Control Structure GMP

JOURNALOF NEUROPHYSIOLOGY Vol. 52, No. 5, November 1984. Prinfed

Control of Sequential Movements: Evidence for Generalized Motor Programs

M. C. CARTER AND D. C. SHAPIRO

Motor Control Laboratory, Department of KinesioZogy, University of California at Los Angeles, Los Angeles, California 90024

SUMMARY AND CONCLUSIONS

1. The neuromotor processes underlying the control of rapid sequential limb move- ments were investigated. Subjects learned to pronate and supinate their forearms rapidly to four target locations in a specific spatio- temporal pattern under two movement-time conditions. The response sequence was first performed in a total movement time of 600 ms. Subjects were then told to produce the movement as quickly as possible while ig- noring any timing pattern that they had previously learned. Electromyographic (EMG) signals were recorded from the biceps brachii and pronator teres muscles. Kinematic and EMG analyses were performed to investigate the temporal characteristics underlying the two movement-time conditions.

2. When subjects produced the response as quickly as possible, average movement time to perform each reversal movement decreased while average peak velocity in- creased. Average total movement time was reduced by - 100 ms. Although movement time decreased, the proportion of total time to perform each movement of the se- quence remained essentially invariant be- tween movement-time conditions. Similar results were obtained for velocity. The time at which peak velocity was achieved occurred earlier in absolute time, although when nor- malized to the proportion of total movement time, the time to reach peak velocity was also invariant. Thus subjects proportionally compressed the entire movement sequence in time.

3. The EMG analysis demonstrated that total EMG time decreased 89 ms on the average when subjects sped up the movement

sequence. Thus average burst durations for both the biceps and pronator teres muscles decreased when movement speed increased. When burst durations were normalized to a proportion of total EMG time, the average proportion of time each muscle was active remained invariant. Therefore, the temporal pattern of activity for the biceps and pronator teres muscles were also proportionally com- pressed.

4. The present experiment provided addi- tional evidence for the structure of generalized motor programs consisting of invariant and variant features. Movement speed was con- sidered a variant feature, which is specified each time the program is executed. Relative timing, the proportion of total time to pro- duce each segment of the response, was con- sidered to be an invariant feature and inherent in the structure of the motor program. Sup- port for the invariance of relative timing was observed at both the kinematic and neuro- muscular levels of analyses. Alternative mod- els (9-l 1, 24) were found inadequate to account for the invariance of relative timing with the variation in movement time ob- served in the present experiment.

INTRODUCTION

Early evidence from insect (39, 40), ver- tebrate (12, 35), and human (17) experimen- tation demonstrated that movements can be performed in the absence of feedback from the responding limb. To account for the central control of these movements, the no- tion of a motor program has been proposed (17). The original formulation, however, sug- gested that there exists a separate motor program in memory for each action (1, 13).

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788 M. C. CARTER AND D. C. SHAPIRO

This assumption creates two problems for the understanding of human motor control. The first is a storage problem, in which an infinite memory capacity to store each move- ment that we are capable of performing is required. The second is the novelty problem, in that a particular response, not previously learned or genetically determined, can be easily generated. As a solution to the storage and novelty problems, it has been proposed that motor programs be considered general- ized in nature (21, 25, 26).

The generalized motor program has been conceptualized as an abstract memory struc- ture composed of invariant and variant char- acteristics (25-27, 32, 33). The invariant characteristics are the fixed elements of the program, whereas the variant features allow for the flexibility in the execution of the motor response. For example, each individual possesses a unique signature pattern, presum- ably governed by a motor program. The signature program can be generated using different muscle groups, as when signing a check or writing on a blackboard; the signa- ture can be written at different speeds as well as darker or lighter by varying the force exerted on the pen. All the signature patterns, however, are similar and clearly recognizable as belonging to the particular individual. The notion of a generalized motor program sug- gests that by modifying different parameters of the motor program (e.g., force and speed) the same underlying pattern will emerge.

Kinematic evidence from a variety of movements has suggested that an invariant feature of generalized motor programs is relative timing, defined as the proportion of time to produce each segment of a movement sequence (2, 30, 3 1, 34, 36-38). Armstrong (2) observed that subjects performing a se- quential, spatiotemporal positioning task tended to extend or compress the entire movement sequence proportionally in time, although the total movement time of the sequence varied. By use of a similar task, Shapiro (30, 3 1) trained subjects either to rotate a lever in a complex spatiotemporal pattern or to select their own temporal pattern to perform the movement sequence. After training, subjects were asked to execute the entire sequence as rapidly as possible while ignoring any timing that they had learned. Regardless of whether subjects were presented

with a temporal pattern or selected their own, the proportion of time to produce each segment of the sequence remained invariant across the two movement-time conditions, although total movement time decreased. Thus relative timing appeared to be a fixed element of the movement sequence, whereas speed was a variant parameter.

An invariant temporal relationship within sequential movements has also been observed for highly skilIed actions, such as handwriting (7, 14) and typing (36, 37). Denier van der Gon and Thuring (7) manipulated the friction of a pen during a handwriting task and observed that the temporal pattern between letters remained invariant. More recently, Terzuolo and Viviani (36, 37) have demon- strated invariant time intervals between suc- cessive pairs of typed letters. Professional typists, typing several texts, exhibited constant ratios of time between sequential key presses within a word, regardless of the context of the text and of the total time to type the word, and independent of mass added to the fingers.

Thus far, the observations of relative timing have been limited to the kinematic parame- ters of the movement. It is of interest to examine whether the temporal organization of the muscles, as reflected in the neuromus- cular patterning of the EMG activity, also remains invariant when movement time var- ies. EMG analyses may provide further insight into the representation and structure of the generalized motor program and its organi- zation in the central nervous system. There- fore, the experiment examined the temporal relationship between a pair of muscles re- sponsible for generating a rapid sequential action. Preliminary results of these data have been reported previously (5, 6).

METHODS

Apparatus and task The apparatus was similar to the one used

earlier by Shapiro (30, 3 1) and consisted of a D-shaped handle connected perpendicularly to a shaft (Fig. 1). A white display board was attached to the shaft where the shaft and handle joined. Four targets were affixed to the display board at 45,70, 105, and 135 from horizontal, as measured in a counterclockwise direction. Above each target was a number indicating the order in which the targets were to be sequenced. Directly in front of

CONTROL OF SEQUENTIAL MOVEMENTS 789

Target Display \ Oscilloscope

FIG. 1. Illustration of apparatus and target display board. Template was affixed to screen of oscilloscope with angular displacement represented vertically and movement time horizontally. After each trial, response generated by subject was displayed on oscilloscope.

the target board, attached to the handle, was a pointer that was used to align the handle at the appropriate angle for each target location.

A potentiometer was attached at the opposite end of the shaft. Rotation of the handle caused simultaneous movement of the pointer and the potentiometer, and thus angular displacement of the handle could be obtained. The output of the potentiometer was displayed on a storage oscillo- scope, with time represented horizontally and displacement represented vertically. The correct movement pattern was to pronate 90 in 200 ms to target 1, then supinate 65 O in 110 ms to target 2, followed by a pronation of 35 in 130 ms to target 3, and finally supination of 60 to a metal stop in 160 ms to target 4. Thus the task was to produce a forearm response composed of four handle rotations in a total movement time of 600 ms. A template of the correct response was drawn on a clear Lucite square and placed on the oscil- loscope screen (Fig. 1). Subjects were taught to evaluate the correctness of their response after each trial using the oscilloscope by comparing their movement trace to the superimposed tem- plate. The oscilloscope was viewed by the subject only after the response was completed. Both spatial and temporal accuracy were stressed to the subjects.

Procedures The subjects were four normal right-handed

female volunteers. During testing the subjects sat

facing the targets, grasping the handle with their elbow flexed at approximately a 45 angle. The subjects elbow rested in a comfortable position on a desk top directly in front of the handle. Elbow position was maintained by having the subject place her elbow at a fixed point on the desk during the entire experiment. All subjects received three consecutive days of practice with 200 trials per day, which will be referred to as the experimental trials. For the last 10 trials of the final day of the experiment, subjects were asked to ignore the timing they had learned and to speed up the response as rapidly as possible while maintaining spatial accuracy. These trials will be referred to as the sped-up trials.

Electromyographic (EMG) activity was recorded from the right biceps brachii and pronator teres muscles using Ag-AgCl surface electrodes, 8 mm in diameter. The electrodes were placed -3-4 cm apart over the surface of the muscles. Both raw EMG and potentiometer data were recorded onto FM tape for later analysis.

Data analysis The data analysis was performed on the final

10 experimental trials and on the 10 sped-up trials for all four subjects. The potentiometer data were sampled at 1 Hz using a minicomputer (Hewlett- Packard 2 1MX). Raw displacement data were smoothed with an 1 l-point moving average and numerically differentiated by computer programs.

790 M. C. CARTER AND D. C. SHAPIRO

Handle position and movement time for each response reversal were obtained from the poten- tiometer recording, as was total movement time. Peak velocity and the time to peak velocity were obtained from the differentiated displacement record.

The raw EMG data were printed on a Grass polygraph at 400 mm/s and digitized using a Hewlett-Packard 9830 desk top computer and digitizer. Burst onset and termination were deter- mined by an increase or decrease in the signal above or below a 200% window of background activity. The base-line activity was calculated from the EMG record for each muscle, 50 ms prior to the beginning of the first burst. To be considered a burst, the signal had to exceed 50 ms in duration. Total EMG time was computed from the onset of the initial pronator teres burst to the cessation of the final biceps burst (Fig. 3).

A within-subjects design using a multivariate analysis of variance (MANOVA) procedure was employed to evaluate any changes in the subjects performance from the experimental to the sped- up trials. Response condition (experimental vs. sped-up) was considered the independent variable, whereas data from each of the four response reversals were treated as multiple dependent vari- ables. This statistical analysis was performed for both the kinematic and the EMG data.

RESULTS

Experimental trials vs. template A comparison of the subjects performance

on the last 10 experimental trials against the template indicated that subjects did not learn to reproduce accurately the spatiotemporal pattern displayed by the template. The av- erage amplitude for target I was 9 1 t 4, with average amplitudes of 72 t 5, and 42 + 5 for targets 2 and 3, respectively. Addi- - tionally, all subjects compressed the entire movement sequence in absolute time. This resulted in an average total movement time of 570 ms instead of the desired 600 ms. The greatest deviation in segmental movement time occurred at the first and second target locations, where average movement time was 135 t 16 ms for target I and 150 t 8 ms for target 2. The average deviation in seg- mental movement times from the template were considerably less for targets 3 and 4 and 122 t 12 and 164 t 22 ms, respectively.

As a result of the variation in segmental movement time on the experimental trials, the relative timing pattern between the ex- perimental trials and the template were dis-

parate (Table 1). Subjects tended to simplify the template by performing each response segment in an approximately equal propor- tion of total time. Thus subjects had difficulty, as in previous experiments (30-32), learning the spatiotemporal pattern imposed during the experimental trials. This finding may reflect the difficulty of the template. However, a more important issue was the comparison between the experimental and the sped-up trials to determine whether both movements were controlled by a common generalized motor program. Sped-up trials

Examination of the displacement data pre- sented in Fig. 2 indicated that subjects de- creased movement time between the experi- mental and sped-up conditions. Average seg- mental movement time for targets l-4 were 105 t 7, 127 t 7, 104 t 9, and 125 t 11 ms, respectively. There was a significant de- crease in movement time to each target location, (F(4,3) = 30.85 P < O.Ol), which reduced average total movement time for the entire sequence by about 100 ms. Rather than a gradual decrease in movement time when subjects sped up the response, there appeared to be an initial step decrease in movement time that remained across the 10 sped-up trials. Thus subjects were able to ignore the specific overall timing constraints they had developed during practice and pro- duce the entire response more rapidly. Ad- ditionally, there were no significant changes in peak displacement for any of the target locations when subjects increased movement speed (F(4,3) = 0.80, P > 0.05). Peak dis- placements for the experimental and sped- up trials were, respectively, 91 t 5 and 95 t 5 for target I, 72 t 5 and 75 t 5 for target 2, and 42 t 5 and 43 t 6 for tar- get 3.

To examine whether the movement pro- duced on the sped-up trials demonstrated the same timing characteristics as the experimen- tal trials, the percent of total time to achieve each target location was calculated from the kinematic data, and a comparison was made between the experimental and sped-up trials (Table 1). A MANOVA computed on the proportional data indicated no significant difference in the percent of time to produce each response reversal between the two con- ditions (F(4,3) = 1.11 P > 0.05). Therefore,

CONTROL OF SEQUENTIAL MOVEMENTS 791

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-EXPERIMENTAL TRIALS

---SPED-UP TRIALS

0 100 200 300 400 500 600

MOVEMENT TIME (ms)

FIG. 2. Average angular displacement and movement-time data plotted for experimental (solid line) and sped- up (dotted line) trials. Lines connecting each pattern are for illustration only. *Spatiotemporal locations of each target location from template.

relative timing was maintained when subjects increased movement speed; this is consistent with previous investigations (27, 28). Fur- thermore, although the spatiotemporal pat- terns produced on the experimental and sped- up trials were disparate from the template, subjects generated movements with the same relative timing patterns on the two move- ment-time conditions (Table 1).

Peak velocity for each segment of the movement patterns increased when move- ment speed increased, whereas the absolute

TABLE 1. Percent of total time for template, experimental, and sped-up trials for each target location*

Experimental Sped-up Template, % Trials, % Trials, %

Target 1 33 24 (3) 23 (1) Target 2 18 26 (2) 29 (2) Target 3 22 22 (3 23 (2) Target 4 26 29 (3) 27 (2)

* Values are within-subject means (k SD).

time at which peak velocity was reached occurred earlier (Table 2). To examine whether time to peak velocity was also scaled proportionally when movement speed in- creased, the percent of total time to achieve peak velocity for each response segment was calculated. As can be seen from Table 2, there were no differences between the exper- imental and sped-up conditions in the pro- portion of time taken to reach peak velocity for each response segment (F(4,3) = 0.43, P > 0.05). Both the proportion of time to produce each response reversal and the pro- portion of time to reach peak velocity re- mained invariant with changes in overall movement speed. Thus subjects compressed the entire movement sequence as a unit, such that the temporal structure of the action was maintained between the two movement- time conditions.

EiWG analysis

Typical raw EMG records are displayed in Fig. 3 for the experimental (A) and sped-up trials (B). The first pronator teres burst (PTl)

792 M. C. CARTER AND D. C. SHAPIRO

TABLE 2. Average peak velocity, time to peak velocity, and percent of time to peak velocity for experimental and sped-up trials*

Average Time to Peak Proportion of Time to Peak Average Peak Velocity, O/s Velocity, ms Velocity, %

Experimental Sped-up Experimental Sped-up Experimental Sped-up

Target 1 1,232 (98) 1,419 (93) 78 (6) 63 (7) 48 (4) 49 (4) Target 2 925 (80) 1,131 (129) 78 (15) 63 (14) 58 (3) 57 (6) Target 3 740 ( 102) 923 (106) 48 (9) 37 (6) 38 (4) 36 (6) Target 4 785 (87) 1,005 (141) 73 (13) 58 (14) 42 (6) 46 (6)

* Values are within-subject means (* SD).

initiated the movement, which was followed by biceps activity (B,), a second pronator teres burst (PT& and finally biceps activity (B2), which completed the movement se- quence. Occasionally, tonic biceps activity was observed after B2 as subjects maintained the forearm in a supinated position, awaiting the start of the next trial. An examination of the EMG activity indicated that the bursts were completed prior to the achievement of each target location. Additionally, there was slight cocontraction between the pronator teres and biceps muscles at the onset and cessation of the bursts. For some subjects, there was also EMG activity during the pro- nator teres interburst interval when it would be expected that the muscle would be silent. Since the forearm is supinating, the activity

is probably due to the involvement of the supinator muscle. The supinator muscle is in close anatomical proximity to the pronator teres muscle and difficult to avoid with the use of surface electrodes.

A comparison of total EMG time between the two movement-time conditions indicated average total EMG time decreased from 6 10 + 39 ms on the experimental trials to 521 I 34 ms on the sped-up trials. Additionally, average burst durations for the pronator teres muscle decreased between the experimental and sped-up conditions (Table 3). Burst du- rations for the biceps muscle also decreased when subjects increased movement speed (Table 3). However, the average decrease in burst duration for B1 at target 2 was not as great as for other target locations. Perhaps,

FIG. 3. Raw EMG (pronator teres: top trace, biceps: middle trace) and displacement (bottom trace) from experimental (A) and sped-up (B) trials for one subject for a single trial in each condition. Burst durations were calculated for both muscles (B,, Bz, PT,, PTz) on each trial, as was total EMG time from onset of PTi to cessation of BZ.

CONTROL OF SEQUENTIAL MOVEMENTS 793

TABLE 3. Average burst durations and percent of total EMG time for experimental and sped-up trials*

Average Burst Percent Total Durations, ms EMG Time, %

Experi- Experi- mental Sped-up mental Sped-up

PTI 171 (19) 144 (19) 28 (3 28 (4) B, 116 (13) 102 (14) 19 (2) 20 (3) PT2 126 (9) 120 (10) 20 (3) 23 (3) B2 169 (13) 151 (14) 27 (4) 28 (4)

* Values are within-subject means (t- SD).

the biceps muscle was already near its me- chanical limit on the experimental trials; this resulted in only a slight decrease in burst duration when movement velocity increased.

To examine the relative timing of the muscular activity, the proportion of time that each burst was active was calculated as a function of total EMG time for both condi- tions. As can be observed from Table 3, there were slight variations in the percent of time that the biceps and pronator teres mus- cles were active between the experimental and sped-up conditions. However, the differ- ences were nonsignificant (F(4,3) = 0.89, P > 0.05). The relative time each muscle was active remained essentially invariant, al- though the actual burst durations changed when movement velocity increased. There- fore, relative timing was also reflected in the EMG activity underlying the action.

DISCUSSION

Previous evidence suggested that sequential movements were governed by generalized motor programs consisting of relative timing as a fixed element of the motor program and overall movement time as a variant feature (2, 30, 3 1, 36, 37). Support for the invariance of relative timing was based on the observa- tion that the spatiotemporal pattern generated during execution of the movement was either compressed or extended in time, such that the proportion of total time to produce each segment of the action remained invariant. The present study confirmed these findings in that the relative time to achieve each target location, as well as the proportion of total

EMG time that each muscle was active re- mained invariant across movement-speed conditions. These findings were also apparent, even though subjects were told to ignore any timing that they had previously learned and to perform the sequence as rapidly as possible (3 1, 32). Thus the constancy of the temporal pattern within a given motor program was reflected not only in the kinematic description of the movement, but also in the nqttem of .=a- Y- EMG activity responsible for produc :ing the action. The invariances observed in the ki- nematics and the neuromuscular activity are inherent features of the motor program.

The significance of constant relative timing is not only confined to the generalized motor program notion but is also predicted by MacKay (20) in a theory of representation and enactment of intention. Further support for relative timing has been demonstrated when examining locomotion (34). A temporal pattern analysis of the lower limb kinematics of human subjects walking (3-6 km/h) and running (8- 12 km/h) at a limited range of speeds on a treadmill indicated that within a gait mode (walking or running), the propor- tion of total time to execute each phase of the Philippson (22) step cycle remained in- variant (34). Additionally, examination of temporal coordination in speech demon- strated that although speech stress and rate varied, the timing of consonant articulation was invariant in relation to the accompanying vowel articulation (38). Constant relative timing was also present in the duration of consonant-related muscle activity. Therefore, evidence from a variety of motor actions provides support for the invariance of relative timing in the generalized motor program.

Alternative models (9, 10, 23, 24) of limb control cannot explain how the temporal patterns observed in sequential arm move- ments are specified by the motor program. The equilibrium-point model (3, 23, 24) stresses the importance of the mechanical properties suggests tl rium poin positioned defined as the joint, and exterr

of muscle rat the spe t determin in space.

a position generated

Ial forces, To achieve an intended 1 imb position, a given level of excitation is specified to one

:s on limb con trol and cification of an equilib- les where a liml 3 will be An equilibrium point is where the torqu .es about by antagonist muscles

are equal and ( Ipposite.

794 M. C. CARTER AND D. C. SHAPIRO

or both of the opposing muscles (19), and there is a gradual shift in the equilibrium point until the final equilibrium position is achieved (4). The specific control of move- ment time is not critical to this model and is not specified. Therefore, the equilibrium- point model would not predict that relative timing within a movement sequence would be invariant while overall movement time would vary.

Evidence for the equilibrium-point view of motor control is based on experiments examining the achievement of arm position to a single target in both normal and rhizoto- mized monkeys (23, 24). In these experi- ments, monkeys positioned their forelimbs to different targets, regardless of initial short- duration perturbations to the elbow joint. Recently, experiments examining rapid limb positioning performed by human subjects have provided further support for the equi- librium-point model (16, 27, 29). Subjects were trained to position their limb to a target in a specified movement time. Before at- tempting to position their limb, a mass was unexpectedly added to the lever, which changed the inertial load (27, 29). Although subjects accurately positioned their limb to the targets, the prescribed movement time was not maintained. Additionally, Kelso and Holt (16) functionally deafferented their sub- jects with a pressure cuff and observed that target accuracy was maintained while brief torque pulses were applied to the index finger at different times during a movement to a target.

Support for the equilibrium-point model demonstrated the attainment of endpoint accuracy in single positioning movements when subjects produced a single flexion or extension movement of the limb, with or without movement time constraints. Inter- estingly, this finding was not evident when the limb was required to reverse direction at a target and the time to the reversal point or target location was also specified (27). For example, when mass was unexpectedly added or subtracted to the lever before a rapid flexion-extension reversal movement was ini- tiated, the movement time of the response remained invariant, whereas the reversaI point shifted according to the load (27). Subjects overshot the endpoint when mass was sub- tracted and undershot when mass was added.

Thus movement time remained constant while endpoint accuracy varied, indicating a different style of control than that utilized for unidirectional positioning movements.

The pulse-step model of limb control pro- posed by Ghez ( 10, 11) suggests that limb position is achieved by an initial force pulse of varied amplitude followed by a step force to maintain the limb at the target. The model predicts that the height of the control pulse varies to achieve different target locations, whereas time to peak force as well as the time to peak dF/dt are constant. The ampli- tudes of the EMG burst underlying the force pulse also vary, with EMG burst duration remaining constant. The advantage of the pulse-step model is that different distances can be achieved by an initial pulse modulated in amplitude but not in duration, simplifying the number of variables that the nervous system needs to control. Studies examining cats performing isometric contractions (11) and isotonic tracking responses ( 10) con- firmed these predictions. It is important to note that in the latter studies a criterion time to achieve the targets was not specified and it appeared from the data that, regardless of movement amplitude, movement time re- mained constant.

The speed control system proposed by Freund and Biidingen (9) is similar to the pulse-step model (10). The speed control model predicts that movements of different extents or isometric contractions of different intensities are controlled by varying the am- plitude of the contractions while keeping the duration of the contractions invariant. Thus changes in force requirements are accom- plished by regulating only the single param- eter of intensity and this is reflected in both the EMG and force activity. Freund and Biidingens model is based on humans per- forming both isometric and isotonic experi- mental conditions. In terms of the isotonic condition, the condition most similar to the present experiment, the subjects task was to move to several movement angles as fast as possible. Under these specifications, subjects tended to keep the movement time to the different target locations constant. The results demonstrated that both EMG and time to peak force were constant while the intensities of these two variables were modulated ac- cording to the distances moved.

CONTROL OF SEQUENTIAL MOVEMENTS 795

Lestienne ( 18) reported similar constant agonist burst durations when movement ve- locity was manipulated during a limb posi- tioning task. The invariance of the initial agonist burst was demonstrated only when peak velocities exceeded 3 rad l s-l. At lower velocities, there appeared to be proportional scaling of agonist duration with velocity. Therefore, support for the speed-control model was restricted to the high-velocity responses examined. Furthermore, Lestienne reported that there was a constant ratio be- tween the duration of the agonist burst and the duration of the transport phase, regardless of peak velocity (Ref. 18, p. 413). It is unclear, however, how this ratio remained invariant when presumably transport dura- tion varied as subjects changed movement speed. Perhaps the mixed results obtained for agonist burst duration resulted because movement time was not strictly controlled. Similarly, mixed support for the speed control model was found for the initial two compo- nents of a sequential weight-lifting task with changes in load (8). For the first component of the lift, a constant extensor muscle torque duration was reported when load varied. However, the duration of the flexor muscle torque, required in the second component, varied with load and with level of expertise among lifters. The less skilled athletes de- creased flexor torque duration, whereas the more experienced weight lifters increased the duration. Perhaps the differences between extensor and flexor muscle torque duration were due to variations in the actual move- ment time to perform each component. If movement time of the first phase was con- stant, it would be predicted that extensor duration would also be constant (28). If, however, movement time varied during the

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second segment, changes in flexor torque duration would be expected.

The pulse-step (10) and speed-control (9) models predict that when movement ampli- tude varies, EMG amplitude will also vary, yet EMG duration will remain constant. The generalized motor program view would also predict constancy in the EMG and force durations in conditions where movement time remains constant. However, in the pres- ent experiment the task is different, since movement time decreased between the ex- perimental and sped-up trials while move- ment amplitude remained constant. Neither the pulse-step (lo), speed-control (9), nor equilibrium-point (23, 24) models make any specific reference to conditions where move- ment time changes. The generalized motor program view, however, would predict pro- portional changes in burst duration as move- ment time varies. The present data indeed support the generalized motor program no- tion, since burst duration varied proportion- ally with movement time. In addition, timing and sequencing appear to be tightly coupled components of a movement sequence.

ACKNOWLEDGMENTS

We thank Drs. R. A. Schmidt and J. L. Smith for their thoughtful and critical reviews of an earlier version of the manuscript and the reviewers for their helpful comments. We also thank S. A. Spector for his assistance during the initial stages of the project and C. L. Hager and V. P. Stoakes for their technical expertise in electronic design and computer analysis.

This work has been supported by a grant from the Bureau of Education for the Handicapped (GOO7700997) to M. C. Carter and D. C. Shapiro and by a UCLA Academic Senate Grant and a USPHS Biomedical Re- search Grant to D. C. Shapiro.

Received 4 October 1982; accepted in final form 12 June 1984.

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