap Lever Before Rotating21 T2 Fully Rotated22 Li Light Switch Highest Point23 Bu Button Highest Point24 Pa Page Turning Farthest Left25 Ph Lifting Phone Receiver At Ear26 La Lap At Knees27 W1 Washing Face Left Side28 W2 Right Side29 Brl Brushing Teeth Centre30 Br2 Left Side31 Col Combing Hair Left Side32 Co2 Right Side33 Stl Starting Position Hand Free34 St2 Holding UtensilTable 5-3: Initial Test Positions88Coupled Degrees of FreedomCoupling degrees of freedom may produce a motion that is more suitable for taskperformance than fixing a degree of freedom. All combinations of degrees of freedom wereplotted against one another to investigate potential relationships. The only reasonablerelationships observed were to either couple roll with elbow flexion or to couple wrist flexionwith elbow flexion (Figures 5.2 and 5.3). In both cases, there is an increase in angle as theelbow flexes initially and then a rapid decrease as the elbow flexion brings the hand to theface. While numerically attractive, the coupling and reversal of motion would lead to asomewhat complicated mechanical design.Figure 5-2: Roll vs. Elbow Flexion Coupling FunctionTo couple roll to elbow flexion, the best linear relationship, shown in Figure 5-2, was:roll = 0.882 * elbow flexion - 87.6°^if elbow flexion < 1050= -1.90 * elbow flexion +204.5' if elbow flexion >. 105°89403020fig(3) 1003z —10—20—30—40—5020 40^60^80^100^120Elbow Flexion (Degrees)140^160Cu2Cut411-12Co2W2K41-Figure 5-3: Wrist Flexion vs. Elbow Flexion Coupling FunctionTo couple wrist flexion to elbow flexion, the best linear relationship, shown M Figure 5-3,was:wrist flexion = 0.75 * elbow flexion - 60.0°^if elbow flexion < 128°=-3.185 * elbow flexion + 443.7^if elbow flexion >. 128°Table 5-4 gives the results. Detailed results for all of the simulations can be found inreference [3].Number ofSuccessfulPositionsNumber ofClosePositionsNumber ofUnsuccess.PositionsWhichPositionsUnsuccessfulRoll CoupledwithElbow Flexion33 0 1 ColWrist FlexionCoupled withElbow Flexion28 3 3 Cul, Wl,Co2Table 5-4: Coupled Degrees of Freedom Results90Single Fixed Degree of FreedomEach degree-of-freedom was fixed individually. The results, except the elbow, in whichalmost all of the tasks were unsuccessful, are summarized in Table 5-5.Best Angle(degrees)Number ofSuccessfulPositionsNumber ofClosePositionsNumber ofUnsuccess.PositionsWhich PositionsUnsuccessfulAzimuthFixed71 27 0 7 Fl, Sl, R1A, R3A, R1B,.R3B, St2ElevationFixed63 31 0 3 Li, Bu, W1RollFixed-26 32 0 2 F1, SiForearm Rot'nFixed5 29 0 5 H2, F2, Wl, Brl, Br2Wrist FlexionFixed-5 32 1 1 K1Wrist YawFixed-2 33 0 1 T2Table 5-5: Single Fixed Degree of Freedom ResultsFixing the wrist degrees of freedom produced the best results, especially since the singleunsuccessful task in each case was of a lower priority. Roll had the next fewest unsuccessfultasks when fixed but these were eating tasks whereas elevation affected tasks of lesserimportance.Eating with the hands and with a fork cannot be performed with the forearm rotation fixed inone position. Forearm rotation could be coupled with elbow flexion if the orthosis were onlydesigned for eating. However, a plot of forearm rotation versus elbow flexion showed norelationship if other tasks were included.91The results show that azimuth should not be fixed since, not only were more tasksunsuccessful, but they were the high-priority reach tasks (see Section 3.3 for task priorities).One Coupled, One Fixed Degree of FreedomThe degrees of freedom that were coupled earlier were analysed together with an additionalfixed degree of freedom to further examine the potential for reducing degrees of freedom.The only successful combination, however, was the addition of a fixed wrist yaw to thecoupled roll and elbow flexion. The fixing of wrist yaw caused the relationship betweenwrist and elbow flexion to be more scattered, causing the coupling to be less successful.Also, since elbow flexion is not free to change by very much in approaching a desiredposition (since it defines the distance between the shoulder and the wrist) it is mostly thewrist flexion that must change to achieve the coupled relationship. However, small changesin elbow flexion caused large changes in wrist flexion, adversely affecting the orientation(refer to Figure 5-3). Thus only the combination of coupled roll and elbow flexion with fixedwrist yaw produced reasonable results, shown in Table 5-6.Best Angle(degrees)Number ofSuccessfulPositionsNumber ofClosePositionsNumber ofUnsuccess.PositionsWhich PositionsUnsuccessfulRoll & ElbowFlexion Coupled;Wrist Yaw Fixed-2 28 3 3 S2,T2,Co2Table 5-6: Coupled plus Single Fixed DOF Results92Two Fixed Degrees of FreedomFrom the single degree of freedom evaluations, only fixing elevation, roll, wrist flexion andwrist yaw were considered further. Table 5-7 shows all combinations of fixing these degreesof freedom (except fixing elevation and roll, which resulted in 22 unsuccessful positions).The best angles are given in the order listed in the row title.BestAngles(degrees)Number ofSuccessfulPositionsNumber ofClosePositionsNumber ofUnsuccess.PositionsWhich PositionsUnsuccessfulElevation &Wrist FlexionFixed53 / -5 12 7 15Fl, S2, R1A, R2A, R3A,Po, Kl, Li, Bu, Ph, W2Brl,Br2, Col, Co2Elevation &Wrist YawFixed53 / -2 26 3 5 Po, Kl, Li, Bu, ColRoll &Wrist FlexionFixed-46 / -15 19 4 11H1, Fl, F2, Si, S2, T2,Bu, Pa, Ph, W2, Br2Roll &Wrist YawFixed-40 / 4 29 2 3 Fl, Si, T2Wrist Flexion& Wrist YawFixed-9 / 2 29 1 4 Fl, Kl, T2, PaTable 5-7: Results for Two Fixed Degrees of FreedomThese results show that it is better to fix wrist yaw than wrist flexion if only one is to befixed. Furthermore, although either fixed roll and wrist yaw or fixed wrist flexion and wristyaw produced the fewest unsuccessful tasks, they included the higher-priority eating tasks.Fixing elevation and wrist yaw affected relatively less important tasks: pouring from apitcher, reaching for a doorknob, flipping a light switch (from a seated position), pointing to a93'button' at the light switch height, and combing the hair. Of these, only combing the hair hasa higher priority, yet it is sufficiently complex that it would be difficult to perform with anyof the orthosis configurations. Also, pouring may still be achieved in specific cases sincepouring from the gardening pitcher required a higher elevation than would be needed forpouring from a kettle or beverage pitcher.One Coupled and Two Fixed Degrees of FreedomThe relationship between roll and elbow flexion has greater scatter when both wrist rotationsare fixed. Also, as with the coupled wrist and elbow flexion with fixed wrist yaw, thesteepness of the slope (referring to Figure 5-2) creates problems when elbow flexion changesat higher flexion values. There is therefore no benefit in coupling roll to elbow flexion whenmore degrees of freedom are fixed.Three Fixed Degrees of FreedomIn an attempt to further reduce the degrees of freedom, two combinations of three fixeddegrees of freedom were tested. Table 5-8 gives the results.94BestAngles(degrees)Number ofSuccessfulPositionsNumber ofClosePositionsNumber ofUnsuccess.PositionsWhich PositionsUnsuccessfulElevation,Wrist Flexion& Wrist YawFixed48 / -15 / 3 13 4 17 Fl, 51, S2, Po, Kl, K2,Ti, T2, Li, Bu, Pa, Ph,Wl, Brl, Br2, Col, Co2Roll,Wrist Flexion -46 / -15 / - 15 8 11 H1, Fl, F2, Si, S2, T2,,& Wrist Yaw 2 Bu, Pa, Ph, W2, Br2FixedTable 5-8: Three Fixed Degrees of Freedom ResultsFixing three degrees of freedom produces significantly more unsuccessful tasks than the bestalternatives for two fixed degrees of freedom. Furthermore, the high priority eating andpersonal hygiene tasks are affected in both options. It can therefore be concluded that fixingmore than two degrees of freedom produces an unacceptably restricted device.Torque ConsiderationsTypically, higher torque requirements necessitate larger motors, increasing both the bulk andthe weight of an orthosis. The maximum torques required at each joint for a powered upper-limb orthosis given a one kilogram load were analysed by From [32]. These are listed inTable 5-9.95Max.Torque(N-m)EquationPosition of ArmatMaximum TorqueAzimuth 1.5 T. = [m(df + d„)2 ± Mf('df -I- d„)2 + Modu2± Mu(1/2(1)2] *aarm outstretchedhorizontallyElevation 21.6 T„ = g[m(df + du) + Mf(hdf + du) + MA +1/2Muclularm outstretchedhorizontally with elbowfully extendedRoll 6.5 Tr = g[mdf + 1,/i(Mf+M0ddi] elbow bent 90°, forearm andupper arm both lying in^.horizontal planeElbowFlexion6.5 Teb = g[mdf +1/2(M1+Mo)df] forearm horizontal, movingupward in vertical planeForearmRotation0.5 Tf = gmd, forearm horizontal, load50mm either side of handwhere,Table 5-9: Maximum Required Torque for Each Joint= 1 kg^= point mass loadMf = 1.5 kg = mass of forearmMu = 2 kg = mass of upper armMof = 0.5 kg = mass of orthotic hardware on forearmM,di==3 kg0.050 m= mass of orthotic hardware for whole arm= maximum eccentricity of loaddf = 0.330 m = length of forearm and hand= 0.220 m = length of upper arm= 2 rad/s2 = angular acceleration= 9.81 m/s2 = gravitational accelerationAs shown in the table, the torque required for elevation is more than three times that for anyother joint. In fact, the upper arm length is relatively low so maximum torques could be evenhigher. A spring assist could be used to reduce these torques.Control IssuesFrom a user's perspective, endpoint control is more intuitive and easier for device operationthan controlling individual degrees of freedom. If the shoulder is free and the wrist fixed96then the user simply controls the wrist position in three dimensions, plus forearm rotation andhand grasp. If wrist flexion is powered, then an extra control signal is required to activate theflexion. Powering wrist flexion does, however, provide local movements of the hand. Ifelevation is fixed there is no redundancy in the joints, which could lead to more unnaturalpositions. Fixing elevation also leads to a more restricted work envelope.Conclusions from Preliminary EvaluationFor a more versatile orthosis, only two degrees of freedom should be fixed or coupled. Fouralternatives follow from the initial analysis. Table 5-10 summarizes the advantages anddisadvantages of these alternatives.Advantages DisadvantagesElevation 1) reduces power consumption 1) restricts work envelope& Wrist Yaw 2) reduces bulk 2) requires control signal for wristFixed 3) allows local movements of hand flexion4) affects only lower-priority tasksRoll 1) reduces bulk 1) same as above& Wrist YawFixed2) reduces power consumptionslightly2) affects eating tasks3) allows local movements of handWrist Flexion 1) orthosis as flexible as human 1) increases power consumption& Wrist Yaw arm in positioning wrist 2) limits control over orientationFixed 2) fewer control signals needed 3) affects eating tasksRoll & Elbow 1) given the correct functional 1) more complex design, bulkier;Flexion relationship, leads to more greater power consumption thanCoupled; WristYaw Fixedsuccessful tasks than with rolland wrist yaw fixedfor fixed rollTable 5-10: Advantages and Disadvantages of Preliminary Alternatives975.6.2^Analysis  glIndividual  Subjects The four alternatives listed above were tested further using all of the key points plusadditional intermediate points for each task. An average of 125 points were tested for eachsubject. The purpose was both to test more points along the path and to use the individualsubject data instead of the averaged data used in the initial evaluation.There was a range of success among the subjects for each alternative. All of the alternativeshad more unsuccessful tasks than appeared in the original evaluation. This was due to thegreater variability for a single individual than for the averaged results used above and due tothe additional positions tested for the personal hygiene tasks. Page turning was unsuccessfulin all cases, but this was primarily due to orientation rather than distance; it may therefore bepossible to change the handle to accommodate the orthosis or to turn the pages differently.Page turning is therefore bracketed in the list of unsuccessful tasks below.The relationship between roll and elbow flexion was more scattered for the individual subjectsthan in the initial evaluation; in some cases the relationship was lost altogether. Couplingroll and elbow flexion therefore increases the complexity and bulk without producing asignificant functional advantage over fixing roll. Table 5-11 summarizes the results,excluding coupled roll and elbow flexion.In practical application more tasks will be performed than are included here. Many tasks willfall within the same work envelope as one of the included tasks. Also, people willcompensate through other motions and means that cannot be simulated.98Unsuccessful TasksElevation &Wrist YawFixedPouring from a Pitcher (at full height),Reaching for a Door Knob,Flipping a Light Switch,Reaching to a High Button,(Turning a Page),Brushing the Teeth (some positions),Combing the Hair (some positions)Wrist Flexion &Wrist YawFixedEating with a Fork,Eating with a Spoon,Reaching for a Door Knob,Turning a Tap Lever,(Turning a Page),Brushing the Teeth (some positions)Roll & WristYaw FixedEating with a Fork,Eating with a Spoon,Turning a Tap Lever (at extreme),(Turning a Page),Washing the Face (some positions),Combing the Hair (some positions)Table 5-11: Unsuccessful Tasks for Final Alternatives5.7 Implications  for  Orthosis Design In terms of reducing complexity, fixing roll is equivalent to fixing elevation, but in terms ofreducing torque, fixing elevation is significantly more effective than fixing roll. Since theperformance of the simulated fixed roll orthosis was not significantly better than theperformance of the fixed elevation device, and in fact affects the eating tasks, fixing roll andwrist yaw is not recommended.99The primary advantage of selecting the fixed elevation and wrist yaw alternative is thereduction in maximum torque and therefore the power consumption and bulk. This can be asignificant factor in terms of power requirements, battery discharge and speed of activation.The mechanical need for a lever arm from the body to the upper arm to perform elevationincreases physical bulk; it is also less aesthetically pleasing because of the lack ofstreamlining to the arm. From reinforces these arguments, stating that "since the elevatorjoint consumes the most power during movement and requires the greatest torque, its removalwould significantly enhance the size, mass and power consumption of the device" [32]. Theprimary disadvantage, aside from slightly more unsuccessful tasks, is with respect to control.Choosing to fix elevation as opposed to wrist flexion not only reduces the work envelope andthe flexibility of the shoulder but adds the need to control wrist flexion separately. Theadvantage of controlling wrist flexion is having local control over orientation, thus allowingsmall adjustments to be made without moving the entire arm.The primary advantage of fixing both wrist rotations is being able to reach any location thatthe arm could normally reach. Also, the redundancy of the three shoulder degrees of freedomprovides more than one solution for a given position, allowing for more natural arm positions.The disadvantage is that there is no small-scale control of orientation except forearm rotationand the unsuccessful tasks are of a higher priority. A small aesthetic advantage is that theactuation is kept away from the end of the forearm.Since the importance of the advantages and disadvantages will vary from application toapplication, both alternatives are recommended. In each case, hand grasp is powered as well.100Although fixed at a particular angle, the fixed angles should be manually adjustable to suit theindividual and the individual's circumstances.5.8 Conclusion This chapter has outlined the design and use of a simulation program to establish whether agiven position and orientation can be achieved with a specified configuration of a simulatedorthosis. Based on the results of the simulations, two orthosis designs are recommended. Thefirst is to fix elevation and wrist yaw and power all other rotations. The major advantage isthat the power consumption and bulk are reduced. The major disadvantage is that theshoulder, and therefore the position of the hand, is more restricted in its movement. Thesecond design is to fix wrist flexion and wrist yaw. The major advantages and disadvantagesfor this option are reversed. The major advantage is the greater flexibility of the ann. Themajor disadvantage is the extra bulk and power requirements needed to operate the shoulder.While the first option affects lower-priority tasks, the second option affects the higher-priorityeating tasks. A simpler configuration would be possible if the task requirements were fewer,if the user were able to compensate with the head and trunk, or if the user has residualmotion in the arm. In addition, the user may be able to perform the tasks differently or withdaily-living aids, such as a fork with an angled handle or a rotating spoon.101CHAPTER 6: CONCLUSIONS  AND RECOMMENDATIONS 6.1 Introduction The goals of this research are to identify the needs of potential users of a powered upper-limborthosis and to develop a procedure for determining an optimal configuration. Thecompromise is between simplicity and functionality. Two alternative configurations arerecommended which are more restricted than the motion of the natural arm but provideenough function to perform the majority of the higher-priority daily-living tasks. It wasdetermined that out of the seven degrees of freedom in the human arm, two should be fixedand the rest powered.These recommendations were arrived at through three stages. The first stage involvedinterviewing potential users of a powered upper-limb orthosis to determine which tasks theywould most like to regain. In stage two, the arm motions of able-bodied subjects performingthe high-priority daily-living tasks were profiled. For stage three, alternative orthosisconfigurations were evaluated using a simulation program.6.2 Task  Definition  and  PrioritiesThe objectives pertaining to task priorities were to research the needs and wants of potentialusers of a powered upper-limb orthosis and to establish the priority of various daily-livingtasks. To this end, interviews were conducted with 11 potential users. The interviewscovered the top five desired tasks, task abilities, use of daily-living aids, orthosis acceptance102criteria and medical details. The conclusions and contributions of this portion of the researchare outlined below:• Interviews were conducted with potential users of a powered upper-limb orthosis ratherthan a robotic manipulator. Because an orthosis returns function to the user's own arm,there was a greater emphasis on hobbies, crafts, personal hygiene and dressing tasks, tasksthat would be less personal and more intimidating if performed by a robotic manipulator.• Disabled respondents put a greater emphasis than able-bodied respondents on reaching forand picking up objects. All compilations of potential user task priorities have recognizedthe importance of reaching for and picking up objects.• The most desired tasks, based on the interviews with 11 potential users conducted for thisresearch, were reaching/picking up objects (9), personal hygiene (7), hobbies/crafts (7),eating/drinking (6), housework (4), dressing (4), strengthening grip (4), cooking (2),toileting/transferring (2), reading (1) and using a computer (1). (The number in bracketsshows the number of respondents mentioning the task among their top five choices.)• Separate from the desire to regain independence was a clear desire to regain creativity,through crafts, hobbies, painting and baking. While these tasks are beyond the capabilitiesof a practical whole-arm orthosis, mostly due to the dexterity involved, a person withfunctioning hands but weak arms could use the orthosis to position the hand where needed.• Affordability and cosmesis are both important factors in user acceptance.1036.3 Motion AnalysisThe research objectives for the second phase were to record the motions of able-bodiedpeople performing the top-priority tasks and to analyse these motions in terms of the jointrotations and paths taken during each task. A motion analysis system consisting of two videocameras, an image processing system and customized software was developed and used toprofile six subjects, three male, three female performing 22 daily-living tasks. The tasksincluded eating and drinking tasks, reaching tasks, daily-living activities and personal hygienetasks. The conclusions and contributions of the developed system and the research performedinclude the following:• The literature review and requirements of this research indicated a need for a new motionanalysis study of functional tasks. Few whole arm studies have been conducted; only onehas data on functional tasks and only for eating and drinking. By contrast, this researchprofiled 22 functional tasks. The motion analysis provided the desired positions andorientations and initial joint angle estimates for the simulation program.• Software was developed for this research to control the VCR, load and manipulate thevideo image, track the joint markers, solve for the three-dimensional coordinates of eachmarker, display stick figure diagrams of the movements and calculate the joint angles.• The analysis for this research differed in three ways from previous researchers: a clearerdefinition of shoulder joint rotations, which is more suited to orthosis design, was used;each joint angle was calculated directly, based on a model of the arm, instead of solving104for the three Euler rotations simultaneously at each joint; and a passive carrying angle isdefined which rotates the plane of elbow flexion. Although not as general as the Eulerianapproach, the method used here produces more consistent results. The displacement of themarkers from the joint centres was accounted for as well, improving the accuracy of theresults.• The joint angle results were found to be comparable to previous researchers, except wherethe hand grasp differed, and repeatable. The average joint angle standard deviation for asingle subject was found to be 3.0 degrees; for the six subjects it was found to be 8.0degrees.• Previous studies indicated the importance of elbow flexion, forearm rotation and at leastone shoulder rotation. The motion analysis results from this study indicated that at leastelbow flexion, forearm rotation and two out of the three shoulder rotations should bepowered, while possibly one shoulder rotation and both wrist rotations could be fixed. Thishypothesis was tested with the simulation program.6.4 0 rthosis  SimulationThe objectives for the last phase of the research were to develop a kinematic simulationprogram to test possible configurations of a powered upper-limb orthosis and to use thissimulation program to determine the orthosis configuration with the fewest degrees offreedom that is still capable of performing the highest-priority tasks. The developed programdetermines how close a simulated orthosis is able to come to a desired position and105orientation. It does so by using a cost function and minimization procedure. All reasonablecombinations up to three fixed or coupled joint rotations were examined. The conclusionsand contributions from this phase of the research are provided below:• The literature review indicated that, while other researchers have based designs on jointpriorities or on tests with mechanical models, an examination of the required degrees offreedom has never been quantified before.• Preliminary evaluations were conducted with 34 positions, consisting of the criticalfunctional positions for each task. Fixing azimuth (rotation about a vertical axis throughthe shoulder), elbow flexion or forearm rotation led to a large number of unsuccessfultasks. Therefore, only elevation (rotation about a horizontal axis through the shoulder), roll(rotation about the axis of the upper arm), wrist flexion and wrist yaw were consideredfurther. When two degrees of freedom were fixed, fixing wrist yaw produced better resultsthan fixing wrist flexion. Several joint couplings were evaluated but did not provide asignificant advantage over fixing in terms of the number of successful tasks. Fixing threedegrees of freedom produced significantly more unsuccessful positions than fixing twodegrees of freedom.• Four potential alternatives emerged from the preliminary evaluation: 1) to fix elevation andwrist yaw, 2) to fix roll and wrist yaw, 3) to fix wrist flexion and wrist yaw and 4) tocouple roll and elbow flexion and fix wrist yaw. These were analysed further using up toeight functional points from each task, for each of the six motion analysis subjects.106• The recommended alternatives are to power all but elevation and wrist yaw or to power allbut wrist flexion and wrist yaw.• Both of the final alternatives were unsuccessful in reaching for a doorknob, turning a pageand brushing the teeth (some positions). The additional unsuccessful tasks for the firstalternative were pouring from a pitcher (at full height), flipping a light switch, reaching toa high button and combing the hair (some positions), all requiring a higher elevation. Theadditional unsuccessful tasks for the second alternative were eating with a fork, eating witha spoon and turning a tap lever.6.5 Orthosis  Design As shown in the literature review, a powered upper-limb orthosis that is acceptable to usershas yet to be developed. In most cases, they were too complex, bulky and prone tobreakdown. The more recent UBC-modified HMRC orthosis is much simpler, but is notsufficiently functional.• Both recommended options restrict the number of tasks that can be performed; the loss offunctionality, however, is offset by the advantages of increased simplicity. A simplerdesign leads to reduced costs, fewer breakdowns, and is more aesthetically acceptable.• An even simpler configuration would be possible if the task requirements were fewer, if theuser were able to compensate with the head and trunk, or if the user has residual motion in107the arm. In addition, the tasks may be able to be performed differently or with daily-livingaids.• Fixing wrist yaw affects the least number of tasks; it therefore appears in bothrecommended configurations. Fixing elevation significantly reduces power consumptionand bulk but restricts the work envelope of the hand. Fixing both wrist rotations expandsthe work envelope, but increases power consumption and bulk, prevents local movementsof the hand and affects higher-priority tasks.• Although joints are indicated as fixed they should be adjustable to suit the individual.Also, an individual user's remaining function should be utilized rather than restricted.6.6 Recommendations  for  Future  Work The following recommendations can be made for future work in the areas of this research:• A prototype orthosis should be designed and developed based on the recommendations ofthis thesis, as is planned. The proposed simpler yet versatile design should have a higherprobability of user acceptance.• Throughout the development of the prototype, there should be continued contact with userson design considerations not included here, such as ease of use, appearance etc.. 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Sprague, BiomechanicalAnalyses of Forearm Pronation-Supination and Elbow Flexion-Extension, J. of Biomechanics,12:245-255, 1979.118APPENDICES119Appendix  A: A Brief  Medical  Description  pithe Disability  CategoriesThe following provides a brief medical description of each of the disability categories causingupper-limb weakness. The effect on upper-limb weakness is given in Table 3-1.P (polio): Polio causes muscle weakness due to a viral attack on the muscle nerve root;although eradicated from North America, survivors are now experiencing weakness in musclespreviously unaffected [40].ALS (amyotrophic lateral sclerosis): ALS causes progressive muscle weakness due to adegenerative disease which attacks the motor neurons in the brain and spinal cord; PMA-typeprimarily affects the arms and legs; bulbar-type primarily affects swallowing and speech[12,111].MD (muscular dystrophy): MD causes progressive degeneration of the muscle fibres; allthree types (Duchenne, limb girdle and facioscapulohumeral) are genetically determined withDMD being the most severe and LGMD and FSH -MD progressing more slowly [12,108].SCI (spinal cord injury): SCI is caused by a sudden spinal cord injury during e.g. diving ormotorcycle accidents; muscles are totally ("complete") or partially ("incomplete") paralyzedbelow the injury site [65,117].MS (multiple sclerosis): MS causes demyelination of the central nervous system causing thesignal to not be able to reach the muscle (the strength of the muscle before disease istherefore irrelevant) [57].BPI (brachial plexus injury): BPI is a tearing of the nerve complex at the shoulder (the"brachial plexus") due to a high velocity impact, most commonly from motorcyle accidents;the resulting paralysis depends on which nerves are affected [58].Str (stroke): Stroke is a sudden disorder leading to a lack of blood with enough oxygen tomaintain brain function in a localized area; it usually results in paralysis on a single side;recovery varies from complete (10%) to still needing institutional care (10%) [23,105].CMT (Charcot - Marie - Tooth): CMT causes progressive muscle weakness with the musclesatrophying in the legs and arms [22].120Appendix  B: Task  Priority  QuestionnaireTASK PRIORITY AND MOTION ABILITY QUESTIONNAIREfor the design of aPOWERED UPPER EXTREMITY ORTHOSISconducted byCLINICAL RESEARCH AND REHABILITATION ENGINEERINGUNIVERSITY OF BRITISH COLUMBIAGENERAL  DISABILITY INFORMATIONName:^ Phone Number:Diagnosis:Length of time since first diagnosed:Lesion level (if applicable):^Complete/Incomplete?:Any other medical illnesses?:DEGREE  OF  DISABILITYWeakness?(total/partial/none)Loss of Sensation?(total/partial/none)Hand R: L: R: L:Wrist R: L: R: L:Elbow R: L: R: L:Arm R: L: R: L:Shrug R: L: R: L:Range -of-Motion?(full/limited)Grasping R: L:Forearm Rotation R: L:Bending Elbow R: L:Lifting Arm to front R: L:Raising Arm to side R: L:Shrugging Shoulders R: L:Neck Motion - up/down R: L:- left/right R: L:- forward/backward R: L:121Daily living aids being used? (list all):Any involuntary movements?Any spasms?Any pain?:Ambulatory?:^If not, what device is used?:Any eye problems?Any voice problems?TASK  ABILITYWhich tasks can you not do now but would like to be able to do, which involve the hand orarm?Which of these are most important to you?122Can you perform the following tasks Easily (E)? With difficulty (D)? With an aid (A)? or notat all (N)? If an aid is used, what is the aid? What are the reasons for the difficultiesexperienced?Personal Hygiene TasksReason forAbility^Aid^DifficultyBrushing teethWashing faceCombing hairBlowing noseShavingApplying makeupScratchingGoing to the toilet:unrolling paperpulling paper offwipingrearranging clothesfeminine hygieneTurning tapsWashing handsReaching:to top of headto mouthto waistto kneesto shoes (floor)Dressing:not able to do: ^able to do: Any other personal hygiene tasks?(specify) ^123Domestic TasksReason forAbility^Aid^DifficultyGetting item from fridgeUsing a microwaveMaking a hot drink:filling the kettleplugging/unplugginggetting utensilspouring water/milkadding sugarstirringEating:loading spoon from platespearing with a forkcutting with a knifespreading with a knifeputting food into mouthDrinking:with a strawlifting & tilting the cupUsing electric can openerOpening beverage cansOpening beer/pop bottlesOperating tapsUsing sink plugsTurning stove knobsOpening/closing doors:turning a keyturning a doorknobturning a door leverpulling the doorpushing the doorOperating light switchesReaching, grasping & returningPicking item up from floorPushing/pulling drawersOpening/closing cupboardsTurning screwdriverAny other domestic tasks?(specify) ^124Leisure/Recreation ActivitiesAbility^Difficulty Reason for:Reading a book:holding bookturning pagesReading a newspaper:holding newspaperturning pagesReading a magazine:holding magazineturning pagesPlaying computer gamesOperating remote control(TV, radio, stereo, VCR)SmokingDrawing/paintingPlaying board gamesGardening:indooroutdoorAny other recreational activities?(specify) ^Work - or School -Related TasksAbility^Aid^Difficulty^Reason for:Using a computer:typing at a keyboardusing a mouseinserting floppy discsWriting with pen or pencilPicking & placing objectsPushing buttonsAnswering the telephoneUsing a touch-tone phoneUsing a staplerUsing a photocopierUsing a FAX machineOpening a letterSealing an envelopeUsing a calculatorFiling documentsUsing public transportationRiding in a carAny other work or school activities?(specify) ^125TASK PRIORITYWhat are the top five tasks, in order, that you would most like to do but cannot?1.2.3.4.5.If a device could do some of the above would you consider buying it (Y/N)?Would you be willing to take part in clinical trials of such a device (YIN - note answer forlater)?CRITERIA FOR ORTHOSIS ACCEPTANCEIf an orthosis were available for grasping, rotating the forearm and bending the elbow, howimportant would you rate the following criteria (1=very, 5=not at all):Affordability:Repairability by yourself or an assistant:Having control over all motions vs. preprogrammed motions:Dependability/ Reliability:Durability (expected life):Ease of Donning & Doffing:Ease of Maintenance:Effectiveness of the orthosis in performing tasks:Having choice of grasping/rotation/bending systems:Learnability:Length of time available before recharging:Ease of control:Aesthetics:Acceptability of orthosis when amongst others:Physical Comfort:Physical Safety:Portability (weight & bulk):Speed of operation:Supplier Repairability:Time from purchase to usability:Would anything else be important to you?126PERSONAL INFORMATIONAge:Age at injury/ onset of disease:Sex (F/M):Marital Status:(Married, Single, Cohabiting, Widow/er, Divorced/Separated)Accommodation (Home, Hospital, Institution):If at home, are you Alone, With a partner, With family?If at home, do you have any home help (Y/N)?Employment status (FT, PT, occasional, none):Occupation:Location (Home-based or Outside the home):Educational background:Pasttimes (how do you spend your day?):TelevisionReadingStereoComputer GamesBoard GamesVisitingSleepingEatingOther:THANK YOU!Confirm (based on answer to question above):You WOULD be willing to be contacted for future practical trials of the device.ORYou would NOT be interested in participating in future practical trials of the device.NOTES 127Appendix C: Subject  Task  PrioritiesThe top tasks for each subject, from the interviews conducted with potential users, were:Subject #1:^1. Dressing self;(post-polio) 2. Eating meal by self;3. Housework;4. Cooking, using stove; and,5. Getting into cupboards.Subject #2:^1. Woodwork;(kugelberg-welander)^2. Working on cars/machinery;3. Household renovations;4. Hobbies, e.g. put together remote control airplanes; and,5. Strength & stamina.Subject #3:^1. Getting things out of fridge;(C5/6 spinal cord injury)^2. Stronger grip (opening can, holding knife);3. Picking up something heavy from the floor; and,4. Reaching over the head.Subject #4:^1. Putting things away overhead; and,(kugelberg-welander)^2. Supporting the arm to eat, comb hair etc..Subject #5:(limb-girdle MD)Subject #6:(limb-girdle MD)Subject #7:(limb-girdle MD)Subject #8:(limb-girdle MD)1. Eating;2. Transferring self out of chair, e.g. to bed, toilet; and,3. Lifting things.1. Reading;2. Doing hair;3. Sewing;4. Painting; and,5. Cleaning.1. Feeding;2. Brushing teeth;3. Putting on lipstick; and,4. Crocheting.1. Reaching (holding arms up);2. Dressing;3. Eating;4. Using computer;5. Doing hair;6. Painting, art & crafts; and,7. Gardening.128Subject #9:(limb-girdle MD)Subject #10:(limb-girdle MD)Subject #11:(limb-girdle MD)1. Housework;2. Baking;3. Opening jars;4. Lifting and carrying things; and,5. Travelling.1. Personal grooming;2. Feeding;3. Gardening ("miss terribly!");4. Toileting;5. Dressing (esp. nylons);6. Housework (changing sheets, doing laundry); and,7. Painting, knitting, crocheting.1. Strength;2. Hobby-type work (building, creating);3. Driving (freedom);4. Eating;5. Dressing; and,6. Brushing hair, washing face, brushing teeth, shaving.129Appendix  D: EQUIPMENT SPECIFICATIONS The following equipment was used to perform the motion analysis:V.C.R.:Frame grabber board:TV monitor:Computer:Cameras:Tripods:Tripod Heads:SONY SVO-9500MD S-VHSSharp GPB-1 image processing boardHitachi Model #CT1397B colour monitor486/50MHz with Windows 3.1Panasonic PV-S770-K S-VHS camcordersManfrotto Art # 075Manfrotto Art # 136APPENDIX  E: 3D  COORDINATE  CALCULATIONS Camera  Calibration Eleven parameters are used to describe the calibration of a single camera [107]. Theserepresent the position and attitude of the camera, the principal distance of the camera and ascaling factor. The method presented here uses a central-projection camera model andassumes no optical distortion in the lens.Let (x, y, z) be known three-dimensional "object coordinates"; let (u,v) be known two-dmensional "image coordinates". Using homogeneous coordinates [331,{x y z 1}•-Li L5 1.9L2 L6 LioL3 LI LIIL4 Ls L12= { tu tv t} where L, to L12 are the elements of the transformation matrix. The system is scaled asnecessary to get L12 = 1. Solving for u, v and t:t = L9x + Li0y + Luz + Li2Lix + L2y + L3z + L4U ^— L5x + L6y + Liz + L8V Hence, two linear equations can be defined for each point:= L1 x, + L2yi + L3zi + L4 — L9UiXi LioUtYi^UtZtL5Xi L6yi + Liz, + L - L9v,x, - L10v,y, -131In matrix form this becomes:1.1L2L3xi y1 zi 1O 000x2 h z2 1O 000x. y. Z. 10000O 000x1 y1 Z1 1• •^•^•• •^•^•O 000Jr„ YR za 1-uixi -uiyi -uizi-vixi -viyi -vizi• •^-•^•—U„X„ —11„y„ —1111Z,—VxXi, —Wm —V,,,Z„•L4L,L.L,L.I.91011or,^[P]2i x II {L}Ii xi = {Q}2nx1At least n = 6 calibration points are required to solve for the unknown calibration parameters,L1 to L11. In this study 10 were used in order to improve the accuracy. The minimum-squared-error criterion was used to solve the overdetermined system (20 equations for 11unknowns). Thus,{L}^=^([P]T [PD-1 [P]T {Q}=^[P+]{Q}where [P] is the pseudo-inverse of P.3D Coordinate Calculation Since there are two equations (u, v) for each camera, there are a total of four equations forthree unknowns (x, y, z), the coordinates of each marker. Rearranging the earlier equationsfor u, v and t gives:132L1 -Loth^/2 -Limit'L5 -L9 VI L6 -LioL4-Li'ou2L;-1,5;v2 L‘10v211-L11141 /41 -L4-Ln v1-413-411 142Y =u2 -L414-L111v2^v2-4or,^[A] {x y z}T = (B}where L1 to Li1 are the calibration parameters for camera 1 and L,' to L11' are the calibrationparameters for camera 2.For the least-squares fit,x= GeV] kliTiBIz The three-dimensional coordinates of any point can therefore be found given thecorresponding images of at least two cameras.The general approach used here is called the Direct Linear Transformation (DLT) method.Without it, the geometric parameters of the camera would have to be known precisely,requiring special cameras. First developed by Abdel-Aziz and Karara [lb the DLT method isnow commonly used.133Appendix  F: Euler  Angle Joint Angle  CalculationsThe following discussion examines how joint angles are calculated using the Euler anglemethod as opposed to the direct calculation method used in this study. The Euler methodwas used by Langrana [54], Lipitkas [62] and Safaee-Rad [102].Orthogonal axes are defined at each joint based on the marker positions. Each limb segmentmust have three markers to define a plane. Axes at the elbow reflect rotations at theshoulder, axes at the wrist reflect rotations at the elbow, etc. (Safaee-Rad defines axes suchthat the carrying angle is ignored, however this affects the values for roll, elbow flexion andforearm rotation.) A stationary body axis is also defined to account for movements of thetrunk.Once the unit vectors (xi, y„ z,) of each set of axes have been found relative to the fixedframe of reference (X, Y, Z) the rotation matrices between each set of axes can bedetermined.Given, [F,]^= the unit vectors of the body axes,[RJ = the relative rotation matrices and[FFR] = the unit vectors of the fixed frame of reference,the stationary body axis is defined by:^[F0] = [Ro][FFR],the axis at the elbow is defined by: [F1] =the axis at the wrist is defined by: [F2] = [R21[FFR] andthe axis at the hand is defined by:^ [F3] = [R3][141-1(].By rearranging the equations, and recognizing that [R]-1 = [RIT for orthonormal axes, therelative joint rotations can be defined as:13410^00 COO Sill°0 -Sille COS°[r1] = [Rd[Rof^for the shoulder joint;{1.21 = [R2][R1f^for the elbow joint; and,1r3l^[R31[R2]T^for the wrist joint.Euler angles 10, 0, and NI describe successive rotations about specified axes. For the Eulerangles defined as a rotation about the z-axis, followed by a rotation about the x' axis,followed by a rotation about the y" axis, the rotations can be expressed as:cos4) Rind)= -sin* cos* 0 y0^0 1 zC:os* 0 -sin $r 0 1 0sin* 0 cos*Multiplying the three successive rotations together gives:COS4COS*^Sill°^Sill4C08* +COS. sine sin* -cose sin*-sin4) cose cc•sd) cos°^sinecos. sin* +sin* sine cos* sin* sin* -cos. sine cos* cos() cos* _Matching the corresponding elements of this theoretical matrix with the calculated values ofthe matrices [r1], [r.,] and [r3], each of the three Euler angles can be solved for, for each joint:X I//y[r] =135• =arctan1 33* =arctan=arctan r23cos*1r33However, all three angles are being solved for from a single transformation matrix. Giveninaccuracies in the axis definitions there will no longer be a consistent solution. The errorsare further increased because the relative rotation matrices [r] are based on the multiplicationof two absolute rotation matrices [R]. An inconsistent set of angles has a greater effect onthe calculation of the endpoint position and orientation than on the angles themselves.Although inconsistencies may be tolerated in the motion analysis results, consistent jointangles were required for the orthosis simulations. A consistent, although less general,approach was used in this study, calculating joint angles directly, based on a developed modelof the human arm.136Appendix  G: Derivation  oLLocation  of."2 for  Roll  &Elbow Flexion  CalculationsFigure 0-1: Diagram for Finding Point p2Figure 0-1 is constructed using three known conditions on point p2:1)_Lr2P2^r3P2 (by construction)Therefore, point p2 lies on a sphere of radius V2Ir23 I (i.e. half the forearmlength), centred at c = 1/2 (r02 + 1'03), where 0 is the origin of thecoordinate system.2)^r3P2 .1_ r^(by construction of r3p2In2 and n.2.1.r12) 12Therefore, point p2 lies in a plane normal to 1.12 and passing through point 3.1373)^the angle between r2p2 and r ^Etc = the carrying angle.The intersection of conditions 1 and 2 gives the following four relations:- ^(r23 • ri2r^r2,6^1,1212^12= —3,3^2Ps^231radius, a = —2Ir31,3 IU 2 + V2 = a 2From the intersection of conditions 2 and 3:radius, b = Ir2p31 tane(u - a)2 + v2 = b2The intersection of the two circles is then:b2u = a - —2aV = ±i/(a2 - u2)The position of p2 is therefore:P2 = T3(a+u hIr3p3 ) T3P3 ±^I T3p3 X r ) (r3is x r2)where the two solutions correspond to ± O. The correct solution is that for which7:2 • r23 2 0.138\ AZIMUTHt> ELEVATNo ROLLx ELBOW/ FOREARM+ WRIS FLEXo WRIST YAW\ AZIMUTHELEVATNo ROLLx ELBOW/ FOREARM+ WR1SFLEXo WRISTYAWAppendix  H: Angle-Time Graphs from  the  Motion  Analysis  Study The graphs below are representative angle-time graphs from the motion analysis studydescribed in Chapter 4. Each line represents the raw data for one joint angle. The data wassampled every 1/30th of a second. Each graph is chosen from one of the six subjects.Figure H-1: Eating with the HandsFigure H-2: Eating with a Fork139\ AZIMUTHL> ELEVATNo ROLLx ELBOW/ FOREARM+ WRISFLEXo WRISTYAW\ AZIMUTHt> ELEVATNo ROLLx ELBOW/ FOREARM+ WR1SFLEXo WRISTYAWFigure H-3: Eating with a SpoonFigure H-4: Drinking from a Cup1401.50.0\ AZIMUTH1> ELEVATNo ROLLx ELBOW/ FOREARM+ WRISFLEXo WRISTYAW2.00.5^1.0Time (Seconds)Figure H-5: Reaching to Position 1, Cylinder VerticalFigure H-6: Reaching to Position 2, Cylinder Vertical141\ AZIMUTHt> ELEVATNo ROLLx ELBOW/ FOREARM+ WRIS FLEXo WRIST YAWTime (Seconds)0.0 0.5^1.0 1,5\ AZIMUTHC. ELEVATNo ROLLx ELBOW/ FOREARM+ WRIS FLEXo WRIST YAW2.0Figure H-7: Reaching to Position 3, Cylinder VerticalFigure H-8: Reaching to Position 1, Cylinder Horizontal142Time (Seconds)0.0 0.5^1.0 1.5\ AZIMUTHr> ELEVATNo ROLLx ELBOW/ FOREARM+ WRISFLEXo WRISTYAW2.0\ AZIMUTHI> ELEVATNo ROLLx ELBOW/ FOREARM+ WRISFLEXo WRIST YAW2.0 -750.0^0,5^1,0^1.5Time (Seconds)Figure H-9: Reaching to Position 2, Cylinder HorizontalFigure H-10: Reaching to Position 3, Cylinder Horizontal143\ AZIMUTHr> ELEVATNo ROLLx ELBOW/ FOREARM+ WRIS FLEXo WRIST YAWFigure H-11: Pouring from a Pitcher\ AZIMUTHr> ELEVATNa ROLLx ELBOW/ FOREARM+ WRISFLEXo WRIST YAWFigure H-12: Reaching for and Rotating a Door Lever144\ AZIMUTHI> ELEVATNo ROLLx ELBOW/ FOREARM+ WRISFLEXo WRIST YAW\ AZIMUTHL> ELEVATNo ROLLx ELBOW/ FOREARM+ WRISFLEXa WRIST YAWFigure H-13: Reaching for and Rotating a Door KnobFigure H-14: Turning a Tap Lever145AZIMUTHELEVATNROLLELBOWFOREARMWRISFLEXWRISTYAW\ AZIMUTHD ELEVATNO ROLLx ELBOW/ FOREARM+ WRIS FLEXo WRISTYAWFigure H-15: Flipping a Light SwitchFigure H-16: Pointing to a Button146N AZIMUTHt> ELEVATNo ROLLx ELBOW/ FOREARM+ WRISFLEXo WRIST YAWN AZIMUTHc> ELEVATNo ROLLx ELBOW/ FOREARM+ WRIS FLEXo WRIST YAWFigure H-17: Turning a PageFigure H-18: Lifting a Phone Receiver147AZIMUTHELEVATNROLLELBOWFOREARMWRISFLEXWRISTYAW3 42Time (Seconds)\ AZIMUTHr> ELEVATNa ROLLx ELBOW/ FOREARM+ WRIS FLEX1^ 1^ 1 o WRIST YAW1Figure H-19: Reaching to the LapFigure H-20: Washing the Face148N AZIMUTHD ELEVATND ROLLx ELBOW/ FOREARM-1- WRISFLEXo WRIST YAW\ AZIMUTHI> ELEVATNo ROLLx ELBOW/ FOREARM+ WRISFLEXo WRIST YAWFigure H-21: Brushing the TeethFigure H-22: Combing the Hair149Appendix  I: Summary  Table  gf_Motinn  Analysis Results,  All subjectsTable I-1 gives the average minimum and average maximum of each joint angle for each taskfor all subjects, as found in the motion analysis study performed for this research. Thestandard deviation of these averages is included. The overall minimum, maximum andaverage standard deviation for each joint angle is given as well. A summary table is shownin Section 4.5.3.150AZIMUTH I ELEVATION i^ROLL^1^E-FLEX^I F-ROTN 1 W-FLEX 1 W-YAWAvgMmStddevAvgMaxStdDeAvgMinStddevAvgMaxStdDeAvgMinStddevAvgMaxStdDeAvgMinStddevAvgMaxDevStd-AvgMinStddevAvgMaxStdDeAvgMinStddevAvgMaxDevStd AvgMinStddevAvgMaxStdDeVHANDS 39 8.0 65 6.5 33 3.1 47 5.6 -49 9.8 0 5.9 67 5.5 134 5.1 -70 16.5 36 9.9 -18 6.3 12 4.9 -12 9.7 10 6.0FORK 32 6.6 49 8.9 34 4.9 54 8.1 -40 18.2 1 10.4 73 4.3 129 7.4 -37 6.6 50 12.6 -6 12.7 35 28.2 -13 11.6 10 6.6SPOON 34 8.6 54 10.0 32 2.6 76 4.9 -61 12.6 -4 11.1 75 5.5 123 9.1 -24 9.7 57 12.6 -7 8.6 53 16.0 -7 10.7 17 2.7CUP _ 37 12.2 56 11.4 32 3.6 63 5.2 -62 6.6 -21 10.4 68 7.4 136 7.6 -14 17.5 37 9.4 -24 4.4 16 7.9 -11 5.7 8 5.6RCH1A 7 10.3 40 8.6 29 4.9 35 7.1 -38 12.7 -23 8.9 71 2.4 84 3.1 -24 6.8 -11 8.4 -30 6.0 -6 5.2 -7 6.3 9 6.9RCH2A 38 6.8 76 4.9 31 4.7 39 5.2 -32 8.1 -19 6.5 66 4.1 78 2.5 -26 8.0 -15 9.7 -32 8.2 -19 6.6 -2 5.6 4 4.8RCH3A 35 5.9 108 5.1 30 5.1 42 3.8 -33 6.8 -20 5.5 57 4.8 81 2.6 -29 8.2 -15 8.6 -33 8.3 -15 6.2 -2 5.9 5 5.3RCH1B 8 7.1 43 7.6 31 7.6 36 7.2 -28 4.7 -17 4.2 67 3.8 80 4.4 42 5.6 49 6.7 -17 9.8 -5 13.2 -1 5.6 7 5.1RCH2B 40 6.1 80 4.7 32 6.4 40 5.4 -27 5.3 -19 3.7 64 7.2 77 4.9 39 8.3 47 7.4 -13 16.6 -6 16.3 -2 5.4 4 4.7RCH3B 38 4.5 107 7.0 32 5.1 44 3.6 -28 4.1 -19 3.6 58 6.6 79 3.9 37 7.4 47 7.8 -14 14.3 -6 14.0 -2 4.4 5 4.2POUR 36 7.3 66 7.4 32 4.9 85 9.0 -45 7.8 -16 5.4 65 4.6 86 4.7 -49 3.6 36 7.6 -32 9.5 -1 9.7 -12 8.3 4 5.4DOOR 39 4.9 72 6.3 34 2.4 58 2.9 -50 10.8 -20 6.5 58 6.7 78 5.5 -2 14.4 47 9.1 -32 8.6 -11 7.3 -4 4.3 11 2.8KNOB 37 4.0 69 18.8 37 2.9 64 14.7 -45 11.3 -15 6.8 42 4.2 76 16.9 7 7.8 52 27.6 -38 9.3 -11 14.3 -10 6.4 9 10.0TAP 33 9.9 65 4.9 34 1.9 64 5.2 -45 10.0 -17 9.5 57 9.5 77 4.0 19 6.6 48 9.6 -17 5.6 22 7.3 -39 5.8 9 4.0LIGHT 37 9.1 69 3.4 32 - 1.9 96 6.1 -56 6.8 -21 7.1 45 9.9 88 4.6 -47 9.7 41 9.7 -19 7.7 3 6.5 -23 7.3 1 3.2BTTN 39 4.9 68 5.9 31 7.7 90 1.5 -57 5.5 -27 7.5 51 7.7 88 13.1 20 7.6 40 5.7 -19 5.5 2 4.5 -8 3.5 2 4.5PAGE 7 6.2 73 7.3 30 2.7 45 6.8 -26 6.4 -4 3.4 86 3.2 98 2.2 42 8.0 61 6.4 -13 7.1 30 15.6 -23 9.3 14 8.1PHONE 36 6.5 71 7.6 35 2.5 53 6.5 -82 16.1 -26 9.1 74 6.5 -151 14.5 -26 18.5 48 6.4 -32 7.8 9 16.1 -14 9.9 11 7.1LAP 7 23.2 81 5.6 15 3.3 34 3.5 -31 7.3 20 24.8 49 6.6 84 6.5 31 13.1 45 10.6 -30 5.3 2 13.9 -0 6.8 10 5.0WASH 32 8.3 86 8.2 28 3.6 51 6.6 -75 18.3 -18 7.9 73 10.9 148 12.8 -86 17.7 50 7.0 -42 9.6 14 6.4 -19 10.0 15 8.0BRUSH 35 5.0 68 11.4 34 3.2 69 11.6 -78 16.0 -22 7.8 72 5.4 146 10.3 -46 13.9 41 5.1 -32 17.2 39 18.7 -22 9.9 17 3.4COMB^35 5.7 86 16.1 31 4.5 77 8.5 -85 11.9 -13 16.3 71 6.4 143 10.7 -52 25.8 47 9.1 -35 8.2 36 16.6 -18 8.1 24 9.7EXTREM.I 7 108 15 96 -85 20 42 151 -86 61 -42 53 1 -39 24 -AVG SD 7.8 8.1 4.1 _ 6.3 9.9 8.3 6.1 7.1 11.0 9.4 8.9 11.6 7.3 5.6Table I -1: Motion Analysis Results, All SubjectsAppendix  J: Conversion  oLShoulder  Joint  Angles  from  UM  lo_UBCThe University of Manitoba [102, 103, 104] expressed the three shoulder degrees of freedomas Flexion-Abduction-Rotation whereas the present study at the University of BritishColumbia uses Azimuth-Elevation-Roll, as explained in Section 4.3.1. This Appendixpresents the conversion that was performed to allow the UM results to be compared to theUBC results in Section 4.5.4 of this thesis.The formulation used for this study (detailed in Section 5.2) was:cos01 0^sines, cose2 0 -sine2 cose3 0 sin03sine, 0 -cose, sine2 0 cose2 sin03 0 -cose3010 010 • 0^1 0^_Multiplying this out, it becomes:-cosO1cos02cose3 - sin.O1sin03 -cosO1sin02 cos81cos02sine3 + sine1cos03sine1cos02cos03 + cose1sin03 -sine1sine2 sinO1cose2sin03 - cose1cose3sin02cos(33^cos82^sin02sinO3The University of Manitoba formulation of flexion-abduction-rotation corresponds to the sameaxis rotations as the above formulation except that the arm is first rotated down by 90degrees. The first rotation for the present study is about a vertical axis, starting with the armhorizontally out to the side, whereas the first rotation for the UM study was about a horizontalaxis, starting with the arm vertically down. The above matrix is therefore premultiplied bythe following rotation matrix:1520 0 10 1 0-1 0 0To give:sina2cosa 3^cosa2^sina2sina 3sina 1cosa2cosa3 + cosa 1sina3 -sina1sina2 sina icosa2sina3 - cosa 1cosa3-cos a1c0sa2cosa3 + sina isina3 ccsa isina2 -cosa icosa2sina3 - sina icosa3where a represents the UM angles and 9 represents the UBC angles.Thus, individual elements of the UM matrix and the UBC matrix can be compared.From the 3rd row, 2nd column:cose2 = cosa isina282 = atccos(cosa isina2)elevation = arccos[cos(fkrion).ain(abduction +a)]2From the 3rd row, 3rd column:sin82sin83 = -cosa icosa2sina3 - sina icosa3-cosa icosa2sina3 - sina icosa383 = arcsin^811182 -cos(ficdon).cos(abduction + -1-1).sin(rotation) - sin(flexion).cos(rotation)2 sin(elevation)roll153And from the 1st row, 2nd column:-cose1sine2 = cosa201 = arccos--cosa2sine2 ...-cos(abduction +.1-112 azinuah = =cossin(elevation)Appendix  K: Simulation ValuesThe values of the joint limits used in the orthosis simulations are listed in Table K-1. Theyare approximately equal to the anatomical joint limits compiled by Boone [11].Degree of Freedom Minimum Angle Maximum AngleAzimuth -10° 140°Elevation 00 120°Roll -900 70'Elbow Flexion 00 160°Forearm Rotation -85° 750Wrist Flexion -750 750Wrist Yaw -36° 22°Table K-1: Joint Limit ValuesThe value of the minimum and maximum carrying angle is unimportant as long as theminimum value is set equal to the maximum value to indicate that it is fixed at the value ofthe initial estimate.The initial joint angle estimates were derived from the motion analysis results as an averageof all subjects. If an individual's position or orientation were significantly different from theothers, the values were excluded from the average. The initial joint angle estimates that wereused in the simulations are given in Table K-2. See Table 5-3 for a description of the taskabbreviations.155I Task^II Azim. Elev. Roll Carry Elbow F. Rot'n W. Flex W. Yaw IH1 48.0 38.5 -0.4 13.3 96.6 27.7 6.1 4.2H2 62.8 43.2 -44.9 13.3 134.1 -70.7 -9.6 -12.3Fl 40.7 56.6 2.6 13.3 109.5 50.2 29.4 -4.3F2 44.4 45.9 -36.4 13.3 133.5 -31.0 16.8 -2.2Si 46.1 56.6 -12.0 13.3 106.4 47.6 14.8 12.7S2 47.2 74.3 -51.6 13.3 122.8 -18.3 39.9 7.0Cul 51.9 50.7 -49.5 13.3 114.6 0.5 -8.7 -4.8Cu2 54.8 63.2 -61.6 13.3 133.3 8.7 -7.7 -0.1R1A 6.8 31.0 -29.0 13.3 73.0 -16.5 -11.8 7.8R2A 73.0 37.9 -21.9 13.3 66.8 -22.9 -29.1 1.4R3A 107.8 41.2 -26.3 13.3 57.5 -21.5 -28.7 4.2^1R1B 9.4 32.1 -25.7 13.3 70.1 46.1 -15.4 4.0R2B 80.1 38.1 -25.8 13.3 64.4 43.1 -11.7 -0.6R3B 107.1 42.3 -24.9 13.3 58.1 39.7 -12.5 0.4Po 64.7 85.3 -18.4 13.3 71.2 -25.0 -10.0 -10.1D1 61.9 56.9 -32.7 13.3 59.2 28.8 -23.3 3.4D2 71.5 48.4 -48.5 13.3 61.5 -2.1 -26.5 -1.0K1 64.2 63.4 -31.4 13.3 41.6 48.0 -35.5 2.8K2 68.2 58.8 -41.8 13.3 48.0 10.3 -26.8 -7.1T1 56.0 62.9 -22.0 13.3 61.9 35.9 1.1 0.412 66.4 54.9 -35.9 13.3 66.9 46.9 14.4 -35.6Li 67.8 96.4 -50.5 13.3 47.2 -43.6 -5.1 -17.0Bu 66.9 90.0 -46.0 13.3 51.4 22.9 -0.2 -2.4Pa 73.1 43.8 -20.7 13.3 87.3 55.5 21.7 -16.3Ph 69.5 53.4 -77.1 13.3 149.8 -10.6 -30.3 -8.7La 80.5 33.5 -26.3 13.3 49.3 40.0 -7.3 3.8W1 84.4 48.9 -60.1 13.3 132.3 -82.6 -1.4 -6.1W2 72.3 48.9 -73.2 13.3 149.4 -28.0 -31.0 -5.2Brl 53.4 63.7 -61.1 13.3 135.8 -45.7 21.3 4.1Br2 54.2 57.0 -54.2 13.3 129.2 -43.6 22.4 -10.0Col 71.6 80.3 -54.4 13.3 108.2 -36.2 13.3 5.7Co2 62.1 63.9 -63.8 13.3 125.9 -18.0 -25.1 -0.2St1 43.8 36.6 -24.2 13.3 67.9 29.8 -14.0 -1.0St2 43.4 35.5 -31.2 13.3 72.7 35.6 -1.3 4.1Table K-2: Initial Joint Angle EsimatesThe limb lengths used in the simulations were also based on the average of all subjects:Upper arm: 26.9 cmForearm:^25.3 cm'Hand': 7.2 cm^(wrist to knuckle)The desired endpoint positions, relative to the shoulder, are given in Table K-3.156Task Desired X Coord(+ = to the right)Desired Y Coord(+ = forward)Desired Z Coord(+ = up)H1 -14.2 31.4 -19.9112 -11.9 21.7 2.8Fl -9.4 31.2 -15.0F2 -7.5 22.1 -0.4Si -8.6 32.9 -9.5S2 -6.4 23.0 11.4Cul -5.1 21.0 6.9Cu2 -4.3 18.0 12.5R1A 30.4 28.2 -21.9R2A -11.6 43.9 -22.1R3A -34.0 36.0 -22.3R1B 27.6 31.3 -21.4R2B -17.9 41.8 -22.0R3B -35.2 33.0 -21.9Po -8.7 47.5 10.1D1 2.9 51.1 -5.6D2 2.5 51.0 -9.2K1 7.5 52.7 -4.6K2 8.0 53.6 -6.5Ti 3.4 51.1 -6.6T2 1.3 51.5 -7.5Li 7.1 48.7 27.3Bu 4.6 48.4 23.5Pa -18.7 37.4 -13.9Ph -2.5 12.4 9.4La -13.7 43.5 -31.9W1 -14.8 18.6 6.6W2 -3.8 14.6 8.4Brl -6.9 17.9 9.7Br2 -7.8 22.3 7.5Col -14.3 23.0 20.5Co2 -2.6 21.8 16.9SU 8.1 43.6 -21.6St2 8.2 41.9 -19.7Table K-3: Desired Endpoint PositionsThe values for the orientation vectors, relative to the fixed frame of reference, as well as theweightings are given in Table K-4.157I Task^II^'Up' vector I^Wt Forward' Vector Wt 'Palm Vector Wt IH1 (-0.508, -0.808, 0.170) .05 (-0.818, 0.540, -0.030) .05 (-0.068, -0.154, -0.935) .10112 (0.520, -0.316, 0.782) .05 (-0.705, 0.336, 0.605) .05 (-0.454, -0.866, -0.048) .10Fl (-0.516, -0.688, -0.475) .10 (-0.641, 0.699, -0.315) .05 (0.549, 0.142, -0.802) .05F2 (0.030, -0.830, 0.487) .10 (-0.818, 0.256, 0.437) .05 (-0.487, -0.411, -0.671) .05Si (-0.400, -0.734, -0.550) .10 (-0.844, 0.514, -0.072) .05 (0.335, 0.435, -0.824) .05S2 (-0.179, -0.945, -0.170) .10 (-0.963, 0.152, 0.095) .05 (-0.064, 0.180, -0.937) .05Cul (-0.389, -0.854, 0.049) .10 (-0.451, 0.230, 0.853) .04 (-0.740, 0.310, -0.475) .04Cu2 (-0.474, -0.745, -0.334) .10 (-0.493, -0.077, 0.859) .04 (-0.665, 0.572, -0.331) .04R1A (-0.390, 0.053, 0.900) .10 (0.614, 0.740, 0.241) .05 (-0.653, 0.646, -0.321) .05R2A (-0.330, -0.230, 0.898) .10 (-0.197, 0.936, 0.197) .05 (-0.886, -0.111, -0.354) .05R3A (-0.197, -0.385, 0.885) .10 (-0.607, 0.753, 0.213) .05 (-0.743, -0.504, -0.389) .05R1B (-0.917, 0.377, 0.045) .10 (0.371, 0.888, 0.232) .05 (0.047, 0.229, -0.954) .05R2B (-0.764, -0.632, 0.008) .10 (-0.618, 0.748, 0.165) .05 (-0.110, 0.120, -0.961) .05R3B (-0.438, -0.890, 0.003) .10 (-0.872, 0.431, 0.147) .05 (-0.132, 0.062, -0.964) .05Po (-0.670, -0.578, 0.417) .08 (-0.404, 0.785, 0.414) .07 (-0.566, 0.108, -0.759) .07D1 (-0.931, -0.319, 0.081) .10 (-0.211, 0.783, 0.567) .05 (-0.244, 0.510, -0.796) .05D2 (-0.567, -0.271, 0.760) .08 (0.174, 0.860, 0.446) .05 (-0.774, 0.385, -0.441) .05K1 (-0.928, -0.086, -0.283) .05 (-0.245, 0.722, 0.620) .05 (0.151, 0.644, -0.691) .10K2 (-0.825, -0.042, 0.515) .05 (0.248, 0.832, 0.449) .05 (-0.447, 0.498, -0.676) .10Ti (-0.905, -0.265, -0.222) .10 (-0.326, 0.919, 0.151) .05 (0.164, 0.209, -0.981) .05T2 (-0.944, 0.281, 0.020) .10 (0.285, 0.943, 0.144) .05 (0.022, 0.141, -0.971) .05Li (-0.193, -0.485, 0.808) .05 (0.028, 0.826, 0.523) .05 (-0.922, 0.123, -0.145) .10Bu (-0.963, -0.208, 0.056) .05 (-0.114, 0.721, 0.664) .10 (-0.179, 0.633, -0.718) .05Pa (-0.797, -0.499, -0.242) .05 (-0.523, 0.828, -0.031) .05 (0.215, 0.102, -0.921) .10Ph (-0.145, -0.941, -0.197) .10 (0.051, -0.201, 0.962) .05 (-0.945, 0.129, 0.077) .05La (-0.831, -0.521, 0.109) .05 (-0.535, 0.821, -0.126) .05 (-0.024, -0.163, -0.961) .10W1 (0.671, -0.068, 0.633) .05 (-0.684, -0.015, 0.705) .05 (-0.038, -0.906, -0.056) .10W2 (0.226, -0.901, -0.013) .05 (0.007, 0.012, 0.979) .05 (-0.881, -0.221, 0.009) .10Brl (0.131, -0.897, 0.204) .10 (-0.840, -0.083, 0.451) .05 (-0.388, -0.239, -0.764) .05Br2 (0.106, -0.874, 0.456) .10 (-0.848, -0.117, 0.444) .05 (-0.441, -0.433, -0.729) .05Col (0.252, -0.954, 0.103) .10 (-0.754, -0.134, 0.620) .05 (-0.578, -0.234, -0.753) .05Co2 (-0.127, -0.983, -0.033) .10 (-0.121, -0.009, 0.990) .05 (-0.973, 0.129, -0.117) .05SO (-0.950, -0.105, 0.237) .05 (-0.061, 0.965, 0.207) .05 (-0.250, 0.183, -0.923) .05St2 (-0.938, -0.217, 0.197) .10 (-0.214, 0.940, 0.122) .05 (-0.197, 0.076, -0.931) .05Table K-4: Desired Orientation Vectors and WeightingThe detailed results for the two recommended alternatives are given below. Tables K-5 andK-7 give the distances and angles between the actual and desired endpoint positions andorientations at the final point. Tables K-6 and K-8 give the joint angles at the final position.158If the cost function value had a value less than 6.0 or ten iterations had been exceeded, thesearch was terminated.Task Successful? Distance(cm)UpAngle(Degrees)ForwardAngle(Degrees)PalmAngle(Degrees)CostFunctionValue (cm')H1 Y 1.3 3 5 5 5.31H2 Y 1.1 2 2 2 1.47Fl Y 1.0 2 1 2 1.19F2 Y 1.2 5 4 6 5.4251 C 2.8 11 11 3 23.43S2 Y 2.5 7 5 6 12.87Cul Y 1.2 5 5 6 5.32Cu2 Y 1.2 5 5 5 5.45R1A Y 2.8 10 10 6 21.88R2A Y 1.8 7 7 5 9.99R3A Y 2.4 8 8 5 15.97R1B Y 1.7 6 6 3 8.19R2B Y 1.6 4 3 4 5.14R3B Y 0.9 1 5 6 3.32Po N 5.7 2 3 4 34.39D1 Y 2.1 6 5 3 8.61D2 Y 1.8 3 2 3 4.01K1 N 3.4 9 8 4 18.61K2 Y 1.9 2 2 3 4.69Ti Y 2.6 7 8 2 13.30T2 c 2.4 13 12 4 30.07Li N 19.3 20 20 6 415.04Bu N 16.1 3 3 2 265.20Pa C 2.9 16 16 4 33.98Ph Y 0.3 2 3 4 1.28La Y 1.1 4 3 3 2.43WI Y 0.9 5 2 6 5.13W2 Y 1.2 6 3 6 6.08Brl Y 0.9 5 3 7 5.65Br2 Y 0.5 6 9 4 7.48Col N 6.6 2 7 7 50.40Co2 Y 1.8 3 3 3 4.59Stl Y 1.7 4 2 4 4.08St2 Y 1.2 4 6 7 5.84Table K-5: Actual vs. Desired Values for Fixed Elevation and Wrist Yaw159I Task^II^Aziln* Elev. Roll Carry Elbow F. Rotn I^W. Flex W. YawH1 48 53 9 13 98 13 1 -2H2 54 53 -30 13 133 -73 -14 -2Fl 40 53 1 13 109 51 29 -2F2 32 53 -27 13 137 -39 10 -2Si 41 53 -4 13 113 53 14 -2S2 80 53 -89 13 132 -9 74 -2Cul 37 53 -41 13 138 -6 -12 -2Cu2 55 53 -63 13 141 12 -8 -2R1A -5 53 8 13 83 -43 -39 -2R2A 68 53 3 13 68 -45 -42 -2R3A 106 53 -6 13 54 -40 -37 -2R1B 3 53 9 13 67 17 -30 -2R2B 77 53 3 13 55 16 -24 -2R3B 108 53 -1 13 46 18 -20 -2Po 95 53 -84 13 85 33 23 -2D1 65 53 -40 13 62 35 -20 -2D2 72 53 -46 13 55 -3 -25 -2K1 67 53 -50 13 55 64 -27 -2K2 79 53 -70 13 49 34 -18 -2Ti 61 53 -38 13 68 50 7 -2T2 87 53 -80 13 51 71 6 -2Li 82 53 -91 13 92 -6 4 -2Bu 79 53 -83 13 96 56 15 -2Pa 69 53 -15 13 83 42 16 -2Ph 48 53 -56 13 151 -10 -42 -2La 84 53 30 13 30 -15 -28 -2W1 71 53 -45 13 134 -85 -3 -2W2 53 53 -52 13 151 -28 -45 -2Brl 54 53 -65 13 139 -43 32 -2Br2 52 53 -52 13 130 -43 29 -2Col 106 53 -92 13 122 -12 39 -2Co2 64 53 -42 13 128 5 -40 -2St1 39 53 5 13 62 3 -29 -2St2 31 53 4 13 73 7 -13 -2Table K-6: Resulting Joint Angles for Fixed Elevation and Wrist Yaw160Task Successful?Distance(cm)UpAngle(Degrees)ForwardAngle(Degrees)PalmAngle(Degrees)CostFunctionValue(cm2)H1 Y 1.4 4 6 4 5.83H2 Y 0.8 5 5 2 3.32Fl N 4.1 10 21 19 63.37F2 Y 1.0 5 5 6 5.77Si Y 1.2 3 7 6 5.93S2 Y 2.3 7 8 5 12.61Y 1.1 5 3 5 S4.21CulCu2 Y 1.3 4 1 4 3.30R1A Y 1.3 5 6 4 5.32R2A Y 1.1 1 6 6 4.51R3A Y 1.7 6 8 3 8.88R1B Y 0.8 2 5 5 2.70R2B Y 1.0 2 4 4 2.02R3B Y 1.7 1 4 4 4.26Po Y 2.0 7 8 4 11.33D1 Y 1.7 4 8 7 10.00D2 Y 0.6 4 7 7 5.57K1 N 3.4 5 14 13 36.67K2 Y 1.0 5 6 6 7.04Ti Y 0.8 4 6 8 5.76T2 N 6.0 13 13 4 58.34Li Y 1.5 7 5 5 7.26Bu Y 2.6 1 2 2 8.99Pa N 4.8 12 20 17 75.40Ph Y 0.9 3 9 9 9.37La Y 2.3 3 3 2 5.98W1 Y 1.0 5 3 6 6.42W2 Y 0.8 6 4 6 6.21Brl Y 1.7 5 8 8 10.51Br2 C 2.0 1 16 4 17.04Col Y 1.7 3 4 3 4.77Co2 Y 2.3 6 7 5 12.12S tl Y 0.8 2 5 5 2.69St2 Y 0.5 5 7 6 5.64Table K-7: Actual vs. Desired Values for Fixed Wrist Flexion and Wrist Yaw161I Task^II^Azim. Elev. Roll^1^Carry Elbow 1^F. Roth W. Flex W. YawH1 48 48 13 13 95 20 -9 2H2 50 46 -30 13 135 -68 -9 2Fl 38 70 17 13 100 38 -9 2F2 31 61 -14 13 137 -32 -9 2Si 41 76 8 13 105 36 -9 2S2 28 109 -30 13 131 -34 -9 2Cul 47 42 -48 13 136 2 -9 2Cu2 53 59 -61 13 134 8 -9 2R1A 6 29 -31 13 76 -18 -9 2R2A 86 30 -54 13 66 -6 -9 2R3A 133 37 -78 13 52 7 -9 2R1B 10 33 -26 13 72 46 -9 2R2B 79 38 -26 13 64 43 -9 2R3B 107 42 -25 13 58 40 -9 2Po 68 88 -15 13 61 -28 -9 2DI 68 54 -47 13 63 38 -9 2D2 87 49 -79 13 55 19 -9 2K1 66 57 -50 13 59 60 -9 2K2 86 58 -89 13 44 48 -9 2Ti 57 64 -19 13 56 36 -9 2T2 89 67 -74 13 22 69 -9 2Li 66 109 -10 13 29 -85 -9 2Bu 71 100 -28 13 33 9 -9 2Pa 75 41 -24 13 72 54 -9 2Ph 74 35 -91 13 155 -14 -9 2La 80 33 -26 13 48 40 -9 2W1 69 55 -42 13 136 -86 -9 2W2 80 30 -89 13 151 -32 -9 2Brl 37 84 -42 13 142 -53 -9 2Br2 40 81 -31 13 135 -54 -9 2Col 65 95 -43 13 114 -46 -9 2Co2 85 38 -76 13 133 4 -9 2SO 43 37 -25 13 67 30 -9 2St2 40 37 -24 13 72 35 -9 2Table K-8: Resulting Joint Angles for Fixed Wrist Flexion and Wrist Yaw162

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