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A parallelogram chain designed to measure human joint motion Cousins, Steven J. 1975

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A PARALLELOGRAM CHAIN DESIGNED TO PeSURE HUMAN JOINT MOTION BY STEVEN J , COUSINS B.A.Sc, University of Br i t i s h Columbia Vancouver, Br i t i s h Columbia, 1973 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE IN THE DEPARTMENT OF MECHANICAL ENGINEERING IN CONJUNCTION WITH THE DIVISION OF ORTHOPAEDICS We accept this thesis as conforming to the required standards THE UNIVERSITY OF BRITISH COLUMBIA July, 1975 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i lab le for reference and study. I fur ther agree that permission for extensive copying of th i s thes is for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t i on of this thes i s for f i nanc ia l gain sha l l not be allowed without my writ ten permission. Depa rtmen t The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 ABSTRACT i i This work i s concerned with the problem of measuring the motion of a human joint under dynamic conditions. Past and present solutions to this problem are examined in a literature search. Criteria are established for the evaluation of designs, based on one year's c l i n i c a l experience with a locally built device. A parallelogram chain i s chosen from generated design alternatives using the established evaluation c r i t e r i a . A prototype of the parallelogram chain i s b u i l t . The chain cast-ing has thin flexible p l astic hinges. As each parallelogram scissors, unwant-ed* translations are absorbed while three mutually perpendicular rotations pass through the chain unchanged. This allows the potentiometer motica trans-ducers to be self-aligning with a joint. This w i l l reduce patient f i t t i n g time and increase the reproduceability of results compared to previous devices. The chain i s applicable to any large joint of the upper or lower limbs. A test r i g , simulating human joint motion, i s b u i l t . Test results indicate that the parallelogram chain can record dynamic motions of walk-ing and slow running. The chain has a definable working volume within which low error and reproduceablc results can be obtained. The chain pro-duced best results, comparable or better than those obtained by other work-ers, when only one of the three measuring potentiometers was aligned with the corresponding joint axis of rotation. Errors caused by the joint simulator are explained and w i l l f a c i l -itate redesign. The main source of measurement error i s the hinge geom-etry and not the material properties of the chain. As a result, a new chain design i s presented that should give reduced measurement errors. i i i TABLE OF CONTENTS Chapter Page 1 INTRODUCTION 2 1.1 The Problem and Its Relevance 3 1.2 State of the Art . 3 1.2.1 Approach 3 1.2.2 Past Solutions to Problem 4 1.2.3 Present Solutions to the Problem . . 15 1.3 Scope of this Work 19 2 DESIGN CRITERIA 20 2.1 Design Criteria 20 3 PROPOSED SOLUTIONS 23 3.1 Introduction . . . . . . . 23 3.2 S5ngle Parallelogram 24 3.3 Double Parallelogram 26 3.4 Telescopic Unit 27 3.5 Parallelogram Chain 28 4 ELVALUATION AND SELECTION 30 4.1 Evaluation and Selection 30 5 DETAILS OF DESIGN . 32 5.1 Introduction 32 5.2 Material Selection 32 5.3 Hinge Design 33 iv Chapter Page 6 TEST APPARATUS . 38 6.1 Test Apparatus 38 6.2 Test Procedure . . 40 6.3 Results . . 44 6.3.1 Data . 44 6.3.2 Discussion 48 7 SUMMARY AND CONCLUSIONS 54 7.1 Summary" and Conclusions 54 8 RECOMMENDATIONS . . . 56 8.1 Recommendations For Future Work 56 REFERENCES . . . . . . . . . . 58 APPENDIX I Definition,of Terms . 60 APPENDIX II Typical Electrogoniometer Records . . . . . . . . . . . 61 APPENDIX III Casting Technique 65 APPENDIX TV Summary of Manufacturers Data Sheet of the Polyurethane elastomers . . . . . . . . . 67 APPENDIX V The Attenuator Box 68 APPENDIX VI Redesigned Parallelogram Chain . . 74 V ACKNOWLEDGEMENTS I would not have been in a position to do this work had i t not been for Jim Foort's (Orthopaedics) energetic approach to c l i n i c a l and rehabilitation engineering. Under Jim's protection and through his free and open philosophy I have flourished. I would li k e to thank Bob McKechnie (Mechanical Engineering) for his positive, encouraging help throughout the project. Gordon Judge (Health Service, England) deserves special thanks for risking to share his ideas with a stranger for the eventual benefit of patient treatment. Thanks are due the people i n the Mechanical Engineering machine shop for the work they did on the project. Thanks are also due to a l l the people at the Arthritis Center (C.A.R.S.) for their patience with the "engineers" (also, for working space, money and their time). Financial assistance was received from the British Columbia Medical Service Foundation, The Canadian Arthritis and Rheumatism Society, The Medical Research Council of Canada and The National Health and Welfare Department, Government of Canada. Finally, I want to thank Sylvi, my wife to be, for a l l her concern and help the innumerable times when support was needed. 1 A PARALLELOGRAM CHAIN DESIGNED TO MEASURE HUMAN JOINT MOTION 2 C H A P T E R I I N T R O D U C T I O N 1.1 The Problem and Its Relevance '3 This work i s concerned with the problem of measuring the motion of a human joint under dynamic conditions. Quantitative measurements w i l l help answer questions involving medical treatment of disabled people. The motion records of patients can be compared to those of normal people for i n i t i a l as-^  sessment and later compared to themselves to measure changes due to disease, d i s a b i l i t y and treatment. The motion measurements w i l l help to: - decide i n i t i a l physiotherapy (rehabilitative treatment), - determine the effects of physiotherapy, - devise new physiotherapy techniques, - decide when to brace a joint (add external support) , - determine the effects of bracing, before and after, - design new braces and improve old ones, - aid a doctor's decision to operate ( a r t i f i c i a l j o int replacement), - determine problems with the implanted device, - design new and improved implants. 1.2 State of the Art 1.2.1 Approach Electrogoniometry measures motion using potentiometer transducers i n direct patient contact. There are remote sensing motion monitoring devices using cine f i l m , television, and low energy x-rays but the data obtained must be reduced to useable form, eg., numbers, graphs. Electro-goniometry gives direct graphical results. * "electro" refers to the potentiometer motion transducer and means angle measurement. 4 1.2.2 Past Solutions to Problem The fifteen year history of electrogoniometry can be summarized by four research groups' a c t i v i t i e s : 1. Karpovich and coworkers (1959 - 1965) in i t i a t e d electrogonio-metry and did many basic studies (References 1 to 6). The "elgon", as he called i t , consisted of a potentiometer and two thin metal bars, one bar attached to the casing and one bar attached to the shaft of the potentio-meter. By strapping one bar above and one bar below the j o i n t , and align-ing the shaft of the potentiometer to the joint axis of rotation*, the motion of the joint i n that plane could be measured. What i s recorded i s the voltage output of the potentiometer, which i s proportional to the ang-ular rotation of the joi n t . (See Figure 1.) See Appendix I for definition of terms marked with asterisks. Flexion-extension* of the hip, knee and ankle joints of normal i n -dividuals and many disabled people were measured during various a c t i v i t i e s , (including swimming). The use of electrogoniometry i n a routine c l i n i c a l way was proposed by Karpovich and Tipton in their a r t i c l e " C l i n i c a l Electrogoniometry" i n 1964. The work of Karpovich and coworkers was significant but limited, since: (a) only the flexion-extension motion could be measured at a j o i n t ; internal and external rotation* and adduction-abduction* were not measured; nor was valgus-varus*; (b) data, was considered from, at most, the hip, knee and ankle of one leg only. The effects of the other leg on the instrumented leg were not considered; (c) since the devices were not self-aligning, guesses as to the a---lignment of the potentiometer with the joint centre of rotation had to be made each time the device was strapped to the patient. Misalignment of a potentiometer with a joint increases the pos-s i b i l i t y of motion between the device and the patient, a major source of error i n electrogoniometry. The problem i s that no matter how carefully the single axis of the potentiometer i s man-oeuvered, i t w i l l never be aligned with a polycentric joint such as the knee, These last problems can be c l a r i f i e d with the aid of Figure 2. A r i g i d bar i n the shape of a T i s rotating i n space. A line on the T, ab, rotates through an angle of 45° in moving from position ab to a'b', the same angle that the part of the T that i s attached to the centre of rotation moves through. The points on the line ab must also translate through space because 6 Figure 2. Translations i n space of a point on a rotating body. they are not sit t i n g at the centre of rotation. For example, point a must translate amount x over and y down as i t moves from position a to a'. If a shaft of a potentiometer were mounted at the centre of rotation shown, the true rotation would be measured. If the centre of rotation moved from under the potentiometer or i f the potentiometer shaft was located at point a, true rotation would not be measured; the off-axis translations would interfere with the measurement. If the potentiometer i n Karpovich's device was not a-ligned with the joint axis of rotation, forces would be generated between the patient and the device because the off-axis translations would be constrain-ed by the thigh and leg strap mountsc'i (A and D of Figure 1). Because this device i s not self-aligning, that i s , does not automatically absorb any off-axis 7 translations, two errors occur: (a) Direct error - the potentiometer does not give true rotations. (b) Indirect error - the constraining forces imposed on the patient by the device (due to misalignment) affect the motion pattern to be measured. 2. Johnston and coworkers (1969 -1972) did the f i r s t electrogonio-metric studies of three mutually perpendicular rotations occurring at a joint (References 7 to 11). The potentiometers (Figure 3) were aligned with the axis of rotation of the joint except for: (a) Internal-External Rotation -Since this axis was internal to the body where a potentiometer could not be mounted the potentiometer was located along the leg and an approximation of the motion was measured. Later, computer studies showed how this error could be corrected, given the location of the device relative to the joint. Their conclusion was that the larger the angular rotation, the larger ( the error. (b) Abduction-adduction or Valgus-varus -They chose to locate this potentiometer on the side of the leg, displaced away from the real axis of rotation. By attaching a long, thin rectangular shaped rod to this potentiometer and a l -lowing this rod to telescope through the lower or d i s t a l leg attachment, any translatory movements generated by being off-axis were absorbed by the sliding rod. Thus, true abduction-adduction was measured. 8 Figure 3. Schematic drawing of Johnston's electrogoniometer Johnston and coworkers improved upon the work of Karpovich, but their solution was also limited: (a) although three perpendicular angular measurements were attempted at the knee and hip, the measuring device was not self-aligning and had to be positioned on the patient each time i t was used. (b) because the measurement of internal-external rotation was ap-proximated using a potentiometer aligned parallel to the rota-tional axis (the location of this axis cannot be readily found), an error that varied with the degree of rotation was occurring. (c) from their computer study some of the reported errors were (for motions at the hip): 9 Motion Error Flexion-extension 14.4%, 13.45°/93.45° Internal-external rotation 18.8%, 5.23°/27.76° Abduction-adduction* 6.2%, 1.45°/23.54° *The low error i s because the electrogoniometer i s self-aligning i n the measurement of abduction-adduction motion. 3. Lamoreux (1970 - 1971) has extensively tested simultaneously, the joints of the leg of one normal subject walking. (Reference 12). An external hip analog was built consisting of a frame that attached to the pelvis, could be adjusted so as the movements of the hip were "duplicated in the external joint system by three revolute joints connected i n series." Thus the potentiometers located at these pivots record flexion-extension, ab-duction-adduction and:internal-external rotation at the hip. At the knee and ankle, see Figure 4, he used a self-aligning parallelogram linkage; this paral-lelogram linkage can measure any two out of "the three components of an arbit-rary rotation i n the three dimensions", absorbing the third rotation in the movement of the linkage. The action of the device i s as follows: (a) Measurement of Flexion-extension -Figure 5 shows the side and front views of an equivalent linkage to that of Figure 4, that w i l l allow flexion-extension measurements to be made. Pivot H i s " r i g i d l y " attached to the leg and represents the potentiometer of Figure 4, E. This can be done, since the action of the potentiometer i s in a plane perpendicular to the flexion-ex-tension axis, e.g., perpendicularly mounted with respect to potent-iometer B. As the leg flexes or extends, pivots F, G and H allow the Figure 4. Schematic drawing of Lamoreux's parallelogram linkage Figure 5. Lamoreux's parallelogram linkage modified for measuring flexion-extension at the knee CSee Figure 4 for letter code) 11 linkage to straighten or bend, thus absorbing any translatory movements that occur. However, i f any rotatory movements occur between the thigh and leg cuffs,(what i s to be measured) the paral-lelogram I w i l l transmit the rotation to bar J , thus rotating the shaft of the potentiometer located at K. (b) Measurement of Internal-external Rotation -Figure 6 shows the side and front views of an equivalent linkage to that of Figure 4 that w i l l allow internal-external rotation of the leg to be measured. Figure 6. Lamoreux's parallelogram linkage modified for measuring internal-external rotation of the leg (See Figure 4 for letter code) Pivot F i s r i g i d l y attached to the thigh and replaces the potentio-meter B of Figure 4. This i s valid since potentiometer B i s mounted perpendicularly to potentiometer E and therefore cannot cause a ro-tation of potentiometer E. As the leg internally or externally ro-tates , any translatory movements w i l l be absorbed by the linkage through a combination of parallelogram I pivoting or "scissoring" and motion in pivots F, G and H. For example, i f the potentiometer at E translates forward, parallelogram I w i l l scissor thus shorten-ing the distance between pivots F and G. However, this shortening is accommodated with a corresponding hinging action at pivots F, G and H. If any rotatory movements occur between the thigh and the leg, the parallelogram I w i l l transmit them through bar L to the potentiometer at E, thus recording the desired movement. Lamoreux's self-aligning parallelogram linkage was a major step forward i n electrogoniometry. The problems of aligning a single axis poten-tiometer with a muiti-axis joint were minimized and the resetting errors, in measurement and reproduceability were greatly reduced. But Lamoreux's electro-goniometry had i t s limitations: (a) the overall device was b u i l t (by choice) to study normal people and i s not meant for routine c l i n i c a l use. Its weight was about 3.5 Kgs or 7.5 pounds, quite encumbering for most disabled people. The hip analogue had a cylindrical cuff around the thigh (for i n -ternal-external rotation measurement) which would make use by a knocked-kneed person (valgus deformity) impossible. (b) the hip analogue was not self-aligning. The potentiometers had to be visually aligned with the estimated joint location using sur-face anatomical features; reproduceability was dependent upon the s k i l l of the user. 13 (c) To obtain three perpendicular rotations at the ankle, two of the self-aligning parallelogram linkages had to be used. If three rotations are to be measured this would be a bulky device to do i t with. (d) The accuracy of measurement of the parallelogram linkage on i t s own was not established but the overall measurement accuracy of the device on the subject was estimated ( i t i s not explained how). The "measurement precision" varies from 0.5° in 65° knee flexion (0.81) to 4° in 16° rotation (25%) to 4° in 8° of pelvic rotation (50%). 4. Kinzel and Hillberry, (1970 - 1971) have proposed a system for measuring a l l six possible movements between the bones that comprise a joi n t , that i s , three translations and three rotations. Their device (References 13, 14), which has experimentally been pinned to dog legs, uses a space link-age with six potentiometers attached, Figure 7. The six recordings obtained do not relate to the standard c l a s s i f i -cation of movement, that i s , flexion-extension, abduction-adduction, and i n -ternal-external rotation. To get the standard movements from the data, a : d i g i t a l computer i s necessary for the data reduction. Kinzel and Hillberry mention these points: (a) "If four of the potentiometers would become parallel during some phase of the motion, in that position: the linkage would not accurate-l y follow the joint motion". (b) "Care must be exercised when the linkage i s b u i l t i n order to eliminate "play" due to tolerance build-up i n the linkage joints." (c) "A d i g i t a l computer i s almost mandatory. The use of the space 14 mechanism measurement system i s obviously not warranted i f the po-tential accuracy of the space mechanism cannot be used." B - TYPICAL POTENTIOMETER D - LEG CUFF Figure 7. Schematic drawing of Kinzel and Hillberry's space linkage Kinzel and Hillberry's space mechanism i s a valid approach to the measurement and self-aligning problem. However, the use of a d i g i t a l computer severely limits i t s widespread use c l i n i c a l l y . Measurement of a l l six degrees of freedom at a joint may end up to be functionally quite significant. Init-i a l l y however i t would seem adequate to measure the three perpendicular rota-tions (grosser movements than the three translations) on each of the lower 15 limb joints of both legs simultaneously. It i s the author's opinion that measurement of the interdependence of these motions during functional act-i v i t i e s and the effects of disease and subsequent treatment on this inter-dependence w i l l be as or more significant than individual joint studies. The attachment of an electrogoniometric device to a patient (beyond the scope of this work) must be faced eventually by a l l workers i n the electro-goniometric f i e l d . Kinzel and Hillberry barely touched on this area but use of pins into bone, being practical with dogs, i s impractical for human patients. The use of small suction cups and small amounts of spray-on med-ic a l grade adhesives over boney landmarks along with angular attachment brack-ets which, when tightened down, deform and grip the flesh, preventing rotary movements, may lead to some answers. 1.2.3 Present Solutions to the Problem Jim Foort, Orthopaedics, UBC, and later the author, designed, built and test-ed an electrogoniometer, Figure 8, which monitors the movements of the knee and ankle: Figure 8: The electrogoniometer used at the Canadian A r t h r i t i s and Rheu-matism Society's Vancouver B.C., Canada centre. 16 (a) flexion-extension (knee) (b) valgus-varus (knee) (c) inversion-eversion (ankle) (d) plantar-dorsiflexion (ankle) Although this device has some of the drawbacks of the equipment used by previous researchers, a year of c l i n i c a l experience was obtained that allowed Foort and Cousins to: (a) define the c r i t e r i a necessary for the evaluation of existing and new electrogoniometric devices, (b) quantitatively assess patient function under dynamic condition:;, (c) gather enough information of a r t h r i t i c joint movement to design a new a r t h r i t i c knee brace (Reference 15). Typical patient records from this device can be seen i n Appendix I I . Current work on electrogoniometry includes: (a) Dr. R. Jackson's work at the Toronto General Hospital which involves using an electrogoniometer with six potentiometers for studying the knee i n the c l i n i c . The device i s very similar to that of Kinzel and Hillberry. (b) At London, England, Gordon Judge an Engineer with the Bio-mechanical Research and Develpoment Unit, has designed a mechan-ism (at the balsa wood model stage) "for maintaining output rota-tion parallel to input rotation but absorbing a l l translation movements" i n three dimensions (Reference 16). Gordon Judge's drawing of this i s shown i n Figure 9. The mechanism consists of two double parallelograms mounted at right angles to one another one v e r t i c a l l y and one horizontally. A double parallelogram, two Figure 9. Gordon Judge's double-double parallelogram mechanism single parallelograms put together, has the same characteristics that Lamoreux's single parallelogram plus a hinge had. Any trans-lations in a plane can occur unrestrained (to the limit of the link lengths), but as soon as a rotation i s imparted to one end of the system, the rotation i s transmitted through unchanged to the other end of the system, where i t can be used to rotate a potentiometer shaft. The central bar of the vertical parallelogram "has to be external to avoid fouling the other central cross-member" of the horizontal double parallelogram. To complete the action of the 18 mechanism, pivoting i s allowed through the input/output shaft mounts at arrows marked A, B, C, and D. The three potentiometers used with this mechanism can be mounted as a cluster above or be-low the device as Gordon Judge suggests, or s p l i t , two above, one below, i n a similar manner to Lamoreux's. This "double-double parallelogram" i s an excellent concept. It allows three perpendicular rotations to be measured at a joint independently (within the limits of the link lengths) of the location of the center of ro-tation of the joint or how this center moves (self-aligning). The device could be designed as a module that would f i t any or a l l of the lower limb joints on both legs, hip, knee and ankle. A few problems with the device may be: (a) About 20 hinges or pivots are present i n the design and care w i l l have to be taken in i t s manufacture to prevent free-play. Re-design is necessary to reduce the number of pivots and the depend-ence of the hinging action on manufacturing tolerance. (b) A double parallelogram can only collapse to one half of i t s out-stretched length i n an unconstrained manner. Beyond that, the par-allelogram bars begin to move in arcs about each other. When attemp-ting to measure three perpendicular rotations at a human disabled or deformed joint simultaneously, using this mechanism, only one of the three potentiometers can be approximately aligned; the other two will.be quite far off axis (8 to 10 cms perhaps). To do the job of absorbing the resultant off-axis translations, a double-double parallelogram i s needed twice the size of the motions that must be absorbed. This may result i n a bulky and heavy device. 19 Bulkiness w i l l result i n a device getting i n the way of walkers, canes, crutches, stair r a i l i n g s , patients' swinging arms, ( i f the device i s at the hip), chairs, etc., that may be present incident-a l l y or as part of a functional test. Also, i f the device i s too heavy, i t w i l l affect the motion patterns that are being measured. 1.3 Scope of this Work This work i s concerned with finding a solution to the problem of measuring the motion pattern of human joints (both lower limbs simultaneously) under dynamic conditions. A c l i n i c a l l y viable electrogoniometric solution to this problem i s sought in the form of a single module that w i l l work at any and a l l of the six lower.limb joints. Criteria for evaluation of this device have been established, based on a year's c l i n i c a l experience with an electrogoniometer. Several alternative solutions are considered and evaluated using these established c r i t e r i a . The parallelogram chain (picked out of the concep-tual design alternatives) i s designed in d e t a i l , fabricated and dynamically tested on a specially made joint simulator. The device i s tested i n terms of: (a) the effect of the accuracy of measurements when the device i s located at various positions with respect to the joint simulator; (b) two different grades of material used i n fabricating the chain; (c) the effect of varying the number of parallelograms used; (d) the effect of varying the speed of movement of the join t , and how the device i s able to follow the true motions from slow walk to slow run. Conclusions and recommendations for future work are outlined at the end of this thesis. 19 (a) C H A P T E R I I D E S I G N C R I T E R I A 20 2.1 Design Criteria Most of the design c r i t e r i a mentioned i n this chapter have been indirectly considered and explained in the discussions of chapter one. Most of the remaining c r i t e r i a are obvious in their meaning, but for completeness are included. In establishing these c r i t e r i a , an overall system to measure the motion pattern of the lower limb joints was kept i n mind as the central problem. This was done so as the module that w i l l result from the design work w i l l be compatable to use at a l l lower limb joints in a c l i n i c a l setting. The c r i t e r i a w i l l be used to evaluate the problem solutions. The c r i t e r i a are organized from two points of view - the patient's, and the c l i n i c team's: (a) Patient: 1 1. low weight (minimize effect On movement patterns) 2. small size (minimize encumberances with surroundings) 3. minimal constraining forces (minimize effect on movement pattern) 4. good f i t and comfortable attachment (adjustable to f i t a l l patients) 5. easily f i t t e d (quickly and easily attached, on and off) 6. good aesthetic affect on patient (feel, look, noise, etc.) 7. good protection from device (pinch-free, etc.) 8. minimal discomfort (pain for example) (b) Clinic. Team: 1. a b i l i t y to monitor: (i) Hip: flexion-extension abduction-adduction internal-external rotation 21 ( i i ) Knee: flexion-extension valgus-varus (dealing with abnormality) internal-external rotation ( i i i ) Ankle: flexion-extension inversion-eversion internal-external rotation 2. a b i l i t y to monitor hip, knee and ankle of both legs simul-taneously 3. good reproducability of data: (i) self-aligning or not ( i i ) good fixation of device to the patient ( i i i ) minimal constraining forces in action of the device 4. easy to f i t to a l l patients with allowances for varying amounts of deformity 5. minimal use of assessment time for: (i) calibration of the device ( i i ) putting the device on and removing i t ( i i i ) recording the data: a. quickly done b. easy equipment to operate c. accurate data d. a b i l i t y to compare data easily 6. minimal amount of equipment used - direct measurements made - minimum number of transducers used 7. minimum cost in manufacture of system and components 8. maximal r e l i a b i l i t y 9. minimal repair costs 22 C H A P T E R I I I P R O P O S E D S O L U T I O N S 23 3.1 Introduction The solutions proposed i n this chapter to solve the motion mea-surement problem are presented as conceptual ideas only; they are not de-tail e d , completely workable solutions, but rather, rough proposals presented for the evaluation that follows i n chapter f i v e . These proposals are pre-sented in the order they are found i n the author's design journal and show the process of synthesis gone through i n learning how past devices worked, ...' how they could be improved and how this learning and improving process res-ulted i n new ideas being generated. By the time the f i r s t proposal (next section, 3.2) had been start-ed the literature had been reviewed and six months c l i n i c a l experience with electrogoniometry had been completed. At this point two decisions were made which shaped the subsequent design work: (a) A module was wanted that could be attached across any joint of the lower limb (but also looking ahead to the p o s s i b i l i t i e s of the upper limbs and head) to measure at least the three components of rotation that can occur i n normal and abnormal joints. (b) It had been decided to locate a l l the equipment to the outside or lateral sides of the limbs thus eliminating the problem of at-!- -tachment of equipment to knock-kneed patients (valgus deformity). The p o s s i b i l i t y of attaching to boney landmarks present on the l a t -eral side of a limb also made this last idea attractive. These landmarks are: 1. the creats of the i l i a (hip bones) 2. the greater trochanters and lateral epicondyles of the femurs in patients where this i s feasible (thigh bones) 3. heads of the fibulae and lateral malleoli ( l e g bones) 24 4. Calcanea (where possible) and the heads of the f i f t h meta-tarsals (foot bones) At these points where the bones are subcutaneous (just under the skin)-or nearly so, a small amount of medical grade adhesive on small rub-ber suction cups or rubber V-shaped fingers, with accompaning-straps, would give as positive attachment (short of pins into the bone) as electrogoniomet-ry could hope for. The modules could then attach across the joints to adjust-able telescoping members, themselves supported at the boney landmarks. 3.2. Single Parallelogram )':.:. • In the action-of Lamoreux's device, besides the parallelogram and the lower hinges that allowed the whole mechanism to shorten or lengthen as the thigh and the leg approached each other, the position of the parallelogram on the limb was important. With the plane of the parallelogram p a r a l l e l to the limb (in a plane perpendicular to the flexion-extension axis, or i n the sag-i t t a l plane) and allowing small amounts of hinging out from the limb, only flexion-extension could;'.be measured; there was no parallelogram effect be-tween the supporting cuffs, on the internal-external rotation potentiometer .r no self-aligning action. If the plane of the parallelogram was perpendicular to the limb (in a plane perpendicular to the internal-external rotation axis or i n the transverse plane) then only internal-external rotation could be measured because there was no parallelogram effect or no way of making the flexion-extension potentiometer self-aligning without a functioning paralleo-gram between the supporting cuffs. With the parallelogram at some intermediate position, however, both flexion-extension and internal-external rotation could be measured in a self-aligning manner. How would a mechanism function i f the 25 parallelogram in i t was mounted skewed to a l l three perpendicular planes, that i s , skewed to the sagittal, coronal and transverse planes and not just the transverse and sagittal planes as was Lamoreux's device? The schematic drawing of this device i s shown i n Figure 10. The potentiometer at B i s for measuring flexion-extension, at E internal-external rotation and at H abduction-adduction (or valgus-varus). To allow for the proper action of the parallelogram, a universal mount J i s needed instead of the simple double hinge of Lamoreux. The parallelogram i s shown ve r t i c a l l y in the figure but would be t i l t e d out from the page to give the true alignment. Figure 10. Schematic drawing of the single parallelogram The addition of the abduction-adduction (varus-valgus) potentiometer introduces a problem into the system. For the proper action of the parallel-26 ogram in recording flexion-extension, motion i n and out from the limb is neces-sary in the universal linkage. These motions w i l l cause an error in the abduc-tion-adduction reading. Tentatively, i t may be possible to add potentiometers at the axes F and G and suitably add or subtract voltages to obtain the proper abduction-adduction readings. Therefore, this design w i l l have five potentio-meters to measure the three movements. 3.3 Double Parallelogram The double parallelogram w i l l allow unconstrained collapse (within the limits set by link lengths) but w i l l transmit a rotation. If this device were used not as Gordon Judge used i t but more as Lamoreux did the single one, the number of potentiometers and hinges required (compared to the previous ex-ample) may be reduced. Only one of the few ways this could be done is con-sidered, and a schematic drawing of this way i s shown i n Figure 11. Figure 11. Schematic drawing of the double parallelogram 27 Again, probably another potentiometer would have to be added at axis F to allow for corrections to be made to the abduction-adduction measurement. This leaves this design requiring four potentiometers to measure three move-ements. 3.4 Telescoping Unit A telescoping rod electrogoniometer could be built consisting of a telescoping rod mounted between universally joined ends, one end to the thigh cuff and the other end to a leg cuff (Figure 12). Three potentiometers mounted at each end of the rod would be sufficient to deduce three perpendicular rotations occuring at the joint. For example, take the measurement of flexion-extension. With two potentiometers mounted, one on the thigh cuff and one on Figure 12. Schematic drawing of the telescopic unit 28 the leg cuff with the telescoping connecting bar between them, i f one knows the rotation of the bar with the thigh cuff (thigh potentiometer) and in turn the rotation of the bar with respect to the leg cuff (leg potentiometer) then one can deduce the rotation of the thigh cuff with respect to the leg cuff, e.g., add the appropriate angles and subtract from 180°; this could a l l be set up by adding and subtracting voltage levels. Hie other two angles are analogous. At worst, this data manipulation could be done by a micro pro-cessor (a small programmable calculator valued at from $300 to $400). 3.5. Parallelogram Chain The device shown conceptually i n Figure 13 w i l l match the actions Figure 13. Schematic drawing of the parallelogram chain 29 of Judge's device minus the hinge and c o l l a p s i b i l i t y problems. This i s done by stacking double-double parallelogram boxes on top of each other at right-angles. The corners of the boxes are thinned to allow hinging without free-play. By adding more boxes to this growing chain, theoretically, any amount of c o l l a p s i b i l i t y can be obtained. A small and light weight plastic t r i p l e -t r i p l e parallelogram chain i s depicted i n Figure 13. The parallelogram could be a double-double, that i s , 2-2, or 3-3, or 4-4, or 2-3, 3-4 etc. A typical plastic hinge i s shown at point G. The size and number of parallelograms w i l l be determined by the motion one wishes to absorb. 29 (a) C H A P T E R IV E V A L U A T I O N AND S E L E C T I O N 30 4.1. Evaluation and Selection Out of the c r i t e r i a presented in Chapter I I , thirteen relevant to the modular linkage design have been selected for evaluation purposes. These are: (a (b (c (d; (e (f (g (h ( i 0 (k; (1 weight size forces resisting motion mechanical safety aesthetics a b i l i t y to measure three rotations applicability to any joint self aligning accuracy of results minimal number of potentiometers r e l i a b i l i t y cost of repair Looking generally at the four ideas of Chapter I I I , the single and double parallelogram concepts could be considered essentially the same. The double parallelogram would probably be lighter, be more aesthetically pleas-ing, have one less potentiometer and would probably be cheaper to make. In comparing the telescoping unit to the double parallelogramy the telescopic unit would probably be safer i n operation, aesthetically simpler looking, and cheaper to build. In other areas they are almost equal except that the t e l -escopic unit needs two more potentiometers than the double parallelogram. The parallelogram chain i s equal to or better than the other designs when compared using these c r i t e r i a . The parallelogram chain uses the minimum three 31 potentiometers, minimizing the complexities of the el e c t r i c a l system. By varying the number of parallelogram units for each chain, the device can be adjusted to optimally perform at any join t , given the v a r i a b i l i t y of motions at different joints; truly;" a modular design. The cost of manufacturing i s at \rorst equal to the other designs because the chain can be cast from a plas t i c , the unit cost dropping as more are made. The parallelogram chain also compares well with the designs l i s t e d i n Chapter I I . Hie self-aligning feature makes i t c l i n i c a l l y more viable than the devices of Karpovich and Johnston. The chain w i l l give an extra set of angular information at a joint as compared to Lamoreux's device, with the use of one small mechanism. The parallelogram chain does not need a com-puter to give c l i n i c a l l y useful results.as does Kinzel and Hillberry's space mechanism. Compared to Judge's design, the chain w i l l reduce the hinging and c o l l a p s i b i l i t y problems associated with the double-double parallelogram. Following from these many subjective arguments, the parallelogram chain was chosen for detailed design, fabrication and testing with the thought that an improvement in techniques of electrogoniometry and patient assessment could be effected. 31 (a) C H A P T E R V D E T A I L S OF D E S I GN 32 5.1 Introduction The detailed design that follows i s limited to the plastic paral-lelogram chain shown positioned between the potentiometers of Figure 13. The exploration of alternative methods of attaching the potentiometers (and in turn, the parallelogram chain) to the patient i s l e f t for future work. The selection of the working material and the manufacturing techniques used for fabricating the f i r s t prototype are discussed in 5.2 and Appendix III and serve to c l a r i f y parts of the discussion of 5.3, hinge design. 5.2 Material Selection The material f i n a l l y selected for prototype fabrication and test-ing was the family of polyurethane elastomers. Out of the many other plastics considered, polypropylene i s very representative with some to the best material properties. Very tough and fatigue resistant, polypropylene i s used i n many commercial applications. However, to make the parallelogram chain out of poly-proylene, injection moulding i s mandatory. The moulds used for this need to be made by sk i l l e d people and require a large injection moulding machine for making the part. The expense involved i n experimenting with different hinge thicknesses and geometric configurations makes polypropylene unsuitable for the i n i t i a l prototypes. It may make sense to use polypropylene to obtain optimum properties once the design has been finalized. The polyurethane elastomers are not ideal for experimentation, but have these advantages: (a) Polyurethanes can be easily handled. They are commercially available in a two component k i t , resin and hardener, and can be mixed and easily poured into and removed from unpressurized moulds. 33 (b) Since polyurethane can be poured unpressurized, the moulds are relatively less expensive to make. Therefore, more experi-mental t r i a l s can be done i n comparison to polypropylene for the same expenditure of time and money. (c) Polyurethanes are available i n hardnesses from that of a soft rubber to hardnesses of structural plastics such as vinyls, poly-propylenes and some epoxies. So the scope for experimentation us-ing a single hinge configuration, for example, i n a wide range of available material properties i s possible. (d) The polyurethanes are wear and fatigue resistant (rubber-like) and tough in thin sections. (e) Being able to cast polyurethanes as a liquid w i l l allow design possibilities such as: 1. including various plastic or cloth-like fibers or straps in the hinge (thinne'd) sections of the mould to take advantage of composite material properties, e.g. strength and unidirectional f l e x i b i l i t y at the hinges. 2. inclusion of metal stiffeners i n wall sections. Refer to Appendix III for the casting techniques used with the poly-urethane. Refer to Appendix IV for manufacturer's data on polyurethanes. 5.3 Hinge Design Conceptually, the parallelogram chain uses the thin section f l e x i -b i l i t y of the material of which i t i s made to allow the necessary parallelo-gram scissoring action. To turn this concept into r e a l i t y , a few variables must be considered: 34 (a) hinge thickness (b) hinge geometry 1. at the necked section 2. surrounding the necked section When considering the forces that are needed to cause scissoring of the parallelograms (the higher the forces, the more error because the forces are transmitted back to the subject tending to change the subject's motion pattern) i t becomes evident that the variables under consideration are depend-ent upon each other. This implies that a t r i a l and error iteration process be undertaken to arrive at a workable pattern configuration. Because of the ex-pense of having accurate patterns milled and a large volume of work being done in the University machine shop, only two patterns became a -reality. The t h i r d one i s on paper, but will'.not be machined u n t i l after this work i s completed. Basically, two hinge thicknesses and two hinge geometries, one necked down using sharp corners and one necked down using rounded corners, were t r i e d . The two patterns which were made used an asymmetrical hinge while the one s t i l l to be done (see Chapter VIII) uses a symmetrical hinge geometry. (a) Hinge Thickness: Figure 14 shows the drawing of the f i r s t pat-tern made i n the machine shop. This design was a result of discussions with the machinist on what materials and techniques were available to him. This was after attempts to make a wood-paper pattern were unsuccessful. Discussions with a professional wood pattern maker about making a completely wooden pat-tern showed this approach to be impractical. The minimum hinge thickness of the f i r s t pattern was 0.254 mm or 0.010 inches, an estimated minimum value arrived at by examining thin films of polyurethane obtained from flash around mouldings (material over-flowed or squeezed out of mould cavities). This f i r s t pattern was made starting f i r s t 35 with a rectangular frame made of 0.010 inch thickness brass plate (shim stock). The rectangle, formed by bending the plate was closed by soldering the ends together in a small lap joint. The brass thick wall sections, (shaded area in Figure 11) were then soldered i n the appropriate places to leave small 0.010 inch thick hinges in the corners. The dimensions of the hinge sections ended up being 0.794 mm x 0.254 mm x 19.05 mm or 1/32" x 0.010" x 0.75". A shore A 70 polyurethane chain was cast i n four t r i a l moulds. The hinges of the chains were failures. The polyurethane formed beads along the hinge sections i n two moulds, producing hinges that f e l l apart when the moulds were handled for casting removal. The castings that survived mould removal failed after they had undergone a few flexes. At this point the hinge sections of the pattern were f i l l e t t e d to obtain a 1.6 mm or 1/16" radius with fiber-glas putty. This also increased the hinge thickness to about 0.75 mm or 0.030". Figure 14. First parallelogram chain prototype pattern i 36 Again, a Shore A 70 polyurethane was cast in four t r i a l moulds but this time a l l the castings were good. These hinges were not too s t i f f , but i t could be envisioned that harder polyurethanes at this hinge thickness would take larg-er forces to cause the parallelograms to scissor, and this force had to be minimized. It was estimated then that the boundaries upon hinge thickness varied from 0.254 mm to 0.75 mm or from 0.010** to 0.030". The f i n a l hinge thickness tried was that of 0.504 mm or 0.020" on a new, accurately milled pattern. Materials of Shore A 75, 90 and D 60 were cast. A l l the hinges held together and were easy to flex. Hand testing i n -dicated they were fatigue resistant. (It is beyond the scope of this work to do detailed fatigue and force testing i ) These castings were adequate for the subsequent testing imposed on them. (b) Hinge Geometry: Of the hinges of 0.254 mm thickness, one side of the hinge was part of a 90° corner, the other part of a 135° corner. The stress raiser effect of the 90° corners plus any entrapped bubbles (result-ant beading effect) may have been the reason why the hinges that did survive mould removal failed after a few pulls and flexes. The 1.6 mm radius on the 0.75 mm thick hinge may have reduced this stress situation, but hinge strength was simultaneously increased. With these tentative thoughts in mind, the ge-ometry of the accurately milled pattern (0.504 mm hinge thickness) was explored. (The f i r s t brass pattern was discarded at this point due to discrepencies in the lengths of the sides causing non-parallelogram action.) Figure 15 shows the various hinge geometries considered at this time. Figure 15 (4) was chosen being close to the shape originally tested and the drawing, Figure 16, resulted. Since the sharp corners would have to be hand f i l e d , a time consuming and less accurate process than using the milling machine, a 1.59 mm radius (1/16" radius) 37 milling cutter (smallest that could be used accurately) was used to cut the hinges in the pattern. This resulted in a hinge geometry as per Figure 15 (1) This hinge geometry i s discussed again in Chapter VIII after some test results have been presented. Figure 16. Second parallelogram chain pattern Figure 15. Some hinge geometries C H A P T E R V I T E S T A P P A R A T U S 38 6.1 Test Apparatus The parallelogram chain was tested in terms of i t s a b i l i t y to mon-itor three perpendicular rotations simultaneously or individually under var-ious standard conditions. A joint simulator (Figure 17) was built to test how well the potentiometers on the parallelogram chain could track the pot-entiometers on the mechanical hinges of a simulated human joint. In Figure 17, the mechanical hinges and corre-sponding potentiometers are A - flexion-extension B - valgus-varus or abduction-adduction, and C - internal-external rotation The corresponding potentiometers on the parallelogram chain are D, E and F respectively. The adjustable connectors attached to rod G (the thigh) and to rod H (the "lower leg") allow the parallelogram chain to be pos-itioned relative to the mech-anical hinges. The "thigh" rod Figure 17. The joint simulator G is driven around i n an elip-t i c a l pattern by the chain and motor shown in the top of Figure 17. The "lower leg" rod H i s mounted r i g i d l y to the base of the simulator. Three per-pendicular rotations are imparted simultaneously to the simulator in each 39 e l l i p t i c a l cycle. The motion pattern through which the "thigh" rod travels with re-spect to the "lower leg" rod i s approximately that of a badly functioning, \tfalking human a r t h r i t i c knee joint; that i s , 0° to 85° of flexion, 0° to 25° of varus and/or (in the simulator's case, and) valgus, and 0° to 20° of internal or external rotation. By varying the voltage to the small gear reduced D.C. motor, the speed of the motion can be changed. A power supply and signal attenuator box was bu i l t to energize the potentiometers and to reduce the signal power from the potentiometers to be compatable with the galvanometers of the ultra-violet light s t r i p chart re-corder. Consideration i n the design of the attenuator box was given to drawing minimal current from the potentiometers so that their l i n e a r i t y was maintained. A c i r c u i t diagram for the attenuator/power supply box, the der-ivation of a formula relating the current drawn from the potentiometers and the other c i r c u i t parameters to the linearity of the potentiometer output are a l l shown in Appendix V. The potentiometers were mounted i n series, perpendicular to one an-other. Care was taken in mounting the potentiometers not to allow any twist-ing moments about the potentiometer shafts to develop as the chain was com-pressed or extended during testing. These unwanted moments would cause errors i n the measurements. Various configurations of the potentiometers were tried; two on top, one on the bottom; two on the bottom, one on top; the f i n a l configuration worked the best, with a l l potentiometers connected in series, each connected to the shaft of the one before i t , mutually per-pendicular, a l l mounted ontop of the chain.- (This can be seen at the top of-Figure 20.) 40 The strip chart recorder used focused beams of ultra-violet light position controlled by small mirrors on the galvanometers. The light ex-poses the photographically sensitive emulsion on the strip chart paper. One useful feature of this recorder was that the light beams could cross, and i t was possible to superimpose them. This allowed the recording of the magni-tude and position, i n the joint simulator's motion cycle, of errors occurring between the parallelogram chain and the mechanical joint. 6.2 Test Procedure Figure 18 shows the coordinate system used to locate the centre of the top and bottom of the parallelogram chain with respect to the mechanical joint (+x is out of the photograph). With various (differing sizes and mater-ials) parallelogram chains located in different positions with respect to this coordinate system, up to four runs were made: + Z Figure 18. Joint simulator coordinate system 41 (1) The starting position for a l l these tests was with the flexion-extension potentiometer of the parallelogram chain aligned with the flexion-extension potentiometer of the mechanical joint. This made the coordinates of the top of the parallelogram chain, x = +8.5 cms y = -1.5 cms z = -6.0 cms The bottom of the chain was in the same x,y position with the z position ad-justed so that the chain would function in any of the extreme positions of the test cycle, a position that was judged to be not collapsing or extending beyond the limits of movement of the parallelogram chain. Figures 19 and 20 show the chain in a typical f u l l y extended or collapsed position. Figure 19. The parallelogram chain in a f u l l y extended position Figure 20. The parallelogram chain in a f u l l y collapsed position 42 (2) The chain was positioned (top at z = -6.0 cms) as far in the positive y direction as possible. The top y and the bottom y and z positions were adjusted (top y = bottom y) to give free action of the chain and to a l -low the chain to clear the mechanical joint i n extreme positions of the motion cycle. (3) The chain was positioned in the maximum x position possible with the top at z = -6.0 cms, y = -1.5 cms. The \x position of the top and the x and z positions of the bottom (x of top equals x of bottom) were adjusted to give free action to the chain. (4) The chain was positioned i n the maximum z position possible with top and bottom at y = -1.5 cms. The x and z positions of the top and bottom (x's equal) were adjusted to allow free action of the chain. Four runs were done with a 4-4 chain of the Shore D 45 or 6403 e l -astomer. Two runs each of the 4-4 and 3-3 chains, of Shore D 60 or 6404 elastomer were done. Before the runs were started, a l l six potentiometers were c a l i -brated using a d i a l clamped to the potentiometer shafts. The d i a l had 100 divisions and was readable to the nearest 0.2 of one division. The trace on the strip chart recorder was readable to within - 0.5 mm or with the c a l i -bration set at 25°/cm, about - 1 degree. The calibration curve ( a l l v i r t u -a l l y the same) for a typical potentiometer i s shown i n Figure 21. (Six Bourns precision potentiometers were used: 10 turns, 10 K ohm resistance, 0.2% independent linearity.,) A l l runs were done at two speeds. These were determined by the i n -put voltage to the driving motor, 5 and 10 volts. Five volts turned out to POTENTIOMETER SHAFT ANGLE, DEGREES Figure 21: Typical potentiometer calibration curve. OA 44 be a moderate to slow walking speed, and 10 volts was comparable to slow run-ning. This conclusion was arrived at by comparison of Lamoreux's results to the results of this work in terms of maximum angular velocity recorded, a direct indicator of walking speed. This was obtained by calculating the max-imum slopes occurring in the angle vs. time curves of both sets of results. For Lamoreux's study the maximum angular velocity for a subject on the verge of running was 420°/sec. In this study, (as seen in the next section, and in Figure 38) the maximum angular velocity calculated from the data at the 10 volt speed was 460°/sec. 6.3 Results 6.3.1 Data Figures 22, 24, 26, 28 show runs 1, 2, 3, and 4 on the parallelogram chains made of Shore D 45 elastomer using 4-4 parallelogram units. These runs were done at a motor voltage of 5 volts, comparable to moderate or slow walking. Figures 23, 25, 27, 29 are the same as 22, 24, 26, 28 respectively except that the motor voltage was 10 volts, comparable to slow running. The le f t hand curves on each of these figures are pairs of recordings from the joint simulator and the parallelogram chain for each of the three mutually perpendicular rotations. These curves are graphs of (vertically or. up/down the page) angular change vs. time. On the right hand side of the figures,, the pairs of curves are superimposed to show the errors occurring between the records. Figures 30 and 32 were of a 4-4 parallelogram chain, runs numbered t 1 and 4, made of a Shore D 60 elastomer with the motor at 5 volts. Figures 31 and 33 are the same as 30 and 32 respectively except that the motor volt-age was 10 volts. The last set of figures 34, 36 (at 5 volts) and 35, 37 45 (at 10 volts) were for a Shore D 45 elastomer used i n a 3-3 parallelogram chain. The letter code for these figures i s shown below: (a) Flexion-extension, joint simulator (b) Flexion-extension, parallelogram chain (c) a and b superimposed (d) Valgus-varus, joint simulator (e) Valgus-varus, parallelogram chain (f) d and e superimposed (g) Internal-external rotation, joint simulator (h) Internal-external rotation, parallelogram chain (i) g and h superimposed One centimeter ve r t i c a l l y = 25° One centimeter horizontally =1.2 seconds The maximum (worst case) value for the measured errors from these runs i s shown i n Table I. These values were obtained by direct measurement for the corresponding run records. The section in each run where the tracings were superimposed was used to establish the angular errors l i s t e d in Table I. The f i r s t digit of the run numbers (top of Table I) refers to: (1) 4-4 chain of Shore D 45 elastomer (2) 4-4 chain of Shore D 60 elastomer (3) 3-3 chain of Shore D 45 elastomer The second di g i t of the run number refers to the test positions l i s t e d i n sec-tion 6.2, Test Procedure. For example, Run 3.1 was done i n the starting or (1) position with the 3-3 chain of Shore D 45 elastomer. Therefore runs 1.1, 2.1 and 3.1 were tests on different materials and chain sizes done i n comparable positions. Table 1: Maximum measured errors between the joint simulator and the parallelogram chain (Degrees). Run Number 1.1 2.1 3.1 1.4 2.4 3.4 1.2 1.3 Flexion-extension (5 Volts) 2.5/85 2/85 5/85 10/85 15/85 6/85 7.5/85 5/85 2,9% 2.3% 5.9% 11.7% 17.6% 7.1% 8.8% 5.9% Flexion-extension (10 Volts) 2.5/85 1/85 5/85 10/85 15/85 7.5/85 10/85 5/85 2.9% 1.2% 5.9% 11.7% 17.6% 8.8% 11.8% 5.9% Valgus-Varus (5 Volts) 8/55 12.5/55 5/55 15/55 20/55 7.5/55 22.5/55 7.5/55 14.5% 22.7% 9.1% 27.3% 36.4% 13.6% 40.9% 13.6% Valgus-Varus (10 Volts) 8/55 12.5/55 5/55 15/55 20/55 7.5/55 20/55 9/55 14.5% 22.7% 9.1% 27.3% 36.4% 13.6% 36.4% 16.3% Internal-external rotation (5 Volts) 1/20 <1/15 1/20 <l/20 2/20 1/20 <l/20 1/20 5% <5% 5% <5% 10% 5% <5% 5% Internal-external rotation (10 Volts) 1/20 <1/15 <l/20 1/20 2/20 1/20 <l/20 1/20 5% <5% <5% 5% 10% 5%- <5% 5% Figure 22: 4-4 Parallelogram Chain, Run 1.1 Top: x = +8.5 cm Bottom: x = +8.5 cm y = -1.5 y = -1.5 z = -6.0 z = -21.5 Material: Shore D45 (#6403) Motor: 5 volts Figure 23: 4-4 Parallelogram Chain, Run 1.1 Top: x = +8.5 cm Bottom: x = +8.5 cm y = -1.5 • y » -1.5 z = -6.0 z = -21.5 Material: Shore D45 (#6403) Motor: 10 volts Material: Shore D45 (#6403) Motor: 5 volts LEAF 46(d) OMITTED IN PAGE NUMBERING. Material: Shore D45 (#6403) Motor: 10 volts Figure 26: 4-4 Parallelogram Chain, Run 1.3 Top: x = +10.5 cm Bottom: x = +10.5 cm y = -1.5 y = -1.5 z = -6.0 z = -21.5 Material: Shore D45 (#6403) Motor: 5 volts Figure 27: 4-4 Parallelogram Chain, Run 1.3 Top: x = +10.5 cm Bottom: x = +10.5 cm y = -1.5 y = -1.5 z = -6.0 z = -21.5 Material: Shore D45 (#6403) Motor: 10 volts Figure 28: 4-4 Parallelogram Chain, Run 1.4 Top: x = +8.5 cm Bottom: x = +8.5 cm y = -1.5 y = -1.5 z = -1.5 z = -18.5 Material: Shore D45 (#6403) Motor: 5 volts Figure 29: 4-4 Parallelogram Chain, Run 1.4 Top: x = +8.5 cm Bottom: x = +8.5 cm y,= -1.5 y = -1.5 z = -1.5 z = -18.5 Material: Shore D45 (#6403) Motor: 10 volts Figure 30: 4-4 Parallelogram Chain, Run 2.1 Top: x = +8.5 cm Bottom: x = +8.5 cm y = -1.5 y = -1.5 z = -6.0 z = -21.5 Material: Shore D 60 (#6404) Motor: 5 volts Figure 31: 4-4 Parallelogram Chain, Run 2.1 Top: x = +8.5 cm Bottom: x = +8.5 cm y = -1.5 y = -1.5 z = -6.0 z = -21.5 Material: Shore D60 (#6404) Motor: 10 volts Figure 32: 4-4 Parallelogram Chain, Run 2.4 Top: x = +8.5 cm Bottom: x = +8.5 cm y = -1.5 y = -1.5 z = -1.5 z = -18.5 Material: Shore D60 (#6404) Motor: 5 volts Figure 33: 4-4 Parallelogram Chain, Run 2.4 Top: x = +8.5 cm Bottom: x = +8.5 cm y = -1.5 y = -1.5 z = -1.5 z = -18.5 Material: Shore D60 (#6404) Motor: 10 Volts Material: Shore D45 (#6403) Motor: 5 volts Figure 35: 3-3 Parallelogram Chain, Run 3.1 Top: x = +8.0 cm Bottom: x = +8.0 cm y = -1.5 y = -1.5 z = -6.0 z = -19.0 Material: Shore D45 (#6403) Motor: 10 volts Figure 36: 3-3 Parallelogram Chain, Run 3.4 Top: x = +8.5 cm Bottom: x = +8.5 cm y = -1.5 y = -1.5 z = -3.5 z = -17.2 Material: Shore D45 (#6403) Motor: 5 volts Figure 37: 3-3 Parallelogram Chain, Run 3.4 Top: x = +8.5 cm Bottom: x = +8.5 cm y = -1.5 y = -1.5 z = -3.5 ' z = -17.2 Material: Shore D45 (#6403) Motor: 10 volts 47 The three angular measurements made at 5 volts and 10 volts are l i s t -ed on the l e f t hand side of Table i . In the 10 volt runs transient effects began to show up. It must be noted that i n getting the angular velocity of 465°/sec, comparable to slow running, an abrupt reversal of angular velocities (+46Su/sec. to -465u/sec.) occurs, much more severe than would occur in human motion. A comparison of a +420°/sec. to a -420°/sec. reversal i n a subject on the verge of running (from Lamoreux's work) compared to the +460^sec to -460°/sec. reversal occurring on the joint simulator i s seen i n Figure 38. The conclusion to be drawn from this i s that the transient impacts are too severe a test and w i l l not be encountered i n practice, so can be ignored. What should be emphasized i s the a b i l i t y of the parallelogram chain to i n i t -i a l l y follow the high angular velocity and to subsequently measure the appro-priate angular change after the transient has died axvay, that i s , give the appropriate steady state response. A comparison of the steady state responses (at 10 volts) i s shotm i n Table 1. The a b i l i t y of the parallelogram chain to follow the i n i t i a l high angular velocity imputs can be seen i n the valgus-varus runs done at 10 volts or slow running. The transient effects shown i n Figure 38 occur i n a l l the 10 volt records at the same time i n the motion cycle. The records shown i n Figures 22 to 37 are arranged so that a ve r t i c a l line (top to bottom of the figure) through the curves intersects the curves at the same time i n the cycle. Using Figure 38 as a guide, the appropriate sections of the curves, Xsfhich can be ignored due to transient effects, can be located. The sections of Figure 27 that are circled denote some examples of transient responses. 48 time time Figure 38, The abrupt reversal of angular velocities obtained with the author's mechanical joint simulator on the l e f t as com-pared to the smooth reversal of angular velocities obtained from Lamoreux's record, on the right, of a normal subject walking. 6.3.2 Discussion With the exception of runs 1.1, 2.1 and 3.1 (runs done in the starting position with flexion-extension potentiometers aligned), a l l runs were done at the extreme limit of the parallelogram free action (see section 6.2 for explanation). Once the parallelogram chain is taken beyond the limits of free compressibility and extensibility, the error between the simulator joint motion and the joint motion measured by the parallelogram chain increases dramatically. (These curves are not presented as they show extremely poor, and in some cases, non-existant motion correlation). Using the parallelogram location data found at the bottom of each figure, (figures 22, 23, 30, 31, 34, 35 excepted) a volume within which the chain functions 49 with relatively low error can be established for the two different lengths of parallelogram chain tested; the 4-4 parallelogram chain unit had an extended length of about 15.5 cms and the 3-3 chain had a length of 13.0 cms.. For the 4-4 chain the volume was bounded by the coordinates: y= 3.0 to -6.0 cms x= 8.5 to 10.5 cms* z=-1.5 to -10.5 cms. * N.B. The minimum x value i s limited by the size of the joint simulator. +8.5 cms i s as close to the mechanism as the chain could be put. This gives effectively a working rectangular volume of 9 cms by 9 cms by 2 cms7 the 2 cms partly limited by the test mechanism. This working. volume i s dependent upon the amounts of off-axis translations that have to be absorbed. If, for example, the joint simulator were set to approximate the motion of a normal knee (and not a severely disabled one as i t was), the working volume could have been increased approximately 5 cms i n each direction to a volume of 14 x 14 x 7 cms. For the 3-3 chain the volume was bounded by the coord-inates: x = +8.0 to + 9.0 cms * y = +1.0 to - 4.0 cms z = - 3.5 to -8.5 cms * N.B. The +8.0 cms was limited by the width of the joint simulator. This gives effectively a working rectangular volume of 5 x 5 x 1 cms, the 1 cm partly limited by the joint simulator. This volume w i l l also i n -crease with reduction in motion of a joint. 50 The concept of a working volume is directly applicable to patient joint motion monitoring. The larger the working volume, the less care and time is necessary for positioning the parallelogram chain (and i t s mounting frame, etc.) on the patient's limb. With non-self-aligning electrogoniomet-ers much time i s taken to align the potentiometers with the axis of rotation of a joint. This has to be done carefully to (a) get accurate results, (b) and get reproducability of results (e.g. comparing records of a patient at two different t r i a l s ) . Take, for example, the 4-4 chain; It may function i f : (a) the potentiometer cluster at the top of the chain i s anywhere within 4.5 cms (1.77 inches) forward or backward of the axis of flexion-extension and (b) the potentiometer cluster i s anywhere within 4.5 cms. up or down from the flexion-extension axis and (c) the chain i s not more than 10.5 cms. (4.14 inches) from the centerline of the limb, front view. Then any recording made w i l l give low error, reproducable results. The self-aligning feature coupled with a suitable working volume w i l l substant-i a l l y reduce patient f i t t i n g time and subsequently greatly reduce . overall monitoring time. This w i l l allow more patients to be monitored and assessed than i s currently possible with any existing device. In most cases the shapes of the corresponding curves on each figure (22 to 37) are similar. With the two traces separated (left hand side of each figure) the curves follow each others bumps and shifts. The superimposed curves show (right hand side of each figure) that while the shape may be maintained, the magnitude of the output was reduced. The chain had absorbed 51 some of the motion. It i s these errors that have been measured from the recordings and li s t e d in Table 1. Although there are errors i n angle mag-nitude, the fact that shape i s roughly maintained would point to the correct-ness of the parallelogram chain concept and point to a change of material or material properties and/or hinge redesign to correct for the errors in magnitude of the output. There is a discrepency between the pair of internal-external ro-tation records partly due to the joint simulator. The problem with the joint simulator i s that the potentiometers measuring flexion-extension and valgus-varus (on the simulator) are mounted, fixed relative to the leg rod, H, of Figure 17, while the potentiometer measuring internal-external rotation (on the simulator) is mounted on the thigh rod G. When a motion i s imparted to the flexion-extension or valgus-varus potentiometers, a motion i s measured relative to the lower leg fixed reference frame. When a motion i s imparted to the external-internal rotation potentiometer, a motion i s measured r e l -ative to the thigh rod which moves relative to the lower leg fixed reference frame. This causes measurement discrepencies because a l l the potentiometers on the parallelogram chain are measuring relative to the lower leg. When the thigh rod G and the lower leg rod H are in line (at 180°, f u l l extension) then and only then can a true internal-external rotation on the joint sim-ulator be measured. In the test results (Figures 22 to 37) the major (up going) peak on the internal-external rotation records i s occurring at f u l l extension (by design). The measurement from the joint simulator i s only a standard of comparison at f u l l extension and no other position i n the motion cycle. The downward drop i n some of the internal-external rotation measurement curves taken from the parallelogram chains may be f a i r l y accur-52 ate but at this position in the motion cycle there i s no true motion measure-ment to compare with. The errors reported in Table 1 for internal-external rotation, are only from the major (up going) peaks on the records. To test the effect of changing material properties on the Results, runs numbered 1.x and 2.x were done. The only difference between the runs (for corresponding speeds and positions) was that runs 2.x had a parallelogram chain made of a Shore D 60 rubber and runs 1.x had a chain made of Shore D 45 rubber, the D 60 having approximately twice the hardness of the D 45 ( a s the manufacturer says). These tests showed an increase i n error with the harder material. The results show a reduction in measured error of one test, no change in another test and an increase i n error in the remaining four tests. This average decrease i n function may be due to inferior thin section material pro-perties at the higher hardness, eg. some translation of each hinge's centre of rotation may be forced to occur because of a decrease in material f l e x i -b i l i t y . The D 60 rubber was observed not to stand up to repeated flexing as well as the D 45 rubber. A thin white line began to appear i n the hinges of the D 60 as testing progressed. (The D 45 did not show this.) This would indicate the material had gone beyond i t s elastic l i m i t and failure was near (some did f a i l ) . The effect of the hinges (hinge geometry) on the measured errors can be seen in a comparison of runs numbered 1.x and 3.x where the only d i f -ference between the two sets of runs (for corresponding speeds and positions) was that for run 1.x, a 4-4 chain with 32 hinges was used and for run 3.x, a 3-3 chain with 24 hinges was used. These tests showed less error with the smaller number of hinges. The flexion-extension results of runs 1.1 and;3.1 were the only exception to this, showing an increase in error while a l l five 53 other tests showed a reduction i n error. This would indicate that the hinge design could be improved. (See Recommendation For Future Work, 1, page 56.) In comparing the results obtained at a 5 volt motor voltage (slow walking) and a 10 volt motor voltage (slow running) approximately the same errors occur. Again, the shapes of the curves are maintained (between the simulator and the chain) but the magnitudes are diminished by the parallelo-gram chain absorbing some of the angular change. It could be concluded then, that the parallelogram chain was able to follow the dynamic motions of sim-ulated slow running. 53 (a) C H A P T E R V I I S U M M A R Y AND C O N C L U S I O N S 54 7.1 Summary and Conclusions 1. (a) There i s a need for a device to measure motions of a disabled person's joint or many joints simultaneously under dynamic conditions, for (a) determining the patient's functional status and (b) assessing the effects of medical treatment. The parallelogram chain w i l l meet this need. (b) There is a need for a motion measuring device that w i l l measure joint function i n the c l i n i c , as the patient i s seen by the c l i n i c team. This device must be quickly and easily f i t t e d and give instant, accurate results. The parallelogram chain w i l l meet this need. 2. Because of (1) above, the c r i t e r i a established for evaluation of motion measuring devices were patient and c l i n i c oriented f i r s t and research oriented second. 3. The parallelogram chain design i s modular and applicable to any large joint of the upper or lower limbs. 4. The original design generated in this work, the parallelogram chain, in concept has these advantages over other devices: (a) Accurate and time consuming alignment with joint axes of rotation is not necessary with the self-aligning feature of the parallelogram chain. (b) Complete angular rotational information w i l l be available at any large joint. (c) Simple, direct, instant results are available at any large joint. (d) Reproduceability of results is maximized by the parallelogram chain's self-aligning feature. 5. The hinges of the parallelogram chain are cast integral to the mechanism. This reduces production cost as the number of chains produced increases. 55 6. (a) The parallelogram chain was tested on a mechanical joint simulator. A l l previous electrogoniometric work either assumed perfectly operating mechanisms or used a computer to simulate the action of the mechanism. The advantage of the joint simulator is that i t can double as a tester to quality control the parallelogram chain castings. (b) Because the parallelogram chain absorbs off-axis translations the potentiometer motion transducers can be mounted as a cluster atop the chain. This helps minimize the size of the chain-potentiometers combination. 7. (a) The test results show that the parallelogram chain is a sound, workable concept. Cb) The parallelogram chain w i l l follow and measure the dynamic motions of at least slow running. (c) The 4-4 parallelogram chain has a working volume of 9 x 9 x 2 cm and the 3-3 chain, 5 x 5 x 1 cm, within which low error results can be reproduceably obtained. (d) The best results obtained from the parallelogram chain (which are comparable or better than those obtained by other workers) occur when the flexion-extension rotational axis of the chain i s closely aligned (near) with the flexion-extension axis of the joint while the other two rotation-a l axes are not specifically aligned. (e) Errors introduced into the results by the joint simulator can be explained and this w i l l allow a new joint simulator (future work) to be constructed. (f) The test results point out that the main source of error was the hinge geometry of the chain and not the material property variations. 55 (a) C H A P T E R V I I I R E C O M M E N D A T I O N S 8.1 Recommendations For Future Work 56 1. Redesign of the plastic hinge of the parallelogram chain is necessary. Figure 39 shows what happens to the hinge design of Figure 15, (1), under load. This buckling w i l l shift the centre of rotation of the hinge im-parting a small error into the action of each parallelogram. The smaller the number of hinges in the parallelogram chain, the smaller the overall error of the functioning chain. This was observed with the test results of the 32 hinge 4-4 chain and the 24 hinge, 3-3 chain. Figure 40 shows the cross-section of an improved hinge design that gives good support to the necked section of the hinge. Figure 49 of Appendix VT shows how this hinge geometry could be incorporated into a new chain design. 2. A light frame that can easily and quickly be f i t t e d to a wide range of patients must be designed and tested. 3. A device to remove potentiometer data from the moving patient must be designed and tested. 4. A fatigue failure analysis should be done on the hinge to determine load load Figure 39: Buckling of the parallelogram chain hinge under load. 57 Figure 40: A new parallelogram hinge design. the l i f e of the polyurethane elastomer and other suitable materials. 5. The joint simulator should be rebuilt to: (a) make testing easier, (b) eliminate errors due to the placement of the internal-external rotation potentiometer, (c) test larger parallelogram chains. 6. It may be necessary to redo tests varying the material properties of the chain to determine the effects on measurement error, once the redesign-ed chain has been b u i l t . 7. Once the size and properties of the parallelogram chain are finalized an investigation into cost and avai l a b i l i t y of injection moulded poly-propylene parts should be done. 58 REFERENCES 1. KARPOVICH, P.V., et a l : 2. KARPOVICH, P.V., et a l : 3. KARPOVICH, P.V., et a l : 4. TIPTON, CM., et a l : 5. KARPOVICH, P.V., et a l : 6. TIPTON, CM., et a l : 7. JOHNSTON, R.C, et a l : 8. KETTELKAMP, D.B., et al : 9. KETTELKAMP, D.B., et a l : 10. LAUBENTHAL, K.N., et a l : 11. CHAO, E.Y.S., et a l : Electrogoniometric Study of Joints. U.S. Armed Forces Med. J. 11:424 (April) 1960 Electrogoniometric Study of Locomotion and Some Athletic Movements. Fed. Proceed. 21:313 (March-April) 1962 Effect of High Heels on the Knee, Ankle and Foot. Fed. Proceed. 22:685 (April) 1963 Clin i c a l Electrogoniometry. Am. Cor-rective Therapy J., formerly Assoc. for Physical and Mental Rehab. J., J-18 (July and August) p. 90, 1964 Goniometric Study of the Human Foot in Standing and Walking. Indust. Med. and Surgery J. p. 338, July 1960 Electrogoniometric Records of Knee and Ankle Movements in Pathologic Gaits. Arch. Phys. Med., 46:276, 1965 Measurement of Hip Joint Motion During Walking: An Evaluation of an Electro-goniometric Method. J. Bone Joint Surg. (Amer) 51:1083, 1969 An Electrogoniometric Study of Knee Motion in Normal Gait. J. Bone Joint Surg. (Amer) 52:775, 1970 Gait Characteristics of the Rheumatoid Knee. Arch. Surg. Vol. 104, Jan. 1972 A Quantitative Analysis of Knee Motion During Activities of Daily Living. Phys. Therapy J. Vol. 52, No. 1, Jan. 1972 The Application of 4 x 4 Matrix Method to the Correction of the Measurements of Hip Joint Rotations. J. Biomechanics, Vol. 3, p..459, 1970 sa Kinematic Measurements i n the Study of Human Walking. Bulletin of Prosthetics Research - Spring 1971 A Method for Measuring the Total Motion Between Two Body Segments. Presented at the Biomechanics Symposium, Indiana Univer-s i t y , Bloomington, Ind. 1970 Measurement of the Total Motion Between Two Body Segments - I. Analytical Dev-elopment. J. Biomechanics, Vol. 5, p. 93, 1972 15. COUSINS, S.J. and FOORT, J. , An Orthosis for Medial or Lateral Stabil-ization of A r t h r i t i c Knees. Going to Press. 16. JUDGE, G., Personal Communication, Nov. 1974 Department of Health and Social Security, Biomechanical Research and Development Unit (Measurements Lab), Roehampton, London, SW15 5PR , England. 12. LAMOREUX, L.W., 13. KINZEL, G.L., et a l : 14. KINZEL, G.L., et a l : 17. THOMAS, D.H., et a l : An Electrogoniometer for the Finger. A Kinesiologic Tracking Device. Amer. J. Med. Electronics, April-June, 1964 APPENDIX I - Definition of Terms 60 valgus (abduction) 61 APPENDIX II - Typical Electrogoniometer Records Only level walking and flexion-extension of the knee and ankle are presented here for i l l u s t r a t i v e purposes. Figure 41 shows the curves obtained for a normal subject, level walking. The two curves can be thought of as graphs; the vertical axis, degrees (angular change of the j oint), the horizontal axis, time. The three vertical lines through the figure de-lineate the points in time when heel strike occurred. Looking at the knee curve f i r s t : At heel strike, 1, the leg is f u l l y extended. As the leg moves into stance phase of the walk-ing cycle the knee flexes to a max-imum of about 20 degrees, 2. Then the knee extends almost to maximum and again flexes s l i g h t l y as toe off (stance phase contralateral leg) occurs at 3. Now in swing phase the knee flexes to a maximum of about 65 degrees, 4, and again extendes back to zero degrees at heel strike, 5. Looking at the ankle curve: At heel strike, 1, the ankle is in a neutral position and plantarflexes (toes down) to a f l a t foot at 2. As we move through stance phase and approach toe off at 3 the ankle dorsiflexes (toes up) through a range of about 25 degrees, 2 to 3. After toe off the foot moves \ANKLE Figure 41: Level walking pat-terns of a normal subject. 62 through swing phase parallel to the floor plantarflexing to point 4 where the foot dorsiflexes i n preparation for heel strike at 5. What information can we get from these records? By running the equipment continuously from start to end of the walk and knowing the dis-tance per lap (350 meters walked in 25 meter laps) we can get: 1. Cadence (steps per minute). 2. Stride length. 3. Variations in: Cadence and stride length. This indicates endurance or fatigue. 4. Knee range of motion used in walking: eg. stance phase 20° eg. swing phase 65° 5. Ankle range of motion used in walking: eg. range 25° 6. Impacts or restrictions in motion: - where i n the walking cycle they are occurring - magnitude of motion 7. Shakiness or oscillations. 8. Comparisons between: (a) patient's curve and normal subjects curve, (b) same patient before and after procedures: eg. surgery therapy, bracing, etc. 9. Direction and amount of ins t a b i l i t y . 10. etc. Figure 42 shows the walking curves obtained from an a r t h r i t i c patient, superimposed upon the normal curves shown i n Figure 41. This i s a record of a 53 year old woman with a fifteen year history of progressively worsening rheumatoid ar t h r i t i s in both knees. She has a.Mcintosh arthro-Figure 42: Level walking patterns of an arthr i t i c subject (black) superimposed on the level walking patterns of a normal subject. 63 plasty (joint replacement) in her right knee and the l e f t knee, the one tested, has had a synovectomy (surgical procedure) i n 1968 and a Mcintosh arthroplasty in 1971. The l e f t knee caught painfully oc-casionally. The records (black lines i n figure 42) are noticeably abnormal, especially the knee record. In stance phase, 1, the knee does not flex at a l l ; normal stance phase flexion i s 20°. In swing phase, 2, she only flexes 35°, half that of a normal person. Her comfortable cadence decreased throughout the test and she was only able to com-plete 100 meters. Although she could only walk the 100 meters the patterns were steady with l i t t l e or no shakiness. However i n sub-sequent testing, stairs especially, marked amount of shakiness was noted (the average value of the amplitude of the oscillations Figure 43: Level walking patterns of a patient with the instrumented leg longer than the non-instrumented leg. 64 can be measured). Because the knee channel was not completely tuned the day of the test (the ankle record was good however) noise or artifact ob-scured the effect of the painful clicking i n the knee observed by the patient but this was reflected i n the ankle pattern at point 1. This clicking occurring every six or seven steps is located at 35% into the walking cycle, that i s , in stance phase just as the leg i s to become totally body weight bearing. Figure 43 shows the walking curves obtained from another patient. The knee record is significant here. It was noted that at heel contact the knee was not going into a normal pattern of extension. The i n i t i a l section of the curve is displaced upward as can be seen by comparing i t with the lighter shaded line representing her "normal pattern". The crucial thing was that there is a leg length discrepency. When the shoe was adjusted to bring the limbs closer to equal length, the curve obtained was shifted close to the normal shape. 65 APPENDIX III - Casting Techniques A flow chart of the process used i n casting the parallelogram chain is shown i n figure 44. The pattern, A, of the parallelogram chain is enclosed i n a wooden frame, B, and has RTV (Room Temperature Vulcaniz-ing) mould making rubber mix F, poured around i t . After a 24 hour cure the wooded frame is stripped from the mould and after the pattern i s removed a mould is l e f t , C, into which can be poured the polyurethane mix, G. Before either the RTV or the polyurethane is poured they need the bubbles entrap-ped by mixing removed in a vacuum chamber, E. The casting, D, is removed Figure 44: The casting process 66 from the mould before or after oven curing depending upon the strength of the uncured casting. As a rule of thumb the castings poured from the polyurethanes of hardness Shore A90 or less can be removed after one or two days room temperature air cure. The Shore D50 and above polyurethanes don't have the i n i t i a l strength i n thin section to resist the forces on the casting as i t i s removed from the mould. According to the manufacturers data sheet and personal experience mqst of the physical properties of the material can be obtained in seven days room temperature a i r cure of some-what better properties with cure at 82° C (180° F) for 16 hours. The vacuum chamber, E, of figure 44 was constructed of a 12 inch length of 8 inch O.D., 0.25 inch wall circular steel pipe. A wooden base was set in place with a fiberglass resin. The top was a 0.5 inch thick piece of plexiglass with a gas f i t t i n g for a i r removal threaded in place. A small vacuum pump was used to evacuate the chamber to about -28.0 inches Hg gauge. Appendix IV : Summary of manufacturers data sheet of the Polyurethane elastomers . Product Volumetric Wt. Ratio Cu. In./Lb. Hardness Tensile* Strength ASTM-412-66 Test Speed 20 IPM/PSI Elongation* ASTM-H-12-66 Test Speed 20 im-(%) Graves Tear* Strength ASTM-D-624 Die "C" -PSI (Lbs/in.) Compression Set ASTM-D-395-B fo/PSI Shore I I J J I I Shore "A" RP-6400 Shore A-H-5 - Green 26.6 45 850 1000 390 HOO 100 120 7-8 170 RP-6401 Shore A-60 - Blue 25.9. 60 1020 2000 530 +^20 110 IS5 5-1 330 RP-6H02 Shore A-75 - Red 25.6 75 1500 2600 310 3S0 220 350 11.6 690 RP-61+03 Shore A-90-Yellow 25 -2 ^5 90 '2500 3^)0 2k0 390 ^70 580 16.7 1250 KP-6k0k Shore D-60 - Orange g'5 .2 60 2500 1*500 kio km 860 950 22.8 3120 RP-6405 Shore D-70 - White 25-9 70 3^00 5000 25 25 H-6o oOO * Top figure represents results after cure at room temperature for 7 days and bottom figure after cure for 16 hours at l80 degrees F. 68 APPENDIX V - The Attenuator Box The attenuator box had two functions: 1. apply a voltage to the potentiometers, 2. reduce the signal amplitude from the potentiometers to a level compatible with the galvanometers of the strip chart recorder. The f i r s t function was accomplished using a commercially avail-able sealed 30 volt power supply. The second function was accomplished with care because i f too much current was drawn from the potentiometers (the word means potential or voltage measuring) the voltage being measured would be changed by the current flow, causing non-linearities in the measurement. Of key import-ance is the size of the resistor i n the circ u i t removing current from the potentiometer. If this resistor i s too small i n comparison to the resistance of the potentiometer then excessive current i s drawn from the potentiometer making i t function non-linearly. The following then i s a derivation of a formula that w i l l relate the linearity of measurement to the size of resistor used i n the signal c i r c u i t . Figure 45 shows a simplified ci r c u i t diagram of the potentiometer (voltage across i t ) and the signal c i r c u i t (V^ voltage drop). and R^  always total the value of resistance of the potentiometer but these values vary as the potentionmeter shaft i s turned. i s applied to the potentiometer and V2 i s the measured output. I, 1^, ^  are currents flow-ing i n each section of the c i r c u i t . R^  is the resistance of the signal c i r c u i t . 69 Figure 45: A simplified ci r c u i t diagram of a potentiometer and signal c i r c u i t . Using one of Kirchhoff's laws the following equation can be written: I = I 1 + I 2 CD 0 r V l - V2 = V/2 + V2 R l R2 R3 (2) where a direct substitution of the general relationship, V = IR or I = V R C3) has been made into (1). Rewritting (2) gives; V l = V 2 ^ 1 + X L + X L^ iq ^1 *~2 *3 or V2 = V l < V s R 2R 3 + R 1R 2 + R 1R 3 (4) The potentiometers used i n this work were 10 turn, 10 K ohm. Therefore R-L + R2 = 10 K ohm. V1 was 30 volts. By varying R3 for dif-ferent R^  - R2 values (resistance change for a given angular change) the following curves can be generated. Figure 46 shows how the potentiometer output becomes progres-sively non-linear as the signal resistor, R^ , i s reduced i n size from 50 K ohm to 1 K ohm. Each 1 K ohm on the R^  - R2 axis represents one shaft revolution. Figure 47 shows the v i r t u a l l y linear response of the potent-iometer when less than one half of a shaft revolution i s used to take measurements. In this work a l l angular measurements were under a 100°, less than one third of a shaft revolution, a resistive change of less than 300 ohms. The potentiometers used in this work could therefore (with R^  a minimum of 2.5 K ohms) be considered as linear as the manufacturers specifications, that i s , 0.2% linear. The cir c u i t diagram for the attenuator box is shown in Figure 48. The minimum R^  value i s 2.5 K ohms i f the variable resistors have a 0 ohm value. The 60 ohm resistor across the output plugs was sized by: 1. Obtaining a nominal value for this shunt resistor that con-trols the electromagnetic damping of the str i p chart galvan-ometers, from the recorder manual, and 2. Experimenting with other similiar resistor values u n t i l the maximum amplitude output signal was obtained with the min-imum noise. The 1000 K ohm variable resistors were used to adjust the signal amplitude for each attenuator box channel at the time of potentiometer calibration. V2, VOLTS Figure 47: The linear output of the potentiometer when the potentiometer shaft is rotated less than half a turn (less than 180 degrees). — potentiometer power supply outlets X « m • • • • Figure 48: Attenuator Box cir c u i t diagram (a l l resistance values in ohms). APPENDIX VI - Redesigned Parallelogram Chain Figure 49: Redesigned parallelogram chain pattern currently being machined. 

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