Experimental BrainResearch

Exp Brain Res (1988) 69:355-367

9 Springer-Verlag 1988

Rapid movements with reversals in direction II. Control of movement amplitude and inertial load

D.E. Sherwood, R.A. Schmidt, and C.B. Walter Motor Control Laboratory, Department of Kinesiology, University of California, Los Angeles, CA 90024, USA

Summary. Transformations of the underlying movement control of rapid sequential (reversal) responses were examined as the movement amplitude (Experiment 1) and moment of inertia (Experiment 2) were altered, with constant movement time. Increases in amplitude and inertia were both met by sharply increased joint torques with a constant temporal structure, suggesting that the alterations may have been governed by a single gain parameter. The durations of various EMG bursts were essentially constant across changes in inertia, supporting a model in which the output of a fixed temporal representation is amplified to alter joint torques. The EMG amplitudes increased greatly with both amplitude and load. However, the fact that the EMG durations increased systematically with increases in distance provided difficulties for this model of amplitude control. The data suggest an economy in motor control in simple agravitational movements, whereby relatively simple transformations of an underlying representation can accomodate large changes in movement amplitude and moment of inertia. Key words: Rapid arm movements - Motor programs

Introduction

This article is the second in a series of studies (see Schmidt et al. 1987) dealing with the general problem of how rapid limb movements can be produced slightly differently on different occasions, and yet retain some fundamental characteristic pattern. For example, with handwriting large changes in speed or amplitude can be accomplished with little alteration in form, even across changes in the muscles or joints used (e.g., Hollerbach 1981; Merton 1972; Raibert Offprint requests to: R.A. Schmidt (address see above)

1977). These findings suggest a representation more abstract than the level of individual muscles and joints, and which can be activated to produce many separate movements with identical form, but with different "surface" features (e.g., size, speed, etc.). If so, this suggests an economy in movement control, whereby each of the actions does not have to be separately represented. With this focus, several investigators have asked whether relatively simple variations in the kinematic, kinetic, and electromyographic (EMG) patterning in rapid actions could accomodate changes in these various "surface" features. Movement time (MT) has been a particularly important variable (Gentner 1987; Gielen et al. 1985; Lestienne 1979; Schmidt et al. 1987; Shapiro and Walter 1986), studied in quick movements where other kinematic properties such as distance and load are held experimentally constant. When MT is decreased, in addition to the wellknown increase in EMG amplitudes to generate the increased torques required, a rather uniform temporal "compression" of the acceleration- and EMGtime functions was produced. Such findings, together with others (e.g., Schmidt 1987), suggest that changes in MT do not simply emerge from the torque (or velocity) variations, but rather are one of the controlled variables in rapid, programmed actions. The present experiments extended this search for relatively simple modifications in movement control to accomplish various environmental goals. Here, we examined two other common movement variables movement amplitude (Experiment 1) and inertial loading (Experiment 2) - seen in many every-day situations, such as reaching for objects at various distances or swinging baseball bats of varying weights. In the first experiment, we followed the lead of several earlier studies which manipulated movement distance in (usually) maximal-speed movements (e.g., Berardelli et al. 1984; Benecke et al.

356 1985; B r o w n a n d C o o k e 1981, 1984; C o o k e et al. 1985; F r e u n d a n d B u d i n g e n 1978; G h e z 1979; G h e z and Vicario 1978; H a l l e t t a n d M a r s d e n 1979; W a d m a n et al. 1979). H e r e i n c r e a s e d m o v e m e n t distance p r o d u c e d systematic increases in the a m p l i t u d e s of E M G activities to a c c o m o d a t e the i n c r e a s e d t o r q u e r e q u i r e m e n t s , b u t with negligible changes in the t e m p o r a l structure. W i t h respect to these temporal findings, h o w e v e r , these earlier studies have h a d the difficulty that M T was n o t usually controlled. O t h e r investigators (e.g., Flowers 1976) have s h o w n that v a r i a t i o n s in m o v e m e n t a m p l i t u d e are usually a c c o m p a n i e d by small changes in M T (e.g., a d o u b l i n g of m o v e m e n t a m p l i t u d e m a y result in a 10% c h a n g e in M T ) . Also it is n o w k n o w n that, e v e n with a m p l i t u d e held constant, variations in M T p e r se can have systematic effects o n the t e m p o r a l p a t t e r n of a c c e l e r a t i o n - t i m e a n d E M G - t i m e f u n c t i o n s ( G i e l e n et al. 1985; Schmidt et al. 1987). T h e r e f o r e , if in the earlier studies the t e m p o r a l s t r u c t u r e of the E M G p a t t e r n were affected by m o v e m e n t a m p l i t u d e , the effect o n the E M G s could have b e e n c o n t a m i n a t e d , or e v e n nullified, by c o n c o m i t a n t changes in M T . H o w e v e r , a few r e c e n t studies have e x a m i n e d m o v e m e n t a m p l i t u d e effects in simple tasks, while holding M T strictly c o n s t a n t (e.g., G i e l e n et al. 1985; Shapiro a n d W a l t e r 1986; W a l l a c e a n d W r i g h t 1981). H e r e , particularly in the G i e l e n et al. studies, w h e n M T was held c o n s t a n t , increases in m o v e m e n t a m p l i t u d e were a c c o m p l i s h e d by increases in the a m p l i t u d e s of the acceleration- a n d E M G - t i m e functions, with n o changes in the t e m p o r a l structure. T h e p r e s e n t e x p e r i m e n t s e x t e n d these earlier findings to a s o m e w h a t m o r e " c o m p l e x " m o v e m e n t , in which a reversal in direction is r e q u i r e d , e n a b l i n g the evaluation of these p h e n o m e n a in situations w h e r e m o v e m e n t timing, s e q u e n c i n g , a n d c o o r d i n a t i o n is e m p h a s i z e d s o m e w h a t m o r e strongly t h a n in the earlier u n i d i r e c t i o n a l m o v e m e n t s .

Experiment 1 The first e x p e r i m e n t e x a m i n e d p a t t e r n i n g in a rapid reversal m o v e m e n t as the goal m o v e m e n t a m p l i t u d e was varied e x p e r i m e n t a l l y . M T a n d o t h e r features of the situation were held c o n s t a n t .

Methods Subjects Four right-handed males, whose ages ranged from 23 to 42 years, participated. Three were the present authors, and all had received considerable experience in this task, and in tasks with controlled MT.

Apparatus The equipment used was nearly identical to that in Schmidt et al. (1987). Briefly, a horizontal aluminum lever, supported by a vertical axle free to rotate in ball bearings, was used. A vertical bandgrip was attached 35 cm from the axle, and a plywood shield covered the apparatus to prevent the subject from seeing it. A potentiometer was attached to the axle to record movement position, whose output was delivered to a PDP 11/23 laboratory computer (sampling frequency = 500 Hz) and to a Vetter 8channel analog FM tape recorder for backup.

Task As before, a rapid reversal response was used. The seated subject began with the right hand gripping the handle, with the elbow flexed 60~ (0~ being full extension), and the shoulder horizontally flexed 10~. The upper arm was horizontal. On command from the experimenter, the subject flexed the elbow toward an unseen target varying distances away (in different conditions), then reversed direction and followed through past the original starting position. The time from the initial flexion movement until the reversal point was to be 175 ms, controlled by instructions and feedback after each trial. After the movement, a position-time trace of the justproduced movement was fed back to a terminal visible only to the experimenter. A small box was displayed, whose size and position were adjusted to represent +10% of the goal movement distance and +10% of the goal time to reversal point (175 ms). A movement whose reversal point fell inside this box was considered to be correct, and no statement to the subject was provided unless the movement exceeded either the temporal or spatial boundaries. The intertrial was approximately 10 s.

Procedures EMG activities were recorded with Ag/AgC1 electrodes (8 mm diam.) placed with adhesive collars and electrode paste over the bellies of the lateral head of the triceps and the medial head of the biceps muscles. Resistances were always less than 8 k~. Signals were amplified (Grass Model 7P3 and 7DA), with high- and lowpass filters set a 10 and 10 kHz, respectively. These signals were digitized at 500 Hz by a DEC 11/23 laboratory computer, and also stored on analog FM tape. Six movement amplitudes were used, representing 20~, 30~, 40% 50~ 60~ and 70~ from the starting position to the reversal point, while the MT was held constant. Unlike the situation in Schmidt et al. (1987), all of these conditions were clearly submaximal. All subjects produced 50 trials of each movement distance in a separately randomized order in a single session. Before each condition, 25 practice trials were provided.

Data analysis EMG records were rectified digitally, and low-pass filtered (cutoff frequency = 80 Hz) with a rectangular filter. A Butterworth filter (cutoff frequency = 16 Hz) was applied to the position-time records, which were then differentiated twice to generate the acceleration-time functions. Rectified EMG records for single trials were scored using interactive graphics, where the amplitudes and times of various features were digitized with an accuracy of + 2 ms (see Schmidt et al. 1987; Walter 1984). The duration of the biceps burst, its peak amplitude and area, as well as the interval from biceps onset to the peak triceps burst, were measured on Trials 3-48 of each amplitude condition.

357

Results

Kinematic analyses An important first concern was the kinematic evidence that subjects followed the movement amplitude and MT instructions. Figure 1 contains the averaged (using 46 trials) position-time traces for a single subject for each of the movement amplitude conditions. (All subjects showed the same general trends.) Generally, each of the required movement amplitudes was produced in nearly the same MT, the functions appeared to be nearly symmetrical about the reversal points, and there was no tendency for a sustained stop at the reversal point before producing the second half of the response. The times to reversal varied slightly among conditions, but there was no systematic tendency for the times to reversal to change with movement amplitude. The averaged reversal points computed on individual trials and the times to reversal (together with their within-subject SDs) are shown in Table 1, and confirm the subjective findings in Fig. 1. The average movement amplitudes were very close to their respective goals, with the largest deviation between the mean and the goal being 1.2 ~ in the 50~ condition. There was no systematic effect of movement distance on this constant error, F (5,15) < 1. During the amplitude manipulation subjects produced MTs which were very close to their 175-ms goal (Table 1), with the largest deviation from the goal being 8 ms in the 20~ condition, with the average MT being slightly too short (mean error = 3.6 ms). There was no significant effect of amplitude on mean MT, F(5,15) = 1.2, p > 0.05. Overall, the subjects were able to follow the MT and amplitude instructions very well, varying the movement amplitude with no corresponding shifts in MT.

Acceleration-time functions Figure 2 contains the averaged acceleration-time functions for one subject for the six amplitude conditions, and across-subjects averages of various measures from individual trials are shown in Table 1. The amplitude of peak acceleration increased strongly with movement amplitude, varying systematically from 2871 to 9407 deg/s 2, which was significant with F(5,15) = 81.6, p < 0.05. The SD of peak acceleration tended to increase with its amplitude, but there was a general leveling off of the SD at the larger amplitudes; this effect was significant, with F(5,15) = 5.8, p < 0.05. While the accelerations were increasing in

100

ms

Fig. 1. Average position-time records (46 trials/trace) for a single subject in the six movement distance conditions in Experiment 1; times to the reversal point were approximately constant as the goal reversal point increased from 20 ~ to 70 ~

amplitude across changes in movement distance, there appeared to be nearly no change in the temporal structure, with the time to peak acceleration and the duration of positive acceleration being nearly identical for the various conditions. There were small unsystematic changes in mean time to peak acceleration (ranging from 75.2 ms to 79.9 ms) and in the mean duration of positive acceleration (ranging from 138.9 to 143.6 ms), neither of which was significant, with F(5,15) = 1.6, and 0.6, p > 0.05. The within-subject SDs of the time to peak acceleration did not vary significantly with amplitude [F(5,15) = 1.6, p > 0.05], but the SD of the duration of acceleration decreased uniformly as the amplitude was increased, significant with F(5,15) -- 3.3, p < 0.05. These results suggest that the control strategy used here maintained the temporal structure of the acceleration-time patterns while varying its amplitude to meet the movement distance requirements. The variability of the amplitude of the acceleration-time functions increased, while the variability of the temporal structure decreased, with increased movement distance. This general pattern of results, where changes in average movement velocity (MT constant) are accomplished by modulating only the amplitude of acceleration, differed markedly from the pattern found in our earlier experiment (Schmidt et al. 1987) in which MT was varied systematically with a constant movement amplitude. In that situation, the temporal structure of the acceleration-time traces increased with increasing MT (i.e., with decreased velocity). The results taken together suggest that the control of movement velocity depends on whether or not MT is held constant. When velocity is varied by changing the MT with distance constant (Schmidt et

358 Table 1. Average kinematic features as a function of the movement amplitude conditions (Experiment 1) 20

30

20.5 (1.6) 167.1 (17.2) 2871 (495) 75.3 (12.2) 138.9 (14.5)

30.9 (1.8) 169.6 (13.1) 4348 (586) 75.2 (12.4) 138.0 (13.4)

Movement amplitude condition (degrees) 40 50

60

70

60.4 (2.2) 174.8 (13.0) 8278 (793) 75.5 (10.8) 143.6 (12.1)

69.7 (2.7) 173.3 (14.2) 9407 (864) 72.8 (9.2) 140.3 (10.4)

J

Reversal point (in degrees) Time to reversal (in ms) Peak acceleration (in deg/s2) Time to peak positive acceleration (in ms) Duration of positive acceleration (in ms)

40.5 (2.0) 170.6 (12.4) 5787 (691) 79.9 (9.8) 143.6 (12.5)

51.2 (2.0) 173.2 (13.8) 7293 (822) 77.8 (11.1) 142.8 (12.8)

Summary data are based on 46 responses (Trials 3-48). Averaged within-subject SDs are given in parentheses, where the SD of the reversal position is Wc and the SD of the reversal time is VEt

al. 1987), the temporal structure and the amplitude of the acceleration pattern are altered; but when the velocity is varied by changing the movement amplitude with a constant MT (as in the present experiment), only the amplitude appears to vary, with the temporal structure remaining essentially constant.

%

EMG patterning

o 0 0 0

Fig. 2. Average acceleration-time records (46 trials/trace) obtained from twice differentiating the traces in Fig. 1; the traces are ordered in amplitude according to movement amplitude

1 0 0 ms

Fig. 3. Position-time (upper) and EMG records from the biceps (center) and triceps (lower) muscles from a single typical trial (50~ condition) in Experiment 1; a small cocontraction of triceps with biceps can be seen, but the major antagonist activities responsible for the reversal occur approximately 150 ms later

Figure 3 contains a position-time and EMG-time records from the biceps and triceps, taken from a typical trial in the 50~ condition. The reversal movements were characterized by a biceps burst with rather abrupt on- and offsets, making the biceps EMG durations particularly easy to measure. The second biceps burst served mainly to slow the limb as it passed the starting point again, and is not under consideration here. The triceps activity appeared to be initiated nearly simultaneously with the biceps, with the degree of cocontraction increasing with movement distance. However, the major burst of the triceps, occurring about halfway through the movement after the onset of the biceps burst, appeared to be primarily responsible.for the reversal in direction. Figure 4 contains the averaged rectified EMG traces (46 trials) from the biceps and triceps traces for. each of the six movement distance conditions for one subject. As distance increased, the biceps EMG traces increased sharply in amplitude and area; this was accompanied by a somewhat smaller increase in the triceps activities, both in terms of the major triceps burst, but also in terms of the amplitude of the initial cocontraction with the biceps. These cocontractions have been found previously in rapid positioning tasks (Lestienne 1979) and in reversal responses (Schmidt et al. 1987), but their function is

359 not clear 1. For each of the subjects' average traces, the biceps burst amplitude appeared to change almost proportionally with movement distance, with the initial slopes of the traces being generally equal before the peak amplitude was neared. Also, the duration of the biceps E M G appeared to increase with movement amplitude, and a very weak trend for a delayed triceps peak with increased distance could be seen in some subjects.

EMG amplitudes These general observations were examined more carefully by taking measurements from the rectified EMG traces for each trial separately, summarized in Table 2. As the movement distance increased, the increased torque requirements produced an approximately 2.2-fold increase in the biceps E M G amplitude, which was significant with F(5,15) = 16.6, p < 0.05. The average within-subject SD of peak biceps E M G also increased over the same range, but was not significant with F(5,15) = 2.2, p > 0.05. The area of the biceps E M G burst increased nearly 3-fold across the changes in amplitude, significant with F(5,15) = 18.8, p < 0.05, and the within-subject SD of biceps E M G area more than doubled across this range, F(5,15) = 6.2, p < 0.05. Whereas 130% increases in the peak triceps activity were found, F(5,15) = 3.6, p < 0.05, somewhat surprisingly these increases in triceps amplitude were not paralleled by its within-subject SDs as was the case for the biceps EMGs, F(5,15) < 1. Overall, as the movement amplitude requirement (and, hence, torques) was increased, it was not surprising that marked increases in the E M G amplitudes were found for two participating muscles, with somewhat larger percentage changes for the agonist than for the antagonist. As distance increased, the agonist E M G variabilities increased slightly (but not significantly) but the antagonist variability remained essentially constant.

EMG temporal structure. Along with these modulations of E M G amplitude with increased movement distance, changes in the temporal structure of the EMGs can also be seen from Table 2. The biceps E M G duration increased with movement distance (29 ms, or 19%), which was significant with F(5,15) = 14.6, p < 0.05. There was some tendency for the within-subject SD of biceps duration to decrease slightly, primarily between 20 ~ and 30 ~, but this effect 1 We cannot rule out the possibility in these data that this cocontraction is simply "crosstalk" between the biceps and triceps recording sites

Fig. 4. Averaged (46 trials/trace) rectified EMG traces (arbitrary units) for biceps (upper) and triceps (lower) musclesfrom a single subject in the six conditions of Experiment 1; the increased movement distances produced systematicallyincreased agonist and antagonistEMG amplitudeswith small shiftsin timing (arrow indicates movementonset)

was not significant, F(5,15) = 1.3, p > 0.05. Measures of the duration of triceps activities were more difficult to achieve, due to the early cocontraction of the biceps onset to the peak triceps (see also Schmidt et al. 1987). This interval, on the average, increased slightly (8 ms, or 4%) with increasing movement distance, but this effect was not significant, F(5,15) < 1. The within-subject SD of this variable increased slightly (10%) at the same time, and the effect achieved borderline significance, with F(5,15) = 2.8, p < 0.06. Overall, the duration of the agonist E M G bursts increased slightly as movement distance increased, but the timing of the triceps EMG, at least as we measured it here, was not affected by movement amplitude. This systematic (but small) shift in agonist E M G duration with increased velocity represents a pattern of findings somewhat different from earlier studies of amplitude effects on E M G patterns (Brown and Cooke 1981; Freund and Budingen 1978; Ghez 1979; Ghez and Vicario 1978; Hallett and Marsden 1979; Wadman et al. 1979), where essentially constantduration E M G bursts with changes in amplitude have been reported. One possible reason for this discrepancy is that we used reversal movements here, whereas the studies just cited have involved unidirec-

360 Table 2. Average EMG amplitudes, burst durations, and areas as a function of the movement amplitude conditions (Experiment 1) 20 Peak biceps EMG (in arbitrary units) Biceps EMG area (in arbitrary units) Peak triceps EMG (in arbitrary units) Biceps EMG duration (in ms) Biceps EMG onset to peak triceps (in ms)

0.35 (0.14) 11.6 (3.8) 0.33 (0.09) 149.5 (19.5) 209.6 (33.2)

30

Movement amplitude condition (degrees) 40 50 60

0.52 (0.14) 17.8 (4.2) 0.54 (0.09) 155.0 (15.7) 210.7 (41.6)

0.69 (0.18) 24.6 (6.1) 0.63 (0.10) 160.9 (14.7) 214.3 (21.0)

0.78 (0.21) 29.2 (6.2) 0.68 (0.08) 167.4 (15.4) 218.0 (28.7)

0.90 (0.19) 35.2 (6.7) 0.71 (0.09) 173.5 (15.0) 224.4 (27.5)

70 1.13 (0.23) 45.3 (8.4) 0.78 (0.10) 177.8 (14.7) 217.8 (36.6)

Means are averaged across Trials 3-48 for each subject. Average within-subjectSDs are in parentheses tional positioning movements; this hypothesis is unlikely, however, in view of the fact that Shapiro and Walter (1986), Benecke et al. (1985) and Berardelli et al. (1984) all found lengthened biceps EMG bursts with increased movement amplitude in positioning movements. A more likely hypothesis (Gielen et al. 1985) is that the earlier studies have used maximal-speed movements, whereas the present study (also Gielen et al. 1985; Shapiro and Walter 1986) have used submaximal responses with MT controlled. Gielen et al. (1985) compared both kinds of responses formally for unidirectional actions, and our findings support their viewpoint very well. Finally, our results [also Gielen et al. (1985) and Shapiro and Walter (1986)] showing that increased movement amplitude increases biceps E M G burst durations even with controlled MTs, contradict one version of the generalized motor program view (Schmidt 1976, 1987; Wallace 1981), which holds that the temporal E M G structure of movements with constant MTs should not change with changes in amplitude. The argument cannot b e made that the changes in E M G duration were due to concomitant shifts in MT, or of time to peak acceleration, as these variables were held strictly constant in our procedure. It appears that the simple version of the generalized motor program hypothesis, which holds that E M G burst durations scale only with MT, is in need of revision, at least for the rapid tasks studied here.

Speed-accuracy trade-off effects.

Whereas the average reversal point corresponded well to the experimenter-imposed goals, the variability (within-subjects SDs) of the reversal point increased sharply (about 41%, see Table 1) across the movement amplitudes, which was significant with F(5,15) = 7.1, p < 0.05. This finding of increased movement

inconsistency (often called We, or "effective target width") with increasing movement distance coincides with many other studies showing this speed-accuracy trade-off effect (see Schmidt et al. 1979). However, with the MT controlled at close to 175 ms, the temporal variability of the movements remained nearly constant (Table 1). The average within-subject SD of time to reversal ("variable error in timing", or VEt) showed almost no variation with movement amplitude, except perhaps for the slight decrease from the 20 ~ to the 30 ~ condition, and was not significant, F(5,15) < 1. This (nonsignificant) tendency for decreased timing error with increased velocity is similar to effects found by Newell et al. (1980) using simpler tasks. But the major finding of large effects of movement distance on spatial accuracy, with small effects on temporal accuracy, is consistent with various models of impulse variability (Meyer et al. 1982; Schmidt et al. 1979).

Discussion

The finding that the time to peak acceleration and the duration of positive acceleration remained essentially fixed across the three-fold increases in movement distance suggests that, when MT is held constant, changes in amplitude can be accomplished by scaling of accelerations under a constant temporal structure. Thus, the increases in velocity here were produced in an entirely different way than they were in our earlier experiment (Schmidt et al. 1987); there, when MT was varied (with distance constant) the durations of various phases of acceleration were directly related to MT. Thus, an important point from these two experiments is that the control of movement velocity depends on how velocity is altered experimentally (MT constant, or MT varied).

361 Data from Fig. 2 and Table 1 give the impression that acceleration is roughly proportional to movement distance. Thus, the changes in motor control to achieve changes in distance could be relatively simple. At first glance, however, this possibility for motor control seems unlikely, as a proportionality between acceleration and distance would seem to be possible only in the case of constant accelerations. However, in the context of our work on speedaccuracy trade-off effects in aiming tasks (Schmidt et al. 1979, 1985), we have been able to derive that distance should be proportional to average acceleration if the added assumption is made that the mathematical form (or "shape") of a prototypical acceleration-time functions remains constant as its amplitude is increased (see the appendix in Schmidt et al. [1985], or Leikind [1985], for the proof). No detailed analysis of this "shape-constancy assumption" was attempted here, but an examination of the acceleration-time functions seen in Fig. 2 shows that this assumption is at least not seriously violated. If so, then these data suggest that each of a group of movements differing only in amplitude may not have to be programmed entirely separately; it may be possible to control amplitude via a simple scaling of joint torque throughout the movement sequence, so that movement amplitude may be controlled by a single force "parameter." On the other hand, the present findings were produced in essentially agravitational conditions, with the limb supported by a horizontal lever. This hypothesis of simple proportional scaling of accelerations to achieve variations in distance would not be expected to apply in, say, upward vertical movements where the gravitational effect would require a nonproportional (but perhaps still linear) scaling of accelerations to produce changes in distance, particularly if the movement is slow (Hollerbach 1984), making the alterations in movement distance somewhat more complex than in the horizontal movements studied here. Along similar lines, these interpretations may be limited to the uniarticular movements examined here, where intersegmental dynamics are minimized; in multiarticular actions, such simple scaling might not be possible because of the complex intersegmental interactions (see e.g., Schneider et al. 1987). However, this simple notion of scaling of accelerations is complicated by the E M G analyses, which indicate that the control of movement amplitude is accomplished by an increase in E M G amplitude and small but systematic shifts in E M G duration. Thus, although the temporal structure of accelerations appeared to be held constant, the structure of the central commands necessary to produce them was

not. This finding is consistent with earlier data (Gielen et al. 1985; Shapiro and Walter 1987; Wallace and Wright 1982), and may indicate that the nonlinear relationships between force and E M G particularly in very quick actions with large, suddenly applied forces - will prevent the timing structure of the EMGs to be linear with the temporal structure of the accelerations (see also Benecke et al. 1985). However, such relationships may become more linear as the force (or velocity) requirements of the task are relaxed, as is suggested by the data of Carter and Shapiro (1984) and others. Thus, the deviations from strict constancy in the temporal structure of the EMGs in the present experiment might be a reflection of the relatively high velocities used.

Experiment 2 The control strategy suggested for movement distance, where joint torques are scaled proportionally with distance under a constant temporal structure, could also apply to a situation in which the M T and distance are constant, but the inertial load is varied experimentally. With changes in inertia, the MT and distance goals might be accomplished only by a scaling of the torques proportional to the moment of inertia of the limb-lever system, with a constant temporal structure. Experiment 2 was designed to test this hypothesis with the reversal task.

Methods Subjects

Four healthy, right-handed students at the Universityof Colorado, ranging in age from 21 to 26 years, were used as subjects. None had served in Experiment 1. Apparatus and task

The apparatus was nearly identical to that used in Experiment 1, except that a bracket was added (28 cm from the axle) where lead weights could be secured; the weight of the unloaded lever was 0.98 kg, with a moment of inertia of 0.0768 kg 9m2. The task, and methods for providing feedback, were identical to those used earlier. Procedures

Methods involvedin recording and analysis of EMG and kinematic data were identical to those used before. But, in this experiment, the movement distance (45~) and time to reversal (160 ms) were held constant, and the moment of inertia of the lever was varied in six steps, where either 0,260, 520, 780, 1040, or 1560 g was added to the lever bracket. The six load conditions were presented in a separate randomized order for each subject, with 50 trials being completed in each condition after a short warm-up.

362 Table 3. Average descriptive data and kinematic features as a function of the inertial loading conditions (Experiment 2)

1 Load added (gm) Moment of inertia of lever + load (in kg 9 m 2) Moment of inertia of lever, load, arm, + hand (in kg - m z) Average percentage of maximum torque Reversal point (in degrees) Time to reversal (in ms) Time to peak positive acceleration (in ms) Duration of positive acceleration (in ms)

2

3

Inertial load conditions 4

5

6

0 0.0768

260 0.0972

520 0.1176

780 0.1379

1040 0.1584

1560 0.1991

0.2041

0.2245

0.2449

0.2652

0.2857

0.3264

37.3

47.1

57.8

63.6

75.1

88.9

45.0 (2.0) 156.9 (7.8) 63.6 (8.9) 126.7 (9.8)

45.4 (2.0) 159.6 (8.2) 68.7 (8.3) 127.3 (9.3)

45.4 (2.1) 158.1 (7.6) 59.8 (7.7) 121.7 (7.4)

45.5 (2.0) 164.2 (7.4) 67.6 (9.4) 127.9 (9.9)

45.4 (2.1) 161.7 (7.2) 65.4 (7.9) 126.2 (7.9)

45.2 (2.2) 163.2 (7.3) 61.9 (8.4) 126.4 (8.5)

Summary data are based on 46 responses (Trials 3-48). Average within-subject SDs are in parentheses, where the SD of the reversal position is effective target width (W~), and the SD of the time of reversal is variable error in timing (VEt)

This load manipulation resulted in moments of inertia of the lever-load system from 0.768 through 0.1991 kg 9 m 2, or a 1.6-fold increase, as shown in Table 3. We also estimated the moment of inertia of each subject's forearm arm and hand by standard biomechanical methods (Hay 1973), obtaining values ranging from 0.1176 to 0.1411 kg 9 m z, with the average being 0.1273 kg 9 m 2. The average moments of inertia of the limb, lever, and load are also shown in Table 3, and ranged from 0.2041 to 0.3264 kg 9 m 2, representing a 60% increase in total moment of inertia across the variations in load. Finally, to obtain an estimate of the percentage of maximum torque generated in these conditions, in a separate testing session subjects made several maximal speed movements (45~ to reversal) with the 1560-g load. The largest peak angular acceleration achieved on trials which also achieved the goal reversal point was taken as the subject's maximum. Maximum torques were then computed based on the estimates of the moment of inertia of each subject's hand and arm (plus the lever and load). The various load conditions resulted in from 37% to 89% of the maximum torque, as seen in Table 3.

Results

Kinematic analyses As before, an important first concern was the kinematic analysis indicating the extent to which the MT and amplitude instructions were followed in the various conditions. Table 3 contains the descriptive data for the time to reversal and the distance at reversal (and their respective SDs), where 46 trials/ condition (Trials 3-48) were used. Generally, the subjects appeared to move slightly too far to the

reversal point, 45.3 ~ on the average. There was no shift to compensate for the load conditions, with the reversal points varying unsystematically from 45.0 ~ to 45.5 ~ which was not significant, F(5,15) < 1. The average MT of 161 ms was very close to the 160-ms goal, but there was a very small variation (about 6 m s ) i n the mean MT as the load increased, which was significant with F(5,15) = 13.0, p < 0.05. The subjects were apparently able to follow the instructions to maintain reversal location. And, whereas MT did vary systematically with the load conditions, these shifts were very small and unsystematic, and probably do not provide difficulties for interpreting the load effects.

Acceleration-time patterns. Because the subjects were able to maintain constant reversal points and times to reversal, the patterns and magnitudes of acceleration (based on the twice differentiated position-time traces) were very similar for the various toad conditions. Thus, the superimposed acceleration-time functions analogous to those in Fig. 2 are not particularly informative here. However, a major concern in these studies was the temporal aspects of the movement patterning as the load was changed, and we examined features of the acceleration-time traces for individual trials via interactive graphics (see Table 4). The time to peak acceleration (averaged across subjects) showed an irregular pattern across the load conditions, ranging from 60 to 69 ms, but this effect

363 Table 4. Average EMG measures as a function of the inertial load conditions (Experiment 2) Inertial load conditions 1

Peak biceps EMG (in arbitrary units) Biceps EMG area (in arbitrary units) Peak triceps EMG (in arbitrary units) Biceps EMG duration (in ms) Biceps EMG onset to peak triceps (in ms)

0.37 (0.10) 14.8 (3.5) 0.38 (0.08) 176.4 (18.4) 204.8 (20.0)

2

0.42 (0.12) 17.8 (4.5) 0.55 (0.13) 187.1 (19.3) 213.5 (21.0)

3

4

0.46 (0.12) 17.3 (3.7) 0.50 (0.14) 170.4 (22.7) 199.3 (20.4)

0.49 (0.12) 19.7 (4.3) 0.63 (0.14) 186.6 (24.8) 214.3 (24.8)

5

0.54 (0.10) 21.6 (3.8) 0.68 (0.13) 184.4 (17.7) 209.6 (19.2)

6

0.53 (0.10) 21.4 (3.8) 0.70 (0.15) 181.0 (18.5) 207.5 (20.3)

Means are averaged across Trials 3-48 for each subject. Average within-subject SDs are in parentheses remained nearly constant. These findings for acceleration paralleled those for changing distance in Experiment 1. They support the hypothesis that when the MTs are constant, changes in force to alter either the distance traveled (load constant) or the inertial load (distance constant) in these agravitational situations can be accomplished by scaling the amplitude of muscular forces with a roughly constant temporal structure.

t 100

EMG patterning

mS

Fig. 5. Averaged (46 trials/trace) rectified EMG traces (arbitrary units) for biceps (upper) and triceps (lower) muscles from a single subject in the six inertial load conditions of Experiment 2; moving an increased load with a fixed distance and MT was accomplished by increased EMG amplitudes with essentially no shift in EMG timing (arrow indicates movement onset)

was not significant, F(5,15) = 2.7, p > 0.05. The SD of the time to peak acceleration varied irregularly also, and was not significant, F(5,15) < 1. The average duration of positive acceleration ranged unsystematically from 122 to 128 ms, and did not change significantly with load, F(5,15) = 1.7, p > 0.05. The SD of acceleration duration was stable as well, and was not significant, F(5,15) = 1.7, p < 0.05. Overall, it appeared that the increased load requirements were met primarily by increased muscular force, while the temporal structuring of those forces

Figure 5 shows the average rectified E M G traces for the biceps and triceps muscles for one subject. The major change with increases in inertial load was an increased E M G amplitude, with no obvious chances in the temporal structure of the EMGs. As in Experiment 1, the triceps burst was initiated simultaneously with the biceps, the triceps showing an initial apparent cocontraction with the biceps followed by a larger burst that was reciprocally organized with biceps. Both phases of triceps burst increased with the inertial requirements, and roughly in the same proportion. Whereas these averaged traces give an indication of the gross changes in E M G activities as a function of the load requirements, we prefer to examine the amplitude and temporal structure from individual trials with interactive graphics as before.

EMG amplitude The averaged E M G amplitude and area measurements derived from individual trials are in Table 4, and confirm most of the trends seen in the averaged traces in Fig. 5. The peak biceps E M G increased about 43% as the load was increased, which was

364 significant with F(5,15) = 8.9, p < 0.05. There were irregular changes in the within-subject SD of this activity, with the maximum SD occurring at the middle load values; but this effect was not statistically reliable, F(5,15) --- 2.7, p > 0.05. The biceps EMG area also increased (approximately 45%) as load increased, significant with F(5,15) = 6.4, p < 0.05. However, the within-subject SD of this area did not change systematically with load, F(5,15) = 1.4, p > 0.05. Also, the peak triceps activity increased with load (about 84%), F(5,15) = 5.9, p < 0.05, but the irregular increases in the within-subject SD were not significant, F(5,15) = 2.0, p > 0.05. Overall, the amplitudes and areas of the relevant EMGs increased sharply with the load requirements, but the withinsubject variability of these activities did not.

models of impulse variability (e.g., Meyer et al. 1982; Schmidt et al. 1979). The argument is that, as inertial load is increased, greater force variability (brought about by the larger muscular contractions) is met by an exactly equal and opposite increase in the "resistance" to the effect of this variability on the movement trajectory (i.e., moment of inertia of the limblever system); this greater moment of inertia increases the stability of the limb and lever to variations in muscular force produced by the added torque requirements. It is also interesting that, while the effect of load on movement variability (Experiment 2) was negligible, the effect of increased movement distance (Experiment 1) was to increase the spatial variabilities considerably (Table 1), which is also predictable from the current models of speedaccuracy effects (e.g., Schmidt et al. 1979).

EMG temporal structure Discussion

The temporal measures of EMG activities are also given in Table 4. The duration of the biceps EMG burst increased slightly and irregularly across the load conditions, but the effect was not significant, F(5,15) = 1.5, p > 0.05. The within-subject SDs of this value changed slightly to become maximized at the middle load values, also not significant with F(5,15) = 1.9, p > 0.05. The interval from biceps onset to peak triceps - a measure of the temporal occurrence of the antagonist burst - did not appear to change with the load conditions, F(5,15) = 1.7, p > 0.05. The within-subject SD of this statistic was nearly constant and not significant, F(5,15) < 1. Overall, these data provided no evidence that the temporal structure of the EMG activities were altered as the load requirements changed, the primary modification being in the amplitude (and hence area) of these bursts.

Load-accuracy trade-off effects. A final analysis concerns the effect of the load on the various features of accuracy measured at the reversal point. Table 3 contains the averaged within-subject SDs of the movement reversal points (We) and the averaged SDs of the times to reversal point (VEt). There was some tendency for the largest load conditions to have the largest spatial variability, but this effect was not consistent across subjects, F(5,15) < 1. Als0, there was no apparent shift in the timing variability, and the effect of load was not significant, F(5,15) < 1. At first glance, these effects seemed somewhat counterintuitive, in that added load - in one condition close to the maximum capabilities - seemed to have no important effects on the spatial or temporal accuracy. The findings are, however, consistent with

The analysis of the joint torques (computed from the accelerations) when MT was held constant revealed that the temporal structure of the torque-time functions remained generally constant as the inertial loads were increased, but with markedly increased amplitudes, to maintain the constant movement distance and MT. Again as with the effects of distance in Experiment 1, it is not immediately obvious that a simple scaling of joint torque would accomodate changes in moment of inertia, while maintaining distance and MT, as such would seem only possible with uniform accelerations. But, if the mathematical form of the torque-time functions is maintained across changes in peak joint torque, it is possible to prove that such a simple scaling of torques preserves movement amplitude and MT as the moment of inertia changes. Thus, these data fit well with those in Experiment 1, suggesting that the "same" trajectory can be produced with a variety of inertial loads by changing a single parameter. As mentioned before, however, this simple strategy for the agravitational movements studied here should be complicated considerably in movements where gravity plays a role. The EMG data in Experiment 2 suggested that the major change as the load increased was in terms of EMG amplitude, with almost no changes in the temporal structuring of the EMGs being seen. Of course, with surface EMG techniques, we were unable to detect the temporal structures of all of the muscle activity contributing to the movement at the elbow joint, and our interpretations must be limited to the activity of the major muscle. For this muscle at least, the timing of the EMG events remained

365

constant as the load was changed. Again, this suggests that some temporally organized movement program could accomodate changes in the moment of inertia with a single parameter to increase the amplitude of EMG, without having to reorganize the movement completely. General discussion

The major focus of this series of experiments has been on the general question of how the motor system is organized to produce particular variations of a given movement pattern while at the same time retaining some essential features of it. The patterning of the acceleration-time traces in these agravitational conditions indicated that, if the MT requirements of the task are held constant, changes in movement distance (Experiment 1) or adjustments for inertial loading (Experiment 2) were accomplished by holding the temporal structure constant, and meeting the increased torque requirements by changing the amplitude of accelerations only. These findings are reasonably well supported by the EMG analyses, where the amplitudes of the EMGs were increased markedly as the torque requirements increased, with the duration of the agonist burst and the temporal onset of the antagonist burst being generally unaffected. The one exception was that the duration of the biceps activity, and time to peak biceps EMG, were both lengthened by increased movement distance (but not by load). However, these alterations were relatively small (35 and 21 ms, respectively), and changes in biceps duration here was considerably smaller than the corresponding changes produced when MT was varied experimentally (78 ms) in our companion article (Schmidt et al. 1987). Even so, these data provide some suggestion that compensations for load and distance may not be identical in these situations. We cannot be certain, of course, that the changes in net joint torques and in surface EMGs that occurred here were representative of the functioning of each of the muscles operating at the joint, as it is possible that different muscles would come into play only when the torque requirements were very high (or low); but at the same time, there is no evidence that the muscles did act differentially as the torque requirements were increased. If the various muscles acting at the elbow did increase their torques in a similar way, then these data suggest a movement strategy whereby the increased distance or load requirements can be produced by a relatively simple scaling of a single parameter that affects the amount of joint torque produced, while holding the temporal structuring of the movement constant.

At first glance, such a simple view of the control of movement amplitude and inertial load seems unlikely. In general, it is not true that changes in distance (load constant) or changes in load (distance constant) can be achieved by a simple linear scaling of the amplitude of joint torques, as such a relationship would apparently be correct only in the case of constant accelerations, and not correct for the usually sinusoidal accelerations found in movement control. But, if the added assumption is made that the mathematical form of the acceleration-time traces is preserved as the average acceleration is increased, then it is possible to prove that the distance traveled is proportional to the average acceleration (see Schmidt et al. 1985 for a proof). And, if the movement distance is constant, then it is easily shown that changes in inertial load are also met by a proportional scaling of joint torques, again with a constant form of acceleration-time function. The important assumption that the mathematical form of the acceleration-time functions remains constant with changes in its amplitude has not been evaluated here, as doing so was be beyond the scope of the present experiments. But the forms of the acceleration-time traces in Fig. 2 do appear remarkably similar (typical of every subject), and our analyses of the time to peak and duration of acceleration did not reveal any important shifts in the structure with changes in the response requirements. Others have done more careful analyses of the forms of acceleration-time traces, and have similarly failed to detect important shifts in form with changes in movement amplitude (Sherwood 1983) and movement load. Thus, while this issue of "shape constancy" is far from settled, it does not appear that this assumption is violated in the simpler responses that have been analyzed in movement control research to date 2. And, if this assumption does hold in general, it suggests an important biophysical principle, in which distance and/or load changes (MT constant) can be met by a relatively simple scaling of joint torques with a constant temporal structure from the CNS. The simplest version of this hypothesis is that the activities in all of the muscles contributing to the joint torques are scaled in proportion to distance and/or load, with the same temporal structure. But other models, in which the forces are scaled differently for different conditions, or even in which the temporal structures for different muscles may be different, are possible, but our methods used here do not provide a basis for discriminating among these views. 2 One important exception to this shape-constancy assumption occurs in the acceleration-time functions of three dimensional stylus-aiming tasks (e.g. Schmidt et al. 1985; Zelaznik et al. 1986)

366

A second concern about these models is their generality to common movement behaviors. One issue is that the present movements were conducted in essentially agravitational conditions, with horizontal moves and the limb supported by the lever. Here, it is at least reasonable to consider that the amplitude of the torque/time function should be scaled proportionally to movement amplitude or inertial load. But in vertical or unsupported movements where gravity plays a role, the relationship between the amplitude of the torque-time function and movement distance or load should not be proportional (although it could still be linear), making the CNS's problem of controlling amplitude and loads considerably more complex. Also, when other torques from intersegmental dynamics are considered in vertical multi-joint actions as we have done recently (Schneider et al. 1987), the hypothesis of simple scaling of joint torques to account for changes in various "surface" movement features seems particularly unlikely. Even so, the relatively parsimonious view that emerges from the present data suggests important control principles in at least these simpler actions. A second major point that comes from Experiment 1 concerns the control of movement velocity. As distance was changed from 20~ to 70 ~ (3.5-fold increase in average velocity), there were no systematic shifts in the temporal structure of the accelerationtime functions. This was in strong contrast to the effects seen in an earlier experiment in this series (Schmidt et al. 1987), in which the velocity was changed 2.5-fold by changing the MT instructions with a constant movement distance. There, the temporal structure of the acceleration-time functions was altered markedly, with the durations of various features of the traces being scaled in rough proportion to MT. These findings together suggest that velocity may be controlled in at least two ways - with a constant temporal structure of the accelerationtime functions if distance is varied and MT is essentially constant (e.g., Enoka 1983; Freund and Budingen 1978; Ghez 1979), or with an accelerationtime structure that "expands and contracts" in rough proportion to MT if the movement distance is constant and the MT is varied (e.g., Carter and Shapiro 1984; Schmidt et al. 1987; Schneider et al. 1987; Shapiro and Walter 1986). How movement velocity is controlled depends strongly on whether the experimental manipulation of velocity holds MT constant or not. Overall, our data taken at a variety of levels of analysis suggest that the control of movement amplitude and inertial load in these horizontal, agravitational reversal responses is accomplished by a relatively simple scaling of the amplitudes of the

joint torques with a constant temporal structure. Such findings, coupled with our earlier mathematical proofs regarding shape constancy, suggest an important economy in the motor system whereby altering movement distance and load can be accomplished by the adjustment of a single parameter. A model of motor programming, in which the representation of the action in the CNS has a fixed temporal structure, but whose output to the musculature is amplified by a simple gain parameter, is supported for the variations in inertial load, but shifts in the EMG durations with changing movement amplitude seem to prevent such a simplified viewpoint in general.

Acknowledgements. Supported by grant no. BNS 80-23125 from the National Science Foundation (Memory and Cognitive Processes Program) to the second author, and by contract no. MDA90385-K-0225 from the U.S. Army Research Institute to R.A. Schmidt and D.C. Shapiro. D.E. Sherwood is currently at the University of Colorado, Boulder, and C.B. Walter is at the University of Illinois, Chicago. Thanks to Douglas E. Young for help with data collection and analysis. References Benecke R, Meinck H-M, Conrad B (1985) Rapid goal-directed elbow flexion movements: limitations of the speed control system due to neural constraints. Exp Brain Res 59:470-477 Berardelli A, Rothwell JC, Day BL, Kachi T, Marsden CD (1984) Duration of the first agonist EMG burst in ballistic arm movements. Brain Res 304:183-187 Brown SHC, Cooke JD (1981) Amplitude- and instructiondependent modulation of movement-related electromyogram. activity in humans. J Physiol 316:97-107 Brown SH, Cooke JD (1984) Initial agonist burst duration depends upon movement duration. Exp Brain Res 55: 523-527 Carter MC, Shapiro DC (1984) Control of sequential movements: evidence for generalized motor programs. J Neurophysiol 52: 787-796 Cooke JD, Brown S, Forget R, Lamarre Y (1985) Initial agonist burst durations changes with movement amplitude in a deafferented patient. Exp Brain Res 60:184-187 Enoka RM (1983) Muscular control of a learned movement: the speed control system hypothesis. Exp Brain Res 51:135-145 Flowers KA (1976) Visual 'closed-loop' and 'open-loop' characteristics of voluntary movement in patients with parkinsonism and intention tremor. Brain 99:269-310 Freund HJ, Biidingen HJ (1978) The relationship between speed and amplitude of the fastest voluntary contractions of human arm muscles. Exp Brain Res 31:1-12 Gentner DR (1987) Timing of skilled motor performance: tests of the proportional duration model Psych Rev 94:255-276 Ghez C (1979) Contributions of central programs to rapid limb movement in the cat. In: Asanuma H, Wilson VJ (eds) Integration in the nervous system. Isaku-Shoin, Tokyo, pp 305-319 Ghez C, Vicario D (1978) The control of rapid limb movement in the cat. Scaling of isometric force adjustments. Exp Brain Res 33:199-202 Gielen CCAM, van den Oosten K, ter Gunne FP (1985) Relation between EMG activation and kinematic properties of aimed arm movements. J Mot Behav 17:421-442

367 Hallett M, Marsden CD (1979) Ballistic flexion movements of the human thumb. J Physiol 294:33-50 Hay JC (1973) The biomechanics of sports techniques. Prentice Hall, Englewood Cliffs, NJ Hollerbach JM (1981) An oscillation theory of handwriting. Biol Cybern 39:139-156 Hollerbach JM (1984) Personal communication Lestienne F (1979) Effects of inertial load and velocity on the braking process of voluntary limb movements. Exp Brain Res 35:407-418 Merton PA (1972) How we control the contraction of our muscles. Sci Am 226:30-37 Meyer DE, Smith JEK, Wright CE (1982) Models for the speed and accuracy of aimed limb movements. Psychol Rev 89: 449-482 Newell KM, Carlton LG, Carlton MJ, Halbert JA (1980) Velocity as a factor in movement timing accuracy. J Mot Behav 12: 47-56 Raibert MH (1977) Motor control and learning by the state space model. Technical Report No. AI-TR-439, Artificial Intelligence Laboratory, MIT Schmidt RA (1987) Motor control and learning: a behavioral emphasis (rev edn). Human Kinetics, Champaign, IL Schmidt RA, Sherwood DE, Walter CB (1987) Rapid movements with reversals in direction. I. The control of movement time. Exp Brain Res 69:344-354 Schmidt RA, Sherwood DE, Zelaznik HN, Leikind BJ (1985) Speed-accuracy trade-offs in motor behavior: theories of impulse variability. In: Heuer H, Kleinbeck U, Schmidt K-H (eds) Motor behavior: programming, control, and acquisition. Springer, Berlin Heidelberg New York Tokyo

Schmidt RA, Zelaznik HN, Hawkins B, Frank JS, Quinn JT (1979) Motor-output variability: a theory for the accuracy of rapid motor acts. Psychol Rev 86:415-451 Schneider K, Zernicke RF, Schmidt RA, Hart TJ (1987) Learning of unrestrained rapid arm movements. II. Coordination of intersegmental dynamics. (submitted) UCLA Shapiro DC, Walter CB (1986) The control of rapid positioning movements with spatiotemporal constraints. J Mot Behav 18: 373-395 Sherwood DE (1983) The impulse-variability model: tests of the major assumptions and predictions. Ph.D. dissertation, University of Southern California Wadman WJ, Denier van der Gon JJ, Geuze RH, Mol CR (1979) Control of fast goal directed arm movements. J Hum Mov Stud 5:3-17 Wallace SA (1981) An impulse-timing theory for reciprocal control of muscular activity in rapid, discrete movements. J Mot Behav 13:144-160 Wallace SA, Wright L (1982) Distance and movement time effects on the timing of agonist and antagonist muscles: a test of the impulse-timing theory. J Mot Behav 14:341-352 Walter CB (1984) Temporal quantification of electromyography with reference to motor control research. Hum Mov Sci 3: 155-162 Zelaznik HN, Schmidt RA, Oielen CCAM (1986) Kinematic properties of rapid aimed hand movements. J Mot Behav 18: 353-372

Received February 26, 1987 / Accepted June 15, 1987