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An electronic simulation of the human handwriting system McDonald, Robert Glen 1970

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AN ELECTRONIC SIMULATION OF THE HUMAN HANDWRITING SYSTEM by ROBERT GLEN MCDONALD B . A . S c , The Uni v e r s i t y of B r i t i s h Columbia, 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of E l e c t r i c a l Engineering We accept t h i s thesis as conforming to the required standard Research Supervisor. Members of Committee Acting Head of Department Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA August, 19 70 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l no t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tment o f ABSTRACT A simple model of an antagonistic muscle system i s developed based on several published p h y s i o l o g i c a l observations and i s found to be a l i n e a r f i r s t order approximation to mammalian muscle. The model response i s compared to that of the human hand i n various tests including impulse response, frequency response, step response and the e f f e c t of s l i d i n g f r i c t i o n . The r e s u l t s of these tests are used to s e l e c t the mechanical parameters of the proposed model. The f i n a l model simulates many of the observed responses of the human hand when executing motions s i m i l a r to handwriting. A con t r o l scheme i s proposed f o r use with the mechanical model and an e l e c t r o n i c simulation of the whole system i s conducted using a d i g i t a l and an analogue computer. Good matches of displacement and a c c e l e r a t i o n waveforms from human handwriting were produced by the simula-t i o n . A discussion of some p h y s i o l o g i c a l evidence supporting the proposed c o n t r o l scheme i s given. LIST OF CONTENTS Page 1 . Introduction 1 2 . Development of a Mechanical Model of Muscle 6 3 . Analogue Simulation and Testing of Model 1 3 a) Comparison with the impulse response of human muscle 1 3 b) Response to s l i d i n g f r i c t i o n disturbances 1 6 c) Frequency and step response comparisons 1 8 4 . Results of E l e c t r o n i c Handwriting Simulation 2 1 5 . Discussion of Results 2 4 6 . Conclusion 2 9 Appendix I E l e c t r o l y t i c tank measurement system 3 0 Appendix II Computer c o n t r o l l e d simulator 3 2 Appendix I I I Constant current stimulator 3 6 References 3 9 LIST OF ILLUSTRATIONS Page Figure l a P o s i t i o n Feedback Model 3 Figure lb Time Delay Feature 3 Figure 2a Chart Recordings of Handwriting 5 Figure 2b X-Y P l o t of Figure 2a 5 Figure 3 Antagonistic Muscle System 7 Figure 4 Proposed Mechanical Model 8 Figure 5 Length-Force-Velocity Phase Space for Mammalian Muscle (from Bahler) 11 Figure 6a Isolated Muscle Model 12 Figure 6b Length-Force-Velocity Phase Space for Muscle Model 12 Figure 7a Human Twitch Response 15 Figure 7b Simulator Response to an Impulse Input 15 Figure 8a Model Response to S l i d i n g F r i c t i o n 19 Figure 8b Human Response to S l i d i n g F r i c t i o n 19 Figure 9 Comparison of Model and Human Response 20 Figure 10a Displacement an-1 A c c e l e r a t i o n Matching 23 Figure 10b X-Y Pl o t of Figure 10a 23 Figure 10c Displacement and Acc e l e r a t i o n Matching 23 Figure lOd X-Y Plot of Figure 10c 23 Figure 11a Comparison of Displacement and Control Signals 25 Figure l i b Time Plot of Figure 11a 25 Figure 12 S i m p l i f i e d Muscle Innervation 26 Figure Al-1 Measurement System 31 Figure A2-1 Computer Controlled Simulator 32 Figure A2-2 Force Generator , 34 Figure A2-3 F i n a l E l e c t r o n i c Simulator Figure A3-1 Constant Current Stimulator ACKNOWLEDGEMENT I would l i k e to acknowledge and thank the following people who have helped me during the course of my work. My supervisor Dr. John MacDonald provided h e l p f u l suggestions and recommendations on many occasions. Dr. Mike. Davies read the thesis and provided valuable comments. Rick Corman and Tony Leugner gladly gave t h e i r assistance with the experimental work and always provided entertaining conversation. S i m i l a r l y my office-mates, Paul Aube, John Cossalter, Barry Crawley and E r i c Alexandre, provided assistance and conversation on many occasions. Herb Black did the f i n a l photographs f o r the thesis and Heather DuBois quickly and e f f i c i e n t l y , typed the manuscript. The f i n a n c i a l assistance of the National Research Council of Canada both through research grant 67-3350 and through two Student Bursaries i s g r a t e f u l l y acknowledged. This thesis could not have been completed without the love and under-standing of my wife, Lorraine, who sat through many nights alone while I worked with the computer and who helped with the typing of two rough d r a f t s . AN ELECTRONIC SIMULATION OF THE HUMAN HANDWRITING SYSTEM 1. INTRODUCTION Several questions of an engineering nature come to mind when studying the neuro-muscular co n t r o l of human handwriting. Is there closed loop c o n t r o l or does the system lack feedback? Does the b r a i n exert a continuous c o n t r o l on the hand or i s the c o n t r o l done at d i s c r e t e times according to a programmed schedule? I t can e a s i l y be proved that v i s u a l feedback i s not necessary f o r l e g i b l e handwriting. Sensory feedback from the limbs i s also not e s s e n t i a l f or rapid accurate movements. As early as 191.7 a paper by Lashley (12) found that a person could accurately c o n t r o l movements of the knee without sensory feedback. Although the subject was not aware of the knee's exact p o s i t i o n due to a s p i n a l i n j u r y , rapid movements could be made accurately. These rapid movements were the most accurate, but the time delay of nerve propagation made p o s i t i o n feed-back impossible for such rapid movements. This led to Lashley's proposal that an e f f e c t o r mechanism could be preset to discharge at a f i x e d i n t e n s i t y f o r a f i x e d duration without any sensory c o n t r o l . More d i r e c t l y r e l a t e d to handwriting was another paper by Denier van der Gon and Thuring (6). They studied the handwriting process and found that; "1. For f a s t handwriting the p r i n c i p l e of p o s i t i o n feedback does not hold; 2. There i s p h y s i o l o g i c a l evidence for res o l v i n g the w r i t i n g movements in t o two more or le s s perpendicular d i r e c t i o n s ; 3. The shape of a word i s determined by the timing of the muscle contractions, and not by the magnitude of the forces used; 4. A general change of s i z e i s coupled to a proportional change i n the magnitude of the forces."1 Denier van der Gon and h i s colleagues (5) also b u i l t an e l e c t r o n i c simulator i n which a two-valued trapezoidal s i g n a l was used to represent a muscle force. By using two s i m i l a r systems to represent the h o r i z o n t a l and v e r t i c a l d i r e c t i o n s they were able to obtain good copies of handwriting a f t e r i n t e g r a t i n g the forces twice to y i e l d a displacement s i g n a l . They achieved c o n t r o l over the w r i t i n g by adjusting the timing of the zero crossing of the force waveforms. MacDonald (13) , using improved measurement instrumentation, found that the a c c e l e r a t i o n s i g n a l from human handwriting can approximately be resolved in t o a m u l t i l e v e l trapezoidal time function. An e l e c t r o n i c simulator using a m u l t i l e v e l trapezoidal force could duplicate handwriting very w e l l . The mechanical analogue used represented a point mass driven by the trapezoidal force. Since there was no feedback inherent i n t h i s model, i t was very s e n s i t i v e to s l i g h t disturbances. Because there was n e g l i b l e damping, a small perturbation i n the force waveform at the beginning of a word grossly d i s t o r t e d the whole word. Both Lashley and Denier van der Gon concluded that p o s i t i o n feedback was not used. MacDonald however concluded that some form of feedback must be present since small disturbances have l i t t l e e f f e c t on handwriting. MacDonald (13) proposed the following c o n t r o l scheme (shown i n f i g u r e la) to f i t the experimental data. A force generator was given the two inputs corresponding to the slope and f i n a l value of a segment of a trapezoidal waveform. The force generator output was fed to an analogue system c o n s i s t i n g of two i n t e g r a t o r s . A comparator sensed the output of the analogue system and a preset p o s i t i o n . When the 1. J . J . Denier van der Gon and J.Ph. Thuring, "The Guiding of Human Handwriting Movements", Kybernetik, Band I I , Heft 4, Feb. 1965, p. 145. analogue system output reached the preset value the comparator sent a s i g n a l to the command generator causing three new values f o r f i n a l value, slope and p o s i t i o n to be issued to.the force generator. The advantages of t h i s model . are two-fold. It ret a i n s the advantages of p o s i t i o n feedback while allowing a time delay between the command generator and the re s t of the system. Figure lb i l l u s t r a t e s the time delay feature. I f a new set of inputs i s required at p o s i t i o n A, the preset displacement can be set at B so that a f t e r a time delay d, the new set of values come in t o e f f e c t at point A. This model also provides the d i s c r e t e c o n t r o l of force ind i c a t e d by the previous research. md2x/dt2;f(t) COMMAND GENERATOR FINAL VALUE SLOPE FORCE GENERA TOR fit) ANALOGUE SYSTEM PRESET POSITION xft) RECLUEST - FOR COMPARATOR NEW VALUES FIGURE la POSITION FEEDBACK MODEL position XA force FIGURE Ib TIME DELAY FEATURE Sensory organs, known as muscle spindles, are connected i n p a r a l l e l with most muscles. These provide length information from the muscle and are thought to form the sensors of the s t r e t c h r e f l e x loop. The s t r e t c h r e f l e x i s the natural tendency of a muscle to oppose unexpected muscle s t r e t c h i n g . The muscle spindles also provide a p o s i t i o n s i g n a l to the higher centres of the b r a i n . In the human system the muscle spindle could provide the p o s i t i o n information required for the proposed model. The force generator would be analo-gous to the muscle and the command generator to higher centres of the c e n t r a l nervous system (CNS) i n the spine and br a i n . The d i s c r e t e nature of handwriting c o n t r o l i s apparent from the seg-mented nature of the a c c e l e r a t i o n of the hand during w r i t i n g . This i s i l l u s t r a t e d i n fi g u r e 2a where h o r i z o n t a l and v e r t i c a l p o s i t i o n , v e l o c i t y and a c c e l e r a t i o n of the pen point are recorded as functions of time. Figure 2b i s an X-Y p l o t of the p o s i t i o n s i g n a l . The discovery of the segmented a c c e l e r a t i o n implied that any model of the handwriting system should be composed of a seri e s of segments with a minimum of co n t r o l between the beginning and end of any segment. The instrumentation used to obtain f i g u r e 2a i s described i n Appendix I. The basic component of the measurement system i s an e l e c t r o l y t i c tank. The object of the present work was to develop a simple e l e c t r o n i c model of the handwriting system. I t was hoped that such a model might provide a better understanding of the way a person controls and executes rapid s k i l l e d movements such as handwriting. An e l e c t r o n i c simulator c o n t r o l l e d by a d i g i t a l computer was b u i l t to test the model proposed by MacDonald. D e t a i l s of the simulator are given i n Appendix I I . The simulation proved to be d i f f i c u l t to c o n t r o l i n the form o r i g i n a l l y proposed. 5 1 i 1 i I I I l l i ! I I i I I ! • H 4 i ii u-ml u! ii »t!! i ]! ! 1 ! I I ! I H I t I H- I I 1 4 1 1 I I j ' f I t t i ( i f 11 ( I I ' ' i l l I I | t I i _ j i 1 i_j L I I I 7TTT i I I I I I VERTICAL DISPLACEMENT VERTICAL VELOCITY VERTICAL •H ACCEL. ] VERTICAL \ ACCEL. ' WITH APPROXIMATION HORIZONTAL DISPLACEMENT FIGURE 2 b, X-Y PLOT OF 2a TTT i HORIZONTAL VELOCITY HORIZONTAL ACCELERATION HORIZONTAL ACCELERATION Wl TH APPROXIMATION FIGURE 2d. CHART RECORDINGS OF HANDWRITING A mechanical model c o n s i s t i n g of a point mass with viscous and e l a s t i c damping was added and the con t r o l scheme was modified s l i g h t l y to allow easier s e l e c t i o n of the preset displacement. With these a l t e r a t i o n s the simulator could produce good copies of handwriting. Unfortunately the simulator had a high s e n s i t i v i t y to small changes i n i n i t i a l p o s i t i o n . A s i m i l a r s e n s i t i v i t y i n the human system i s u n l i k e l y since a person i s capable of w r i t i n g at almost any point within the range of the f i n g e r s . The simulator also had d i f f i c u l t y producing a c c e l e r a t i o n wave-forms to match those of human w r i t i n g even though the displacement output of the simulator was a good copy of the human w r i t i n g . Several other comparisons between the model and human w r i t i n g revealed more discrepancies i n the model's performance. A system which can match an a r b i t r a r y sample of handwriting i s not n e c e s s a r i l y analogous to the human system. An improved mechanical model appeared to be necessary since a point mass driven by two perpendicular forces i s not a good representation of the human hand. 2. DEVELOPMENT OF A MECHANICAL MODEL OF MUSCLE There are several things to be considered when attempting to model a muscle system. Since muscle i s not completely r i g i d , some e l a s t i c i t y must be taken into account. Tendons also have e l a s t i c i t y , an important f a c t i n the case of the human hand, where most of the muscles are located i n the forearm and are connected to the fingers and wr i s t by long tendons. Many studies have been made of the a b i l i t y of muscle to shorten against various loads when maximally ( t e t a n i c a l l y ) stimulated (1,3,11,18,23,24). I t has been found that the v e l o c i t y of shortening i s l i m i t e d , and depends on muscle length and external load. Therefore some form of viscous damping must be included i n the model. As with most p h y s i c a l systems, the e l a s t i c i t y and damping are not l i n e a r , but depend on muscle length, external force, v e l o c i t y of shortening and time. Some form of angular to l i n e a r conversion i s required since most muscles e s s e n t i a l l y rotate a bone about some fi x e d point by shortening t h e i r length. Such a conversion has been neglected i n t h i s work, since i t does not e f f e c t the r e s u l t s of the model to any great extent. Since muscles can only exert a force while contracting, i n order to achieve c o n t r o l of p o s i t i o n they are arranged i n antagonistic p a i r s . A s i m p l i f i e d p i c t u r e of a t y p i c a l antago-n i s t i c muscle p a i r i s shown i n f i g u r e 3. FIGURE 3 ANTAGONISTIC MUSCLE SYSTEM The following model was based on the above considerations and on models used i n other papers (3,11,16,23,24). However, the exact arrangement of the mechanical components was somewhat i n t u i t i v e . The model i s shown i n f i g u r e 4. The various mechanical components are a c t u a l l y d i s t r i b u t e d parameters i n the human system, but they have been lumped for ease of modelling. Non-l i n e a r i t i e s have been neglected since this i s only an approximate model and 81 data on the n o n l i n e a r i t i e s are not a v a i l a b l e . The angular to l i n e a r conversion has been neglected as previously mentioned. 7r> CE 2 limn w / / / / / JTYUJ CE 7 Z ^ - muscle elasticity k{ - tendon elasticity kv = viscous damping CE=contractile element L is the desired mass position X=L in the steady state FIGURE 4 PROPOSED MECHANICAL MODEL It i s assumed that the c o n t r a c t i l e element represents an i d e a l i z e d muscle which w i l l shorten when stimulated. I f the antagonistic muscle i s stimulated the unstimulated muscle x ^ i l l completely relax and o f f e r no resistance. In the human case t h i s i s approximately true. One dif f e r e n c e between t h i s and other models i s that the c o n t r a c t i l e element i s a c o n t r o l l e d length, not a c o n t r o l l e d force. The v a r i a b l e to be c o n t r o l l e d i s assumed to be the p o s i t i o n of the mass. A c o n t r o l s i g n a l from the brain t e l l s the appropriate c o n t r a c t i l e element to shorten to a length L. In fi g u r e 4 i f dL/dt <_0 c o n t r a c t i l e element 1 i s c o n t r o l l e d and c o n t r a c t i l e element 2 i s relaxed. I f dL/dt >_0 the s i t u a -t i o n i s reversed. The f i n a l p o s i t i o n of the'mass w i l l be equal to the length L. Since i t i s not p o s s i b l e f o r a p h y s i c a l element to shorten instantaneously the c o n t r a c t i l e element w i l l shorten at a p a r t i c u l a r rate u n t i l the correct value i s reached. In t h i s scheme i t i s assumed that the CNS issues a slope or v e l o c i t y of movement and a f i n a l value for the desired p o s i t i o n of the mass. Depending on the sign of the d e r i v a t i v e of the desired p o s i t i o n the CNS also decides which muscle must shorten. Expressed mathematically, the whole system becomes three coupled d i f f e r e n t i a l equations with two c o n s t r a i n t s . dw dt j 2 d x + k + k m t v + dt dv 2k m. k + k , m t + — : v dt k k k m , t — z + -— x k k v v k — (w + v) m m . t V V L represents the desired value of x i f < o z = w CE #1 i s dt — y = L p u l l i n g i f dL n z = L CE 2 i s dt — y = v p u l l i n g I t x i s assumed that the springs have zero i n i t i a l length, and there i s no r e s i d u a l tension i n the system. The r e s i d u a l tension would correspond to muscle tone. These e f f e c t s could have been included but would have only added constants to the equations. Due to the d i f f i c u l t i e s previously mentioned, there i s l i t t l e data a v a i l a b l e on the mechanical parameters of the human muscle. There i s , however, extensive data a v a i l a b l e f o r animal muscle (3,11,17,18). A paper by Bahler i n the IEEE Transactions on Bio Medical Engineering (3) o f f e r s a good analysis of mammalian s k e l e t a l muscle; s p e c i f i c a l l y , the r i g h t g r a c i l i s anticus muscle 10. of the r a t . The muscle was removed from the rat and attached to a mechanical apparatus. It was bathed i n a s o l u t i o n to prolong i t s response to e l e c t r i c a l s t i m u l i . The force, v e l o c i t y and p o s i t i o n produced by the muscle were measured. The mechanical apparatus could also be used to s t r e t c h the muscle i n a known way. The r e s u l t s of the paper can be summarized by a quotation from the paper's abstract: " . . . f o r lengths le s s than 120 percent of rest length, mammalian s k e l e t a l muscle can be modeled as a non-l i n e a r force generator, a function of length and time, bridged by a nonlinear v i s c o u s - l i k e element, a function of time, length and v e l o c i t y , i n s e r i e s with a non-l i n e a r e l a s t i c element, a function of length."2 Figure 5 i s taken from Bahler's paper. I t represents the dynamic le n g t h - f o r c e - v e l o c i t y phase space of the c o n t r a c t i l e element during a t e t a n i c contraction. (Bahler's " c o n t r a c t i l e element" includes the force generator and the viscous element but not the s e r i e s e l a s t i c element). The length and force have been normalized to the r e s t length and maximum te t a n i c tension. These experiments were for t e t a n i c stimulation only and i t must be assumed that the muscle behaves l i n e a r l y f or l e s s e r amounts of stimulation. In order to compare the model of f i g u r e 4 with Bahler's r e s u l t s i t must be reduced to the form shown i n f i g u r e 6a since Bahler was working with only one i s o l a t e d muscle. The d i f f e r e n t i a l equation for t h i s configuration i s shown below. k w > F since muscle i s contracting m — ° . k _ z = 0 f o r maximal stimulation dw _m _ F_ dt k W " k w > 0 F > 0 v v — — The equation i s p l o t t e d i n f i g u r e 6b i n the same phase space as Bahler used. 2. A.S. Bahler, "Modeling of Mammalian S k e l e t a l Muscle", IEEE Trans, of Bio- Medical Engineering, Vol. BME-15, No. 4, October 1968, p. 249 From fig u r e 6b i t can be seen that Bahler's r e s u l t s and the model agree to some extent. I t i s apparent that the model i s a l i n e a r f i r s t order approximation to an actual muscle. To produce the r e s u l t s Bahler observed would require the in t r o d u c t i o n of the n o n l i n e a r i t i e s previously mentioned thus complicating the model considerably. The wisdom of using a more accurate model may be questioned when i t i s remembered that the model w i l l be used to simulate e i t h e r the v e r t i c a l or h o r i z o n t a l component of actual handwriting. There are more than f i f t y muscles i n the hand and forearm and to produce an accurate model of these would be extremely d i f f i c u l t considering the many parameters involved. Even i f a reasonable model could be found i t would be 12, necessary to develop a c o n t r o l philosophy i n v o l v i n g a l l these muscles working s y n e r g i s t i c a l l y . I t was decided to test t h i s simple l i n e a r f i r s t order model i n s i t u a t i o n s s i m i l a r to those which could be produced f o r actual handwriting i n the e l e c t r o l y t i c tank. Although the model does not simulate a l l of the c h a r a c t e r i s t i c s of antagonistic muscles, i t represents a considerable improve-ment over the point mass model used by Denier van der Gon (5) and MacDonald (13) W —> CONTRAC TILE ELEMENT i T Y Y Y T T -$3- F FIGURE 6 a ISOLATED MUSCLE MODEL ^VELOCITY -dw/dt w=0 LENGTH w R- REST LENGTH TENSION F FIGURE 6b LENGTH -FORCE-VELOCITY PHASE SPACE FOR MUSCLE MODEL 13. 3. ANALOGUE SIMULATION AND TESTING OF MODEL The d i f f e r e n t i a l equations for the model were simulated on a EAI 231-R PACE analogue computer. Comparators and relays were used to switch the c o n t r o l input taking into account the p o l a r i t y of the input's d e r i v a t i v e . There were four mechanical parameters (k , k , k and m) to be determined and i t was also t v m convenient to time scale the problem so that the model was analogous to the human system. The parameters were selected on an i t e r a t i v e basis using the response of the model to the tests discussed below. a) Comparison with the impulse response of human muscle I t i s d i f f i c u l t to make any mechanical measurements on a human subject since there can be no d i r e c t c o n t r o l over the inputs to the human system. Any voluntary movement must come from the CNS which may override or modify a voluntary muscle command. Resolving any motion into p a r t i c u l a r actions by p a r t i c u l a r muscles i s d i f f i c u l t because of the large number of muscles i n the hand and forearm. Denier van der Gon (6) gives some physiolo-g i c a l basis for r e s o l v i n g a l l motions i n t o movements i n two perpendicular d i r e c t i o n s and since previous work had resolved a l l motions into t h e i r projections on two perpendicular axis t h i s strategy was continued. It would be convenient, however, to get some i n d i c a t i o n of the mechanical properties of a t y p i c a l hand or forearm muscle. A common physiol o -g i c a l technique i s to simulate small numbers of muscle f i b r e s by means of e l e c t r i c a l pulses fed to the muscle or nerves through needle electrodes. Such work i s usually r e s t r i c t e d to animals, or i s c a r r i e d out on humans under very c l o s e l y c o n t r o l l e d conditions. I t i s p o s s i b l e , however, to stimulate muscles by using external s k i n electrodes, although the c o n t r o l of i n d i v i d u a l muscles i s not as p r e c i s e as with needle electrodes. Some research into' the requirements of external stimulation led to the design and construction of a constant current stimulator described i n Appendix I I I . Small (3/8 inch diameter) gold plated electrodes were attached to the skin with adhesive tape a f t e r being covered with a j e l l y containing sodium c h l o r i d e to decrease skin resistance. The l o c a t i o n of the electrodes c o n t r o l l e d which muscle was stimulated. I t was hoped that a s i n g l e pulse of current could be used to obtain a mechanical response analogous to the impulse response of an e l e c t r i c a l system. The electrodes were attached to the forearm or hand. One muscle "twitch" which was convenient used the p o s i t i v e electrode about two inches from the elbow on the underside of the forearm. The negative electrode was positioned on the underside of the wri s t so that the thumb twitched inwards toward the palm. With the negative electrode i n s l i g h t l y d i f f e r e n t l o c a t i o n s , other fingers could be made to execute a s i m i l a r motion, although i t was often d i f f i c u l t to stimulate only one fi n g e r . The current was usually between 1 and 10 milliamperes with a pulse width of about 5 mil l i s e c o n d s . It i s i n t e r e s t i n g to note that the correct p o l a r i t y i s required. I f the p o l a r i t y was reversed a considerable increase i n stimulating current was required to obtain the same muscle movement. When a s a t i s f a c t o r y twitch was obtained, permanent records were made by taping a s t i f f wire to the moving f i n g e r . The wire was put in t o the water of the e l e c t r o l y t i c tank and the hand supported by the remaining f i n g e r s . The hand was oriented so that the twitch was along e i t h e r the v e r t i c a l or h o r i z o n t a l d i r e c t i o n s . A P o l a r o i d p i c t u r e of the displacement, v e l o c i t y and ac c e l e r a t i o n of the finger during the twitch was made using an o s c i l l o s c o p e . A t y p i c a l p i c t u r e i s shown i n figu r e 7a. The o s c i l l o s c o p e was triggered on the leading edge of a 5 milliampere, 3 m i l l i s e c o n d pulse. Ten twitches of the thumb are superimposed i n th i s example. The s l i g h t displacement undershoot POSITION (0.08 inches /div.) VELOCITY (3.0 inches /sec /div.) ACCELERATION (175 inches /sec /div.) TIME : 20 msec/div. FIGURE 7a HUMAN TWITCH RESPONSE _ L • - + r " " — i i — •—(.._ i — * i — i 1— i — i 1—1 1—1 1—1 i — 1—1 1—1 1—i 1— 1— 1— - s s — i ... — i t—f - H — i h—1 r— 1—1 — h— i—1 --1 i — i — i 1— 1—1 1—' - f . . J i-V — -• • —— i — (\-\.-\-\-\-\-•fH—1— — — f i r r i . — - — — I I b :-FF • • : : : - - p . . . . • -J 1 CONTROL "L POSITION VELOCITY ACCELERATION TIME: 25 msec/div. FIGURE 7b SIMULATOR RESPONSE TO AN IMPULSE INPUT at the end of the twitch i s not completely shown because of the choice of time scale. To compare the model with the twitch responses of human muscles, a short trapezoidal pulse was fed to the simulator. This pulse was approxi-mately 25 milliseconds long. With the parameters of the model optimized the shape of the displacement, v e l o c i t y and a c c e l e r a t i o n waveforms agreed w e l l with the responses observed from human muscles. Some differences i n the time scale could be expected since the twitch responses from the tank were eit h e r the thumb or s i n g l e fingers while the model had been adjusted to match the response of the whole hand. Figure 7b shows the simulator response to a s i n g l e t r a p e z o i d a l pulse. b) Response to s l i d i n g f r i c t i o n disturbances By subjecting both the model and human w r i t i n g to some c o n t r o l l e d disturbance a convincing test of the model's v a l i d i t y can be made. S l i d i n g f r i c t i o n i s a good example of such a disturbance and was f i r s t used by Denier van der Gon and h i s co-workers (6) i n t h e i r research. They used an i r o n rod wrapped with many turns of wire to form an electromagnet. Writing was done on an i r o n p l a t e and when the c o i l was energized, extra s l i d i n g f r i c t i o n was added to the human system. Unfortunately, i n the case of the present equipment, the e l e c t r o l y t i c tank's t e f l o n i n s u l a t i o n l i m i t e d the magnetic a t t r a c t i o n and there was not enough f r i c t i o n to disturb the w r i t i n g . To overcome t h i s problem a large electromagnet and a p l a s t i c tank were constructed as described i n Appendix I. Writing was c a r r i e d out with an i r o n rod. Since the s i z e of the magnet was no longer l i m i t e d , i t was possible to get s u f f i c i e n t a t t r a c t i o n . There was a 1/16 inch a c r y l i c sheet over the magnet which acted as the wr i t i n g surface and prevented the magnet from upsetting the e l e c t r i c f i e l d patterns i n the e l e c t r o l y t i c tank. 17. When the magnet was used i t was d i f f i c u l t to get reproducible r e s u l t s with ordinary handwriting. I f the magnet was energized at s l i g h t l y d i f f e r e n t times during d i f f e r e n t t r i a l s using the same word, the r e s u l t s were not consistent. Occasionally the i r o n " p e n c i l " would s t a l l completely when the magnet was turned on. Simulating s l i d i n g f r i c t i o n i n two dimensions on the computer model i s also d i f f i c u l t . The f r i c t i o n force must be di r e c t e d i n the opposite d i r e c t i o n to the v e l o c i t y so that analogue sine and cosine generators are required to determine the appropriate c o r r e c t i o n to the input forces. To overcome these problems the magnet tests were r e s t r i c t e d to experiments i n one dimension. The e f f e c t of the added f r i c t i o n was consistent for each t r i a l i f u n i d i r e c t i o n a l strokes were used. I t was found that the amplitude of the strokes was reduced almost immediately a f t e r the magnet came on but the timing of the strokes remained remarkably constant even over i n t e r v a l s as short as 100 to 200 m i l l i s e c o n d s . This measurement was made by fi n d i n g the time between zero crossings immediately before and a f t e r the f r i c t i o n was applied. Denier van der Gon (6) had observed t h i s decrease i n amplitude and had said that the timing of handwriting appeared to remain constant but h i s instrumentation was not extensive and he had no way of checking the timing of the waveforms over such short i n t e r v a l s . I t would appear that there i s no adaption by the CNS to the increased f r i c t i o n caused by the magnet. Any such adaption would have been delayed by the nerve propagation time which i s greater than 100 m i l l i s e c o n d s . Because the frequency of the strokes remained constant over both short (100 milliseconds) and long periods of f r i c t i o n (more than 1 second) there appears to be no unconscious CNS " i n t e r f e r e n c e " with the timing of the strokes. S l i d i n g f r i c t i o n disturbance tests were responsible f o r one of the 18. major contradictions between the model proposed by MacDonald (13) and human w r i t i n g . That model responded to s l i d i n g f r i c t i o n by decreasing the amplitude of the strokes and by increasing the period of the strokes. This i s a d i r e c t c o n t r a d i c t i o n to the observed response of human w r i t i n g , which maintained the frequency of the strokes. S l i d i n g f r i c t i o n was simulated on the improved mechanical model by adding a constant force to the moving mass. The p o l a r i t y of the f r i c t i o n force was opposite to the v e l o c i t y ' s p o l a r i t y . Figure 8a shows the model's response to a sudden increase i n s l i d i n g f r i c t i o n and f i g u r e 8b i s a recording from the e l e c t r o l y t i c tank f o r v e r t i c a l strokes of approximately the same frequency as the model. I t should be noted that s t a t i c f r i c t i o n i s also present i n the tank. This i s believed to account f o r the impulse-like shape of the a c c e l e r a t i o n from the tank. S t a t i c f r i c t i o n was not simulated i n the model. There i s some s l i d i n g f r i c t i o n between the i r o n " p e n c i l " and the tank bottom before the magnet i s energized. A small s l i d i n g f r i c t i o n force was added to the simulator to duplicate t h i s e f f e c t . c) Frequency and step response comparison From the experiments done i n the e l e c t r o l y t i c tank i t was known that for c e r t a i n frequencies, the a c c e l e r a t i o n of the hand while executing u n i d i r e c t i o n a l strokes was roughly t r a p e z o i d a l . At lower frequencies the a c c e l e r a t i o n tended toward an impulse-like shape and at higher frequencies i t tended to become t r i a n g u l a r . At the t r a n s i t i o n from trapezoidal to t r i a n g u l a r there was an increase i n the amplitude of the a c c e l e r a t i o n . Previous mechanical models had f a i l e d to show a l l three types of response. The model was driven with a trapezoidal input f o r the frequency response tests with u n i d i r e c t i o n a l strokes. This seemed l o g i c a l since the c o n t r a c t i l e element of the model could not be expected to shorten instantaneously. Figure 9 shows the r e s u l t s of the f i n a l model and r e s u l t s from the tank. The d i s -19 FIGURE 8 a MODEL RESPONSE TO SLIDING FRICTION ACC. VELOCITY POSITION FIGURE 8b HUMAN RESPONSE TO SLIDING FRICTION 20 MODEL RESPONSE I— (• 4 • + H)--ft ft f f 1 w Kill HI III JIIJ lillli UU CONTROL ACC, VELOCI TY POSITION FREQUENCY RESPONSE - UNIDIRECTIONAL STROKES HUMAN RESPONSE 3c *^ • I* vii d L d N -T [lip 3q f if 1 l i p I f Ijli M I WW AAA oil11: liMftiSji. i i U in Uiji VELOCITY LLI POSITION 1/ /<VY>>* FIGURE 9 COMPARISON OF MODEL AND HUMAN RESPONSE placement and a c c e l e r a t i o n waveforms show good agreement over the f u l l frequency range. Another test used to compare the model with the human system involved a voluntary rapid wrist movement from one p o s i t i o n to another. The object was to simulate a step response. I t was found that the human overshoot was about 10 to 20 percent. The f i n a l model overshoot was s i m i l a r to the human response. The four tests described above were used to evaluate the values of the mechanical elements of the model. They were adjusted to give the best agreement with human responses to the same s t i m u l i . The values for the. mechanical elements were chosen to be; k = 1.0 k = 1.0 k = 0.5 m = 1.0 m t v The analogue simulation time constant was chosen to be 30 m i l l i s e c o n d s . The proposed model performed well i n the comparisons with human response and had some p h y s i o l o g i c a l c r e d i b i l i t y since i t was i n agreement with Bahler's r e s u l t s . The model was now considered s u f f i c i e n t l y accurate for use with d i g i t a l computer c o n t r o l i n an attempt to simulate actual handwriting. 4. RESULTS OF ELECTRONIC HANDWRITING SIMULATION The system used for c o n t r o l l i n g the mechanical model was s i m i l a r to that of MacDonald (13) and Denier van der Gon (5) i n that the time each segment was i n e f f e c t was preset. The mechanical model required a trapezoidal s i g n a l (L) corresponding to the desired p o s i t i o n of the mass. Three parameters were used to specify each segment; a slope or v e l o c i t y of shortening term, a f i n a l value f o r the p o s i t i o n and a term proportional to the length of time the segment was i n e f f e c t . By using a preset time for each segment the model agreed well with the human response i n the s l i d i n g f r i c t i o n tests since the human response to s l i d i n g f r i c t i o n was to maintain the frequency of the w r i t i n g . A d e s c r i p t i o n of the e l e c t r o n i c simulator i s given i n Appendix I I . A f t e r some experience was gained with the new system, i t was observed that the slope of the co n t r o l s i g n a l (L) was now much more important than i n previous models. The c o n t r o l signals to the analogue computer tended to be almost t r i a n g u l a r at times, implying that with t h i s model the muscle's v e l o c i t y of shortening i s very important. The h o r i z o n t a l and v e r t i c a l d i s -placements as functions of time were matched to samples of handwriting from the tank. When the h o r i z o n t a l and v e r t i c a l accelerations of the model were compared to those from the tank, some general agreement i n shape was found. This was contrary to previous models where the a c c e l e r a t i o n waveforms never matched the r e s u l t s from the tank even i f the displacements were matched very c l o s e l y . Figure 10a shows the r e s u l t s of matching the displacements as time functions. The h o r i z o n t a l and v e r t i c a l accelerations are also shown compared to the tank r e s u l t s . (The tank r e s u l t s are the darker t r a c e s ) . Figure 10b i s an X-Y p l o t of the simulator output compared to the o r i g i n a l handwriting and figures 10c and lOd are the same waveforms f o r a d i f f e r e n t word. Some differences i n the waveforms are caused by noise introduced by the two d i f f e r -e n t i a t i o n s i n the measurement e l e c t r o n i c s . Also, beyond a c e r t a i n point, a long time spent matching the waveforms produced l i t t l e improvement. Another source of a c c e l e r a t i o n disturbances i s the s t a t i c f r i c t i o n of the pen against the tank bottom. I f the pen stops on the tank bottom even for an i n s t a n t , the a c c e l e r a t i o n waveform w i l l show a large spike when the pen suddenly overcomes the f r i c t i o n and begins to move again. Since i t does not simulate s t a t i c f r i c t i o n , the a c c e l e r a t i o n s i g n a l from the simulator i s much smoother. The small spikes i n the simulator a c c e l e r a t i o n waveform are FIGURE 10 a DISPLACEMENT AND ACCELERATION MATCHING FIGURE 10b X'Y PLOT OF FIGURE 10a FIGURE 10c DISPLACEMENT AND ACCELERATION MATCHING 24. due to comparator relay switching i n the analogue computer and should be ignored. If i t i s assumed that muscle can shorten at a f i x e d v e l o c i t y , the c o n t r o l scheme does not require any d i r e c t feedback. Minor perturbations i n the c o n t r o l s i g n a l L do not cause disastrous changes i n the output w r i t i n g because there i s heavy l o c a l feedback i n the mechanical model. The l o c a l feedback i s the r e s u l t of the e l a s t i c and viscous elements and of the antagonis-t i c muscle action. The p o s s i b i l i t y of feedback c o n t r o l of muscle shortening v e l o c i t y i s discussed i n the next chapter. 5. DISCUSSION OF RESULTS It was observed that an X-Y p l o t of the L function was a rough match of the desired w r i t i n g . This implies that the dynamics of the muscles merely serve to smooth out the w r i t i n g . In other words, the c o n t r a c t i l e elements of the muscles follow the w r i t i n g to a l i n e a r i z e d f i r s t order approximation and the dynamics of the muscles smooth the w r i t i n g i n t o i t s c h a r a c t e r i s t i c shape. This i s demonstrated i n f i g u r e 11a where the top trace i s the X-Y p l o t of the displacement while the bottom trace i s the X-Y plo*: of the co n t r o l s i g n a l L. I t should be remembered that the model uses a d i g i t a l method f o r generating the co n t r o l s i g n a l and t h i s produces the d i s c r e t e dots of the lower trace. The c o n t r o l L and the displacement as functions of time are shown i n f i g u r e l i b . In order to gain p h y s i o l o g i c a l support for the type of co n t r o l system proposed, some r e s u l t s of neuromuscular research w i l l be presented. Most of the segments used by the simulator to copy human handwriting were longer than 100 milliseconds with some as long as 300 mi l l i s e c o n d s . I f any feedback i s used by the nervous system f o r the handwriting process, the latency c 25. or delay due to propogation time in the nerves and decision making must be less than 100 milliseconds. It i s possible that feedback control of muscle shortening velocity would not include the brain in the loop. Some routine muscle control, such as maintaining muscle tone and maintaining posture, i s done at the spinal level. The stretch reflex is also controlled from the spine. Control of muscle velocity may be done at this lev e l of the CNS, implying a shorter latency in any feedback loop. FIGURE 11a COMPARISON OF DISPLACEMENT AND CONTROL SIGNALS FIGURE lib V position TIME PLOT OF V control FIGURE 11a 26; I t i s commonly accepted that the la t e n c y f o r a hand-spine-hand nerve path i s about 30 m i l l i s e c o n d s and f o r a hand-brain-hand nerve path, about 100 m i l l i s e c o n d s . From t h i s i t would appear that v e l o c i t y feedback c o n t r o l i s p o s s i b l e w i t h a feedback loop i n c l u d i n g the spine. To explore t h i s p o s s i b l i t y i t i s necessary to know the v a r i o u s nerve paths which are used f o r muscle c o n t r o l . A review paper on muscle s p i n d l e s by P.B.C. Matthews (14) forms the b a s i s f o r t h i s d i s c u s s i o n . In a t y p i c a l muscle there i s one l a r g e motor nerve path (known as the alpha path) which d i r e c t l y c o n t r o l s the muscle. The a d j e c t i v e ' l a r g e ' r e f e r s to the diameter of the nerve f i b r e which i s p r o p o r t i o n a l to i t s v e l o c i t y of propagation. One or more muscle s p i n d l e s are attached approximately i n p a r a l l e l w i t h the muscle f i b r e s . The muscle s p i n d l e i s s u p p l i e d w i t h two sets of s m a l l motor # MOTOR FIBRES PRIMARY ENDING SECONDARY ENDING HEAVY LINES IMPLY LARGE NERVE DIAMETER AND HENCE FASTER PROPAGATION FIGURE 12 SIMPLIFIED MUSCLE INNERVATION 27. nerve f i b r e s (gamma f i b r e s ) . The spindle has two output f i b r e s which are fed by the primary and secondary nerve endings. These f i b r e s are coupled to the spine and are then projected into the cerebellum of the brain which i s responsible f or the p r e c i s i o n of voluntary movements. Figure 12 i s a highly s i m p l i f i e d drawing of the arrangement described above. If the gamma f i b r e s are not stimulated, the primary ending of the muscle spindle responds to dynamic changes i n the muscle length, that i s , i t i s a v e l o c i t y sensor. The secondary ending i s mainly a p o s i t i o n sensor. However i f one of the gamma f i b r e s i s stimulated the primary ending can be made to behave as a p o s i t i o n sensor with almost no dynamic response. If the other gamma f i b r e i s stimulated the dynamic response of the primary ending can be increased. (A c l a s s i f i c a t i o n of gamma f i b r e s into gamma 1 and gamma 2 i s based on anatomical observations of the area of the spindle where each f i b r e ends. It has not been resolved which f i b r e produces the s t a t i c response or which enhances the dynamic response of the primary ending.) I t i s known that the CNS has co n t r o l over a l l three motor nerves (alpha, gamma 1 and gamma 2). I t appears then that the CNS has a c o n t r o l l a b l e muscle sensor which can respond to muscle lengths or various rates of muscle shortening depending on the CNS co n t r o l of the gamma f i b r e s . This evidence in d i c a t e s that a v e l o c i t y feedback loop i s possi b l e . There i s a problem however. Most papers dealing with the response of muscle spindles (2,4,14,17,22) only report a spindle s e n s i t i v i t y to muscle s t r e t c h i n g with no response to muscle shortening. For feedback c o n t r o l of muscle shortening the antagonistic muscle spindle would have to be used. This would not be str e t c h i n g at the same rate as the act i v e muscle was shortening, due to the mechanical components between the two muscles. I t would appear however, that s u f f i c i e n t gamma a c t i v i t y w i l l make the primary ending responsive 28. to muscle shortening. Matthews' paper (14) contains the following quotation which supports the idea of a v e l o c i t y servo c o n t r o l l e d by the spindle of the contracting muscle. "The alpha route would perhaps be most e f f i c i e n t l y employed i n conjunction with s u f f i c i e n t fusimotor a c t i v i t y to prevent any decrease i n spindle discharge occuring during the contraction; t h i s would be achieved i f the r e l a t i v e amounts of alpha and of gamma a c t i v i t y were adjusted to be appropriate f o r the v e l o c i t y of shortening 'expected' under any p a r t i c u l a r set of conditions. Then i f shortening proceeded f a s t e r than 'intended' by the higher centers, i t would be slowed by servo action, and i f shortening were hindered by some unexpected load i t would be speeded up by servo action. Such a mode of action would not s u f f e r from the slowness inherent i n the e x c i t a t i o n of muscle by the gamma route alone and would agree with the experimental f i n d i n g that fusimotor neurons and ordinary motor neurons are often activated t o g e t h e r " 3 The term "fusimotor" r e f e r s to the muscle f i b r e s i n the spindle innervated by the gamma nerve paths. I t should be noted that a l l spindle actions are subconscious and are not used by the bra i n f o r conscious " p o s i t i o n sense". The proposed handwriting model requires a cont r o l of muscle (or c o n t r a c t i l e element) v e l o c i t y of shortening and f i n a l p o s i t i o n . I t also assumes the c a p a b i l i t y of some con t r o l generator to issue "preprogrammed" commands which are i n e f f e c t f o r preprogrammed lengths of time. The physiol o -g i c a l evidence suggests that a feedback system may be present which can cont r o l the v e l o c i t y of shortening of a muscle. The v e l o c i t y sensors (muscle spindles) can also be made to respond to p o s i t i o n so that the same feedback system could c o n t r o l the f i n a l p o s i t i o n of a muscle. One important fa c t should be noted. The computer model simulating handwriting used only 4 b i t s to specif y slope. 3. P.B.C. Matthews, "Muscle Spindles and t h e i r Motor Control", P h y s i o l o g i c a l  Review, Vol. 44, 1964, p. 277. 29. This corresponds to 16 d i s c r e t e v e l o c i t i e s so that a v e l o c i t y feedback system would not r e q u i r e a high degree of r e s o l u t i o n . Both Lashley (12) and Denier van der Gon (6) proposed some form of preprogrammed nervous mechanism which could i s s u e preset commands f o r preset lengths of time. Thus there i s a f a i r degree of p h y s i o l o g i c a l evidence to support the proposed handwriting model. 6. CONCLUSIONS A mechanical model of an a n t a g o n i s t i c muscle system was developed using known muscle c h a r a c t e r i s t i c s . This model was compared w i t h human responses using the f o l l o w i n g t e s t s ; frequency response f o r simple u n i d i r e c t i o n a l s t r o k e s , impulse response, step response and response to s l i d i n g f r i c t i o n d isturbances. The model w i t h i t s f i n a l mechanical parameters compared w e l l w i t h a human subj e c t . The c o n t r o l system developed f o r the model r e q u i r e d the c o n t r o l of v e l o c i t y of muscle s h o r t e n i n g , f i n a l muscle p o s i t i o n and time f o r each segment. The c o n t r o l was of a d i s c r e t e nature, changing only at the r e q u i r e d times. Both displacement and a c c e l e r a t i o n waveforms produced by the mechanical model and the c o n t r o l system agreed w i t h a sample of human w r i t i n g . P h y s i o l o g i c a l evidence was found which supports the proposed c o n t r o l scheme. Although the proposed model and c o n t r o l scheme have not been shown e x a c t l y analoguous to the human system, the model does agree w e l l w i t h obser.ved human responses and a l l the necessary components f o r the c o n t r o l scheme have some degree of p h y s i o l o g i c a l backing. 30. APPENDIX I E l e c t r o l y t i c tank measurement system The f i r s t step i n studying handwriting c o n t r o l i s to obtain a permanent record of the pen p o s i t i o n as a function of time. The equipment used f o r t h i s i s almost i d e n t i c a l to that used by MacDonald (13). A four foot square e l e c t r o l y t i c tank was used as the basic measurement apparatus. Water was used to f i l l the tank to a depth of 3/4 inch. Four brass electrodes were attached along the perimeter of the tank and a small dc current (100-600 microamperes) was i n j e c t e d i n t o the water through the pen. Two opposing e l e c -trodes were connected to the inputs of a d i f f e r e n t i a l a m p l i f i e r which converted the d i f f e r e n c e of the two input currents into a voltage proportional to p o s i t i o n . If the pen was i n the centre of the tank, equal currents a r r i v e d at the opposing sides and the output of the d i f f e r e n t i a l a m p l i f i e r was zero. I f the pen moved cl o s e r to one side, that side received more current and the output voltage increased proportionately. TXJO such arrangements were used to provide v e r t i c a l and h o r i z o n t a l p o s i t i o n s . The whole measurement system i s shown i n Figure Al-1. The output of the d i f f e r e n t i a l a m p l i f i e r was fed through a 100 Hz low pass f i l t e r and through a d i f f e r e n t i a t i n g c i r c u i t to produce a v e l o c i t y s i g n a l . The v e l o c i t y s i g n a l passed through another 100 Hz low pass f i l t e r and through a 180 Hz notch f i l t e r to eliminate the t h i r d harmonic of the power l i n e frequencies. The notch f i l t e r output was again d i f f e r e n t i a t e d to produce a s i g n a l propor-t i o n a l to a c c e l e r a t i o n . The low pass f i l t e r s were necessary to eliminate noise and unwanted signals introduced by the d i f f e r e n t i a t i o n s . 31. to y, system electrolytic tank cons tant current ource -*—x 100 Hz low pass filter .differentiator dx/dt 100 Hz lew pass filter WO Hz notch filter differ en tiator d&/dt2 FIGURE A1-1 MEASUREMENT SYSTEM To eliminate power l i n e interference a small 60 Hz voltage was inj e c t e d d i r e c t l y into the a i f f e r e n t i a l a m p l i f i e r inputs. The phase and amplitude were adjusted to cancel the voltages picked up by the large tank electrodes. The whole measurement system produced, s i x outputs corresponding to the h o r i z o n t a l and v e r t i c a l p o s i t i o n , v e l o c i t y and ac c e l e r a t i o n of the pen i n the tank. These outputs were recorded on an eight channel chart recorder. In addition to the e l e c t r o l y t i c tank, a large electromagnet was constructed and i n s t a l l e d d i r e c t l y under the w r i t i n g area. A p l a s t i c tank was made f o r use with the magnet since the o r i g i n a l tank was t e f l o n coated i r o n sheet. The magnet used a laminated core with a pole face of approximately 2 3/4 inches by 4 inches. A c o i l of 600 turns was wound on th i s core and a 32. dc current of up to 20 amperes was used i n the c o i l . The current was supplied through a relay from three 12 v o l t storage b a t t e r i e s i n se r i e s . The magnet system was used i n the s l i d i n g f r i c t i o n experiments. APPENDIX II Computer c o n t r o l l e d simulator To simulate the system proposed i n the in t r o d u c t i o n , the following equipment was used. A D i g i t a l PDP 9 computer was used to simulate the command generator. This enabled tables of values f o r force, slope and d i s -placement to be set up e a s i l y . An i n t e r f a c e connected the computer to external hardware which was used to represent the force generator, analogue system and the comparator. A block diagram of the system i s shown i n Figure A 2-1. PDP 9 CONTROL interface S T reset x force x slope •' force v slope FORCE GENERATOR Morce x force. —{5= -ANALOGUE SIMULATION preset x y preset y x PI y PI L A ANALOGUE COMPARATORS x y X-Y DISPLAY SCOPE PI = PROGRAM. INTERRUPT f/GURE A 2-1 COMPUTER CONTROLLED SIMULATOR The external part of the simulator was both analogue and d i g i t a l . For each segment the PDP 9 put out an 18 b i t word through the i n t e r f a c e . Seven b i t s of the word corresponded to the f i n a l value of force. Four b i t s represented the slope and 7 b i t s were put i n t o a D/A converter to y i e l d an analogue s i g n a l p r o p o r t i o n a l to the desired turnover displacement. The force generator i s shown i n Figure A 2-2. A d i g i t a l comparator compared the 7 b i t s from the PDP 9 to the contents of a 7 b i t up-down counter. The d i g i t a l comparator enabled e i t h e r an up l i n e or a down l i n e to the up-down counter i f the two d i g i t a l words were not equal. The 4 b i t s f o r slope set the frequency of a v a r i a b l e rate clock which toggled the counter. The up-down counter counted towards the new value from the PDP 9 at a rate set by the 4 b i t s corresponding to slope and when the two d i g i t a l values were equal the counter stopped u n t i l the value from the PDP 9 changed. The number i n the counter was converted to an analogue l e v e l by a 7 b i t D/A converter. Th l e v e l was fed i n t o the analogue section which contained two integrators i n s e r i e s . The output from the second integ r a t o r corresponded to displacement and was compared to the preset value from the PDP 9. In t h i s model the hand was represented as a point mass with n e g l i g i b l e damping. When the analogue comparator found i t s two input values equal, an i n t e r r u p t was sent to the PDP 9 causing a new set .of values to be sent to the simulator. A f t e r the table i n the PDP 9 was f i n i s h e d the integrators were reset and the whole process was repeated. Two i d e n t i c a l systems were used for the v e r t i c a l and h o r i z o n t a l d i r e c t i o n s . 34. up down final value of force 7 bits INPUTS FROM VPDP 9 slope . DIGITAL COMPARATOR] 4 bits 1 X UP-DOWN COUNTER —gB* — VARIABLE RA TE CLOCK D/A CONVERTER force output FIGURE A2-2 FORCE GENERATOR The improved model developed i n the paper used the system outlined above except that the analogue system was simulated on an EAI 231-R PACE analogue computer. The "f o r c e " s i g n a l now corresponded to the desired mass p o s i t i o n (L). The 7 b i t s corresponding to the preset displacement were now used to set up a counter i n the PDP 9. An external clock interrupted the PDP 9 at 500 microsecond i n t e r v a l s and incremented the counter. When the counter overflowed the next set of values for the f i n a l p o s i t i o n L and the slope were issued to the external e l e c t r o n i c s . With t h i s system the PDP 9 and the external e l e c t r o n i c s produced a trapezoidal s i g n a l (L) which was fed to the analogue computer. The PDP 9 also reset the analogue computer when the tables for p o s i t i o n , slope and time were f i n i s h e d . The system i s shown i n Figure A 2-3. PDP 9 CONTROL A interface X lenqth X slope . . fc* y length y slope CONTROL SIGNAL GENERATOR X T" reset Y "U "PACE" ANALOGUE COMPUTER (MUSCLE DYNAMICS) 1 1 Y X FIGURE A 2-3 FINAL ELECTRONIC SIMULATOR The software written f o r the PDP 9 included routines to service in t e r r u p t s from the external simulator and to allow easy modification of the tables while the simulator was running. Tables could be modified or entered from the teletype and the teletype could give a hard copy table l i s t i n g . The whole set of tables could also be dumped or loaded from paper tape. However the majority of table manipulation was done with an o s c i l l o s c o p e display and l i g h t pen t i e d to the PDP 9. Software was written to display graphs of the values i n the tables. Any value could be selected and modified from the display. Segments could also be added or removed from the tables using the l i g h t pen. These modifications could be done while the simulator was running 3b. so that any change was seen immediately. The outputs of the two analogue systems were displayed on an X-Y os c i l l o s c o p e . A proj e c t i o n screen and an o s c i l l o s c o p e camera were arranged so that a photograph of handwriting done i n the e l e c t r o l y t i c tank could be superimposed on the output of the simulator. In th i s way one could compare the simulator and handwriting and e a s i l y modify the simulator parameters to produce an accurate match. APPENDIX III Constant current stimulator A constant current stimulator was constructed with the following c h a r a c t e r i s t i c s . An adjustable pulse width from 100 microseconds to 10 m i l l i -seconds was a v a i l a b l e with r e p e t i t i o n rates from 0.1 Hz to 10 Hz. The pulse could also be manually triggered. Skin resistances of the order of several thousand ohms could be expected and constant pulse currents up to 10 m i l l i -amperes could be delivered i n t o such loads. A synchronizing pulse was a v a i l a b l e to t r i g g e r an o s c i l l o s c o p e . The most important features of the stimulator involved safety. The skin electrodes provide a low resistance path to the body. The stimulation experiments were done with the e l e c t r o l y t i c tank and i t s e l e c t r o n i c s plus the 8 channel chart recorder and an o s c i l l o s c o p e . With t h i s much equipment, the p o s s i b i l i t y of ground loops or f a u l t s existed. There were also other grounded items within reach of the tank such as ground busses on lab benches and water pipes. In accordance with good medical e l e c t r o n i c s standards the whole stimu-l a t o r was e l e c t r i c a l l y i s o l a t e d from other equipment. A high frequency i n v e r t e r was used with the i s o l a t i o n being provided by the in v e r t e r transformer. The os c i l l o s c o p e synchronizing pulse was coupled out through a pulse transformer. 37. The i n v e r t e r supplied 110 v o l t s dc for the constant current source and 20 v o l t s f o r the timing e l e c t r o n i c s . The input voltage to the i n v e r t e r was 12 v o l t s . In order to protect against excess current flowing to the electrodes due to a f a u l t i n the stimulator, the following precautions were taken. The output current of the high voltage supply was l i m i t e d to 25 milliamperes by a r e s i s t o r . An SCR c i r c u i t provided an overcurrent shutdown of the high voltage supply at adjustable current l e v e l s from 1 milliamperes to 10 milliamperes. As a f i n a l + > 12 v. input -> sync out ® n pulse indicator 60 MSEC ]MONOSTABLE\ ISOLATED CIRCUITRY 1 shutdown level H. V. SUPPLY L. V SUPPLY TL TRIGGER "OSCILLATOR OVER CURRENT SHUTDOWN 10 ma. putput JL CONSTANT CURRENT SOURCE T amplitude -VyvV ^MONOSTABLE L freq. -j, manual trigger duration J FIGURE A 3 - 1 CONSTANT CURRENT STIMULATOR 38. f a i l - s a f e precaution 10 milliampere fuses were used i n serie s with each electrode. A block diagram of the stimulator i s shown i n the fig u r e A 3-1. 39. REFERENCES 1. Abbott, B.C. and Wilkie, D.R., "The Relationship between V e l o c i t y of Shortening and Tension-Length Curve of S k e l e t a l Muscle", J. Physiology, London, Vol. 143, 1958, pp. 214-223. 2. Andersson, B. and Lennerstrand, G., "Dynamic Analysis of Muscle Spindles", Muscle Afferents and Motor Control, ed. Granit, Nobel Symposium, Wiley and Sons, New York, 1966, pp. 107-114. 3. Bahler, A.S., "Modeling of Mammalian S k e l e t a l Muscle", IEEE Transactions on Bio-Medical Engineering, Vol. BME 15, No. 4, October 1968, pp. 249-257. 4. Brown M.C. and Mathews, P.B.C., "On the Sub-Division of the Efferent Fibres to Muscle Spindles i n t o S t a t i c and Dynamic Fusimotor F i b r e s " , Control and  Innervation of S k e l e t a l Muscle, ed. Andrew, Symposium at Queens College, Dundee, U n i v e r s i t y of St. Andrews, 1966, pp. 18-34. 5. Denier van der Gon, J . J . , Thuring, J . Ph., and Strackee, J . , "A Handwriting Simulator", Physics i n Medicine and Biology, Vol. 6, No. 3, January 1962, pp. 407-414. 6. Denier van der Gon, J . J . and Thuring, J. Ph., "The Guiding of Human Hand-w r i t i n g Movements", Kybernetic, Band I I , Heft 4, February 1965, pp. 145-148. 7. Granit, R., Receptors and Sensory Perception, Yale U n i v e r s i t y Press, New Haven, 1955, pp. 191-235. 8. Granit, R., Holmgren, B. and Merton, P.A., "The Two Routes for E x c i t a t i o n of Muscle and Their Subservience to the Cerebellum", J. Physiology, London, Vol. 130, 1955, pp. 213-224. 9. Houk, J. and Simon, W., "Responses of Golgi Tendon Organs to Forces Applied to Muscle Tendons", J. Neurophysiology, Vol. 30, 1967, pp. 1466-1482. 10. Houk, J . , "A V i s c o e l a s t i c I nteraction which Produces One Component of Adaption i n Responses of Golgi Tendon Organs", J. Neurophysiology, Vol. 40. 30, 1967, pp. 1483-1493. 11. Jewell, B.R., and Wilkie, D.R., "An Analysis of the Mechanical Components i n Frog S t r i a t e d Muscle", J. Physiology, London, Vol. 143, 1958, pp. 515-540. 12. Lashley, K.S., "The Accuracy of Movement i n the Absence of E x c i t a t i o n from the Moving Organ", Am. J . Physiology, Vol. 43, 1917, pp. 169-194. 13. MacDonald, J.S., "Experimental Studies of Handwriting Signals", M.I.T.  Technical Report //443, Cambridge, March 1966. 14. Matthews, P.B.C., "Muscle Spindles and t h e i r Motor Control", Physiology Review, Vol. 44, 1964, pp. 219-288. 15. Merton P.A., "Speculations on the Servo Control of Movement", CIBA Symposium, The Spinal Cord, London, C h u r c h i l l , 1953, pp. 247-255. 16. Milsum, J.H. B i o l o g i c a l Control Systems Analysis, McGraw-Hill, New York, 1966, pp. 342-352. 17. Rack, P.M.R., "The Reflex Response to Sinusoidal Movement", Control and  Innervation of S k e l e t a l Muscle, ed. Andrew, Symposium at Queens College, Dundee, Un i v e r s i t y of St. Andrews, 1966, pp. 112-118. 18. Richie, J.M. and Wilkie, D.R., "The Dynamics of Muscular Contractions", J. Physiology, London, Vol. 143, 1958, pp. 104-113. 19. Roberts, T.D.M., "The Nature of the Controlled Variable i n the Muscle Servo", Control and Innervation of S k e l e t a l Muscle, ed. Andrews, Sumposium at ' Queens College, Dundee U n i v e r s i t y of St. Andrews, 1966, pp. 160-170 20. Roberts, T.D.M., "Separation of the E f f e c t s on Muscle Servo of the Alpha, Gamma and Renshaw Control Pathways", Muscle Afferents and Motor Control, ed. Granit, Nobel Symposium, Wiley and Sons, New York, 1966, pp. 457-460. 21. Skogland, S., "Anatomical and P h y s i o l o g i c a l Studies of Knee J o i n t Innervation i n the Cat", Acta P h y s i o l o g i c a l Scandiav., Vol. 36, Suppl. 124, 1956. 41". 22. Smith, R.S., "Properties of I n t r a f u s a l Muscle F i b r e s " , Muscle Afferents  and Motor Control, ed. Granit, Noble Symposium, Wiley and Sons, New York, 1966, pp. 69-80. 23. Wilkie, D.R., "The Relationship between Force and V e l o c i t y i n Human Muscle", J. Physiology, London, Vol. 110, 1950, pp. 249-280. 24. Wilkie, D.R., "Measurement of the Series E l a s t i c Component at Various Times During a Single Muscle Twitch", J . Physiology, London, Vol. 134, 1956, pp. 527-530. 25. Wilson, V.J., "Regulation and Function of Renshaw C e l l Discharge", Muscle  Afferents arid Motor Control, ed. Granit, Nobel Symposium, Wiley and Sons, New York, 1966, pp. 317-330. 

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