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Exp Brain Res (1983) 51:135-145 E x men nResearch �9 Springer-Vcrlag 1983

Muscular Control of a Learned Movement: The Speed Control System Hypothesis*

R.M. Enoka

Department of Physical Education, McKale Center, Room 228a, University of Arizona, Tuc~son, AZ 85721, USA

Summary. The "speed control system" hypothesis, which represents an attempt to identify an invariant characteristic of learned movements, postulates that movements of variable extent are controlled by regulating the intensity of muscle contractions such that the contraction duration remains constant. The contingency set originally utilized to develop this hypothesis was expanded by examining a movement that was multidirectional and multiarticular, and executed by large muscle groups generating near maximum torques. The investigation focused on the techniques utilized by weightlifters to control lower extremity displacement during the initial phase of the double knee bend execution of the "clean" in Olym- pic weightlifting.

The combination of the quantified muscle activity and the angular velocity, both about the knee joint, revealed a sequence of shortening-lengthening muscle contractions throughout the movement. The first two periods of net muscular activity, one extensor and the other flexor, were utilized to examine the movement for invariant characteristics. As predicted by the speed control system hypothesis, the duration of the first period of net muscle torque activity (extensor) did not vary significantly, for either group of subjects, over the relative loads examined. The duration of the second period of activity (resultant flexor muscle torque), however, was not constant across loads, and further, the direction of the change depended upon the level of expertise. The more capable lifters tended to increase the duration of the resultant flexor involvement while the less skilled athletes utilized the reverse strategy when the load was increased. Conversely, the intensity of the mus-

* This study represents a segment of the author's Ph .D. disserta- tion and was undcrtakcn in the Department of Kinesiology at the University of Washington where support was provided by Biomcdical Sciences Support Grants 61-2300 and RR-07096 NIH

cle activity for both groups of subjects and both the extensor and flexor periods covaried with load, as predictcd by the hypothesis. The speed control system hypothesis, therefore, provided an appropriate explanation for the first component of the movement, the period of extensor dominated (shortening contraction) muscle torque, but was inappropriate for the subsequent interval, a resultant flexor (largely lengthening contraction) muscle torque.

Key words: Control strategies - Speed control system hypothesis - Equilibrium point hypothesis - Weight- lifting

Introduction

As a basis for inferring the manner by which central processes might organize movement, there has been an interest in identifying the invariant characteristics of a movement sequence (for a select ad seriatim review: Beaunis 1885; Bryan 1892; Richer 1895; Woodworth 1899; Stetson 1905; Freeman 1914; Stet- son and McDill 1923; Stetson and Bouman 1935; Searle and Taylor 1948; Johns and Draper 1964; Freund and Bfidingen 1978; Ghez and Vicario 1978a, b; Lestienne 1979; Polit and Bizzi 1979; Feldman 1980a, b; Wadman et al. 1979, 1980; Viviani and Terzuolo 1980; Marsden et al. 1981; Soechting and Laquaniti 1981; Waters and Strick 1981; Luschei et al. 1982). One such effort, the equilibrium point hypothesis, suggests ~.hat movement may in part be controlled by the specification of some end location as an equilibrium point between any external forces and the length-tension relationships of an agonist- antagonist muscle set (Asatryan and Feldman 1965; Bizzi et al. 1976, 1978, 1982; Bizzi and Polit 1979; Feldman 1966a, b, 1980a, b, 1981). Functionally this

136 R.M. Enoka: Control of a Learned Movement

proposal is attractive since it reduces the traditional degrees of freedom problem (Bernstein 1967) and to a large extent obviates the concern for movement context (MacNeilage 1970).

The model, however, cannot be the sole control mechanism due to its inability to account for either variations in movement dynamics (e.g., Soechting and Laquaniti 1981) or observed electromyographic (EMG) patterns, which, for movements of moderate and fast speeds, are normally triphasic in nature (e.g., Angel 1974; Barnett and Harding 1955; Ghez and Martin 1982; Hallett et al. 1975; Wachholder and Attenburger 1926; Wadman et al. 1980; Waters and Strick 1981) rather than sustained (co-contraction of an agonist-antagonist muscle set) as predicted by the equilibrium point hypothesis. As a consequence, the equilibrium point hypothesis has been postulated to be associated more with postural fixation than with movement elicitation (Lestienne et al. 1980, 1981; Sakitt 1980).

In view of the inability of the equilibrium point concept to account for anything beyond, at best, slow movements, it is perhaps not surprising that specification of some dynamic parameter might provide a viable alternative. The "speed control system" hypothesis (Freund and Btidingen 1978) represents one such possibility and proposes that the control of a rapid learned movement, regardless of the extent, is accomplished by the "amplitude dependent regulation of contraction velocity so that the contraction time remains constant." The postulate suggests that the neural mechanisms underlying this scheme would involve a constant E M G burst duration accompanied by a modulation of spike density (cf. Brown and Cooke 1981; Ghez and Vicario 1978b; Lestienne 1979; Stetson and Bouman 1935). 1 Such a strategy would simplify the determination of joint torques to the mere application of a scaling factor (Hollerbach and Flash 1982).

The speed control system hypothesis, however, has evolved from the analysis of movements exhibit- ing a rather limited set of contingencies; namely, simple unidirectional planar motion (e.g., finger extension-flexion or abduction-adduction, wrist flexion-extension, elbow flexion-extension), uniarticu, lar, smaller muscle sets, minimal inertial loads, speeds greater than 1.5 tad/s, and learned (expected) loads and extent of motion. The intent of this study was to extend the paradigm and to examine the invariant characteristics of a movement that was multidirectional and multiarticular, and executed by

1 The terminology "speed control system" is unfortunate since the hypothesis proposes duration and not speed as the controlled variable

large muscle groups generating near maximum torques. The investigation focused on the first two components of such a movement (weightlifting) and revealed that as predicted by the speed control system hypothesis, the magnitude of the net torque co-varied with load during both components and the duration of the first component remained constant with different inertial loads. The duration of the second component, however, was not constant. Further, the direction of the change in duration of the second component depended on the level of skill of the subject.

Methods

The Movement

With few exceptions, human movement in essence comprises sequences of shortening (c0ncentric)-lengthening (eccentric) muscle contractions with concomitant changes in the direction of the angular displacement of the body segments. The movement selected for analysis, the double knee bend (DKB) execution of the "clean" in the sport of Olympic weightlifting, contained this basic functional element. In addition, the movement incorporated at least two elements, which extend the conventional contingencies for control-strategy analyses. First, the subjects had learned the movement independent of the experimental context which minimized the possibility that the paradigm might impose a strategy on the task. Second, the movement did not represent a triggered reaction to a stimulus provided by the experimenter (cf. Reed 1982).

Figure 1 characterizes the trunk and knee angular displacements associated with such a performance, including the extent of the movement analyzed. This portion of the lift is typically termed the pull. The DKB execution of the movement contains two intervals of extension about the knee joint, separated by a period of flexion - the second knee bend (SKB). In addition, at the onset of the SKB, but of greater temporal duration, the torso rotates backward about 0.75 rad. Since the SKB represents an interval of minimal force application to the barbell, the principal objective of the combined knee flexion-backward trunk rotation is the realign- ment of the lifter relative to the barbell such that the maximum contribution from the back and hip extensors, which occurs post- SKB, results in a greater barbell acceleration (Enoka 1979). Thus the dominant musculature during this movement, and therefore the object of this investigation, is that about the knee joint.

The Measurements

A camera, positioned with the center of the lens 1.07 m above the floor and 11.05 m from the plane of action, was operated at 97.9-98.8 frames/s to obtain a cinematographic record of the lifting performance. A 2.57 shutter factor, in combination with the mean flame rate of 98.4_+0.3 Hz, resulted in an average exposure time of 4 ms.

In weightlifting competition, the largest barbell plates used are approximately 0.46 m in diameter, a size which obscured, from a side view, much of the lower extremities during the portion of the clean which was of present interest. This problem was partially circumvented by utilizing smaller diameter plates (0.30 m) and resting them on 0.08 m blocks so that the barbell retained the

R.M. Enoka: Control of a Learned Movement 137

Extension

KNEE ANGLE (dog)

Flexion

,80[ 1 60[ 140[ 120[

0 Forward ~ TRUNK ANGLE----z~-Backward ro ta t ion (dog) rotat ion

Fig. 1. Temporal relationship between the vertical and forward- backward components of the system inertia force (arrows) at selected positions and the trunk and knee angular displacements during the double knee bend performance of a typical lift of a skilled subject. The movement begins with the subject crouched over the barbell. In essence, the movement comprises a triphasic sequence of angular displacements; namely, knee extension, backward trunk rotation and knee flexion, and knee extension. Temporally the data points (x) are spaced at 10 ms intervals. The vertical component of the system inertia force was determined by substracting the body (1000 N) and barbell (1226 N) weights from the vertical component of the ground reaction force. An upward and forward inertia force represents an acceleration of the system in the same direction. Thus, the segmental angular displacements outlined above are closely aligned to a similar profile in the system acceleration-time record. That is, forward and upward, backward and downward, and forward and upward

regulation initial height of 0.23 m from the lifting platform. In addition, a microswitch located in one of the blocks was connected in a circuit between a power supply and a LED, the latter being positioned in the field of view of the camera. When the plates were moved from their starting location, the switch was closed and it was possible to precisely locate on the cinematographic record the instant of barbell take-off.

During the movement, three orthogonal components of the resultant ground reaction force [i.e., forward-backward (Rx), side- to-side (Ry) and vertical (Rz)] were measured with a Kistler force platform. After amplification, these signals were sampled on-line at 500 Hz by a PDP 11/34. Each orthogonal component represented the sum from four quartz piezoelectric sensors. The summations for Rx and Ry were performed by the force platform amplifier while that for Rz (Rzl, Rzz, Rz3, Rz4) was done by the computer. Thus, the 11/34 received six signals from the force platform, Rx, Ry, RZl, Rz2, Rz3 and Rz4.

Two single-joint muscles were selected as representative of knee extensor (vastus lateralis-VL) and knee flexor (short head of biceps femoris-BF) activity and were monitored from the right lower extremity during the movement with Ag-AgC1 disc electrodes (6 mm diameter). The electrodes were attached in pairs approximately 1.5 cm apart over the belly of each muscle. A ground electrode was placed over the lateral tibial condyle. After

gentle abrasion, cleansing with alcohol and the application of a conductivity gel, the resistance between electrode pairs in all instances was less than 8.0 k ~ (X = 3.5+ 1.7 kf~). Strain loops in the cables minimized movement artifact.

The myoelectric potentials were pre-amplified and displayed on storage oscilloscopes with the plug-in units operating at a gain of 1,000. The input impedance of these units was 1 M~2 with a common mode rejection ratio of 100,000:1. After preamplification the EMG signals were sampled on-line at 2 kHz by the same system used to gather the ground reaction force information. In addition to storage on disk cartridges, the preamplified and displayed EMG data were photographed on the scope face with a 35 mm camera.

The Protocol

Six competitive weightlifters, three of whom were more skillful than their counterparts, were informed of the objectives and procedures of the study and consented to serve as subjects. Each of the subjects performed 10 DKB executions of the clean, five per testing session. The coach and subject specified the maximum weight (hereafter referred to as the 100% condition) that the latter could comfortably control given the experimental regimen. After the subject had performed several warm-up lifts, testing was begun. Each lifter commenced with two sub-100% loads, one at 80% and the other at 90%, with the final three attempts at the chosen 100% resistance. Since efforts were made to have the laboratory conditions resemble the competitive situation, each lifter was required to retire from the testing area between lifts to an adjacent warm-up room where the subject was advised by his coach on various aspects of his performance. The intertrial interval varied from three to seven minutes. In the final count (i.e., including both sessions), the trial distribution for each lifter was two attempts at 80% and 90% of the chosen maximum (100% condition) and six at 100%. For the six subjects, the 100% load represented 86+3% of their presumed maximum competition capability at the time of testing.

The Analysis

A digitizing system with a least reading capability of 0.025 mm was used to record the x-y coordinates of selected anatomical and control reference points from the cinematographic records. The measurements were made frame-by-frame on a projected image, which represented a 40• magnification that was 20% of the actual object size. The digitized coordinates were stored on magnetic tape for subsequent reduction and analysis on a CDC Cyber 170/ 750 computer. Software performed translational and rotational transformations and scaled the data to real-life dimensions.

Analysis of the ground reaction force information involved three procedures. First, calculation of the side-to-side (Ax) and forward-backward (Ay) center of pressure coordinates and con- version of the force records from A/D units to newtons. Second, alignment of the force platform derived information with the cinematographic records by selecting from the force-time data files one value which most closely approximated each frame of film. Thus, the ground reaction force information was in essence reduced from a 500 Hz sampling rate to a frequency which matched the frame rate with which the movement was filmed. Finally, the aligned force and center of pressure data were transmitted from the 11/34 to the 170/750 and output on computer cards.

After the myoelectric potentials had been full-wave rectified, running average values were calculated over 5 ms periods, transmitted to the 170/750 and output on computer cards. In this latter


A 8o% 90%

Flexor 200T'~ " ~ ' ~ ' ~ " ~ ' ~ ' ~ "~ ) ~ ' l

100 ..... TORQUE ......... ~ : : ~ . - " . . . . . . . ~ . . . . ~ .... ~ . . . . . . . . . ;

(N. m) 0 ~ . . . . - t ~

Ext|sore~n 1 0 0 ~ '" ................ ' ....... V " " ....... ~ .... 200 I 6,

6 3 .......................... . ...... ~ ?

_61 "

3 " t ~ 0 2 . '

i

" 20 40 60 80 100 20 40 60 80 100 TIME (%)

100%

�9 . . . . .

" " - _ . 3 "

20 40 60 80 100

B 8096 9 0 % 1 0 0 %

-Flexor 200~ I t loo t / - . t I ........ ............ . . . . TORQUE

...... " . . . . . . . . . . ~.!!iiii~! ...... Exte!sor (N-m) 200 l I _ G , ~ UuI ~ ~ , " ~ ~ ~ ~ .............. '

2 iiiil

(rad) 1 e

0 20 40 60 80 1 ' - - ' ' : - - ' " O0 20 40 60 80 100 ' 20 40 6 0 ' 8 0 ' 1 0 0 TIME (%)

Fig. 2. A, B Mean (solid line) angular position (O)-, angular velocity (8)-, and resultant muscle torque-time histories about the knee joint for the temporally normalized 80, 90, and 100% lifts for the skilled (A) and less skilled (B) subjects. The dotted lines represent plus and minus one standard deviation. Positive angular velocity delineates extension. The intent of the illustration is to focus attention on the similarity of the mean records for the three conditions (80, 90, and 100%) and both groups of subjects. The differences in the standard deviation profiles were largely due tothe variable number of lifts (N) available for each condition. That is, N = 5, 6, 15, and 2, 4, 16 for the 80, 90, and 100% lifts of the skilled and less skilled subjects, respectively. The 100 ms bars refer to the mean epoch

form the EMG records were converted from positive arbitrary units to percentages of the maximum value for each subject and muscle respectively, obtained from the 100% condition for a given session. Thus, from the five lifts a subject performed on a given day, one maximum EMG value for each of the muscles was determined from the three 100% trials and all the other myoelec-

tric potentials for that data collection episode were expressed relative to these.

Dynamic equations of motion were used to calculate the resultant muscle torques between the body segments. The equations of motion (Appendix) were derived by the force-mass- acceleration method by proceeding from a known boundary


constraint, the ground reaction force, in combination with kinematic and body segment parameter (Chandler et al. 1975) data through the eight link model. In such an approach, a free body diagram of the system is equated to a mass-acceleration diagram since, based upon Newton's laws, both have the same resultant.

The segmental acceleration-time histories, which were required for this procedure, were obtained by the double-differentia- tion of the cinematographically derived position-time records. To minimize the inclusion of measurement errors in the displacement signal, since they would be grossly exaggerated by the differentia- tion, the position-time data were filtered with a symmetric second order Butterworth digital filter. The cut-off frequency was set at 6 Hz as it was determined by Fourier analysis that 95% of the signal power for knee angle was contained in the bandwith 0-6 Hz. The acceleration information was then obtained by the application of the first order finite difference technique to the filtered position- time records.

After the acceleration-time profiles, the body segment parameter estimates and the ground reaction force derived data (i.e., Rx, Rz, Ax), had been supplied as input to the appropriate algorithm and the resultant muscle torque-time histories com- puted, the latter were displayed graphically.

Results

Resultant Muscle Torque

To facilitate the collation of data across subjects and lifts, each trial was normalized temporally. Figure 2, therefore, represents the means and standard devia- tions of temporally standardized angular position, angular velocity and resultant muscle torque histories about the knee joint for both groups of subjects.

At a gross level of analysis, the kinematic and kinetic profiles for the three loads and two sets of subjects were comparable . For a general description of the movement , therefore, focus on the 100% condition for the skilled subjects (Fig. 3). The angular displacement about the knee joint was characterized by two periods of extension (i.e., positive angular velocity), the first and top pulls respectively, separated by an interval of flexion, the SKB. The change in knee angle attained peak speeds of - 3 . 0 rad/s during both phases of extension and 2.0 rad/s in the SKB and was achieved by an involved pattern of muscular contributions.

The first pull began with a net concentric (i.e., shortening of activated muscle) employment of the knee extensors that lasted for 37% of the total pull and reached max imum torques of 105 N.m. Since the knee extension continued after the resultant muscle torque became flexor, the net activity represented an eccentric (i.e., lengthening of activated muscle) knee flexor involvement. This eccentric contribution (maximum 55 N.m) accounted for 30% of the pull duration and served to slow the rate of extension, eventually causing a change in the direction of displacement as the first p u l l b e c a m e the SKB. The

Flexor

TORQUE (N.m)

Ext!nsor

(tad/s-)

9 (rad)

I

0 0 ZO 40 60 80 I00

400[ 200 ~ i- . . . . . . . . . . . .~ H

o / �9 , . ".~ ..."

::[ �9 V 3

, I I

lOOms

TIME (%)

Fig. 3. Mean (solid line) angular position (O)-, angular velocity ((~)- and resultant muscle torque-time histories about the knee joint for the temporally normalized 100% lifts (N = 15) of the skilled subjects. The dotted lines represent plus and minus one standard deviation. The bar beneath the stick figures indicates the temporal location of the second knee bend. Positive velocity delineates extension. The solid and dashed bars associated with the torque curve illustrate net concentric (shortening) and eccentric (lengthening) contractions, respectively

torque was flexor dominated, and therefore, concentric, for only a brief period (2% of the pull) during the knee flexion. Ra ther the SKB was characterized by a net eccentric extensor torque which indicated that although the knee angle was decreasing in magnitude, the muscles about the joint were employed for the majori ty (90%) of the SKB to reverse that trend. Subsequently the SKB gave way to the top pull and the resultant torque was a concentric extensor contribution. The extensor torque attained peak values of 80 N . m as the net contraction type changed f rom eccentric to concentric. For the final 6% of the t ime-frame the resultant activity represented a braking of the second period of knee extension as the athletes prepared to move under the bar.


�9 /

3 o

E M G (%) o

6 0 o . .

9O

0

A B

Jt 4 0 " "

2 0

. , ,~o

t :01 . o r . ~4 . 2 o . 2 7 . 3 4 o 2o 4 o so eo ~oo

TIME (s) TIME (%)

C

.o[ t 1,5o F,.0r

1 ol . . . . .:" , , : , , : I oTORQU.E

I ul / ~ ." j (N mJ

f2. 1 4 ~ E x t e n s o r

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0 2 0 4 0 6 0 8 0 I O0

TIME (%)

Fig. 41 A-C Resultant muscle torque (dotted line) and EMG records (solid line) about the knee joint. The short head of biceps femoris (BF) and vastus lateralis (VL) EMG data were expressed as percentages of their respective maximum values obtained for each subject and data collection session. The changes in the torque record mirror the relative EMG changes in the two muscles, with the electromechanical delay approximately 35 ms (Norman and Komi 1979; Ralston et al. 1976). A The profiles obtained for the first 100% trial of Subject 8 (skilled). B The mean records obtained for the temporally normalized 100% lifts (N = 6) of Subject 8. C The mean histories for the temporally normalized 100% lifts (N = 15) of the skilled subjects

Electromyography

Alignment of the resultant muscle torque and EMG histories revealed not only the relationship between the contributions of individual muscles and the quantitative net output but also the manner in which the torque pattern was generated.

Specifically, the EMG histories for VL and BF, expressed as percentages of their respective maxima, indicated that both muscles were active throughout the entire pull and thus their contribution to the resultant torque was due to relative variations in the degree of excitation. Figure 4 illustrates the profiles obtained for the 100% condition for a single trial, the mean for one subject and the mean for the skilled subjects. Qualitatively the records for the other two conditions and the less skilled subjects were comparable to those in Fig. 4C.

The myoelectric activity in VL remained at a relatively constant level for approximately the first half of the movement, that is, well into the period of flexor torque associated with the SKB. Meanwhile, the EMG signal for BF increased from barbell take- off attaining peak values during the first interval of flexor dominated torque, temporally 38-70% of the pull duration (Fig. 4C). By the conclusion of this epoch the level of VL excitation was minimal. Subsequently, a resultant extensor torque (temporally 70-94%) coincided with a substantial increase in VL activity, reaching a maximum as the knee extensor contraction changed from eccentric to concentric (cf. Fig. 3). During this period of increased VL

involvement, but not of relative comparable magnitude, BF also exhibited an increased input. Since BF is located anatomically amongst muscles which contribute to knee flexion and hip extension, perhaps the increased BF excitation was associated with the hip extensor activity that accompanied the net knee extensor torque (i.e., cross-talk). Based upon the observations of Lynn et al. (1978), however, such a suggestion appears improbable. The pull concluded with a final increase in BF activity and decrease in VL.

Duration of Net Muscle Activity

The analysis of the invariant characteristics of the movement was restricted to focusing on the periods of resultant knee extensor and flexor muscle torque that were associated with the first pull and the SKB, respectively. Table 1 outlines the durations of these periods for the expected loads.

The similarity of performance between sessions was examined from two perspectives, a session (days 1 and 2) by percentage (80, 90 and 100%) analysis of variance (ANOVA) for Subjects 3, 4, 8, and 7 and an ANOVA on the 100% condition for all six subjects in which session was the sole dependent variable. Such a design was necessary due to missing data for Subjects 5 and 6. Since there were no significant main (session) or interaction (session- percentage) effects for either the extensor or flexor durations (all p values >0.15), the data were collapsed across sessions.


Table 1. Mean durations (s) of the periods of resultant knee extensor and flexor muscle torque associated with the first pull and the second knee bend, respectively, for the expected loads (80, 90, and 100%) as performed by the smiled, less skilled, and combined subject groups

Subjects" Extensor Flexor

80 90 100 80 90 100

Skilled 0.313+0.102 b 0 .327_+0.117 0 .299_+0 .053 0 .172_+0 .031 0 .239_+0.045 0.287_+0.029 (5) c (6) (15) (5) (6) (15)

Less skilled 0.322+0.007 0 .295_+0.083 0.322+0.089 0.123+0 0.212+0.051 0.168_+0.070 (2) (4) (16) (2) (4) (16)

Combined 0.301 _+0.075 0 .309_+0.101 0 . 3 1 9 _ + 0 . 0 5 9 0.160_+0.030 0.220 _+0.039 0.221 +0.086 (7) (10) (31) (7) (10) (31)

There were 3 skilled and 3 less smiled subjects b Mean + SD c Number of analyzed rifts (N)

The two-way (session by percentage) ANOVA revealed no significant difference (p = 0.78) between the mean extensor durations of 0.308, 0.322 and 0.328 s for the 80, 90, and 100% lifts as performed by Subjects 3, 4, 8 and 7. The mean flexor durations, however, of 0.160, 0.241 and 0.270 s, respectively, were different (p <0.01). These observations were further investigated by an experience (skilled vs. less skilled) by percentage (90 and 100%) ANOVA. As confirmation of the previous procedure, the analysis detected no experience (p = 0.93), percentage (p = 0.75) or interaction (p = 0.34) effects for the extensor durations. Taken together, the analyses indicate that the duration of the resultant extensor muscle torque associated with the first pull remained constant for both groups of subjects over the relative loads examined.

The trend exhibited by the flexor durations, however, was more complex as both the experience [F(1,3) = 7.80, p <0.09] and experience-percentage [F(1,3) = 17.27, p <0.05] effects were significant. The interaction was the dominant influence and reflected a difference in strategies adopted by the two groups of subjects. Specifically, at the 90% load the flexor durations were reasonably comparable at 0.239 and 0.212 s for the skilled and less skilled

athletes, respectively. For the 100% weight, however, the less skilled lifters shortened the duration of their net flexor activity by ~50 ms while the more capable subjects lengthened their resultant flexor contribution by a similar amount. As a consequence, the flexor duration of the latter group was approximately double that of the less experienced l i f ters (0.287 vs 0.168 s) at the maximum resistance. Thus, the data indicated that flexor duration was not constant across loads and that the direction of the change depended upon the level of expertise.

Intensity of Net Muscle Activity

An approach similar to that utilized with duration was used to analyze the average resultant muscle torques during the two periods. A s before, the

similarity of performance between sessions was examined with one- (session) and two-way (session by percentage) ANOVAs on all lifters and on Subjects 3, 4, 8 and 7, respectively. The procedures detected no significant session or session-percentage effects (all p values >0.28) for the average extensor torques. Although the average flexor torques were different (p <0.01) between sessions (26.1 vs.

Table 2. Average resultant muscle torques (N.m) during the periods of knee extensor and flexor activity associated with the first pull and the second knee bend, respectively, for the expected loads (80, 90, and 100%) as performed by the skilled, less smiled, and combined subject groups

Subject Extensor Flexor

80 90 100 80 90 100

Skilled 53.9+-4.9 a 53.9+ 4.9 59.7+11.2 17.8+6.6 27.6+8.2 33.8+10.0 Less skilled 41.3+6.7 50.9+15.7 61.3+11.1 9.5+1.1 20.4+2.4 19.6+ 9.2 Combined 52.5+8.3 53.7+11.0 60.0+ 4.9 15.7+4.7 24.1+6.1 25.0+11.8

a Mean + SD


21.8 N.m) for the four subjects (3, 4, 8 and 7) there was no interaction effect (p = 0.41). A subsequent ANOVA on the 100% flexor torque results further revealed no session-experience interaction (p = 0.34). Thus, while the mean flexor torque was different between sessions the relative differences across percentage and experience were similar. That is, variations which existed in the percentage and experience data for session one were also included in that for the second session. Both the extensor and flexor torques, therefore, were collapsed across sessions (Table 2)

The session by percentage ANOVAs on Subjects 3, 4 8 and 7 found the mean torques for both the extensors (49.8, 51.3 and 58.0 N.m) and f lexors (15.7, 25.7 and 30.5 N.m) to differ significantly [F(2,5) = 5.18, p <0.05 and F(2,5) = 8.69, p <0.05, respectively] across the 80, 90 and 100% loads. No statistically significant differences were detected between the two groups of subjects (experience) for either the extensor (p = 0.98) or flexor (p = 0.11) torques at 90 and 100%. There was also no experience-percentage (90 and 100%) interaction for either the extensor or flexor torques (all p values >0.26). The analyses, therefore, indicated that the athletes lifted greater loads by increasing the intensity of both the extensor and flexor involvement. That is, the average resultant muscle torque co-varied with load.

Discussion

Based upon observations dating from at least the previous century, investigators have suggested that muscle function during rapid learned movements is controlled by pre-programmed as well as feedback influences. In an attempt to identify variables that might be regulated during such motion, considerable effort has been focused on examining the invariant characteristics of movement patterns in the context of various contingency sets. For example, the speed control system hypothesis (Freund and Bfidingen 1978) proposes, for a rapid learned task, that average movement duration represents one such regulated variable and is controlled by co-varying the magnitude of the muscle contraction with load. The term "speed control system", however, is a misnomer since the scheme actually postulates a constant duration and a variable speed.

The object of the study was to examine the merit of the speed control system hypothesis within a more extensive movement paradigm than had been previously utilized. Among the contingencies detailed earlier, one of the differences between the present and prior experimental conditions was the occur-

rence in the weightlifting event of movement about joints other than that being analyzed. Such movement, however, should not be construed as invalidat- ing the study as a test of the hypothesis for while both the equilibrium point and speed control system hypotheses evolved from consideration of single joint systems, each can also be envisaged as a mechanism for generating trajectories in multiarticular movements (e.g., Bizzi et al. 1982; Hollerbach 1982). In this vein, movement about any of the joints (i.e., ankle, knee, or hip), had it satisfied the multidirectional contingency, would have provided an appropriate basis for the analysis.

The results obtained indicate that when the contingency set is expanded (viz., to include multidirectional, multiarticular, large muscle groups and near maximum torque elements) the speed control system theory provides an incomplete account of the regulated variables. The hypothesis, however, was not completely invalidated, for as predicted, the duration was constant for the first component of the movement and the intensity of muscle activation did co-vary with load in both components (cf. Ghez 1979). For the subsequent interval, the period of resultant flexor muscle torque, the duration was not constant and further, the direction of the change depended on the subject skill level.

In elementary learned unidirectional goal- directed tasks, provided the speed of movement is >1.5 rad/s, the EMG record of an agonist-antagonist muscle-set is typically triphasic (Wachholder and Altenburger 1926). According to Feldman (1980a), the myoelectric histories represent a dominant pattern of reciprocal activation that tends to mask a background coactivation. The three bursts of EMG, two agonist epochs separated by antagonist activity, represent an acceleration toward the goal, a braking of the movement (cf. however, Ghez and Martin 1982) and a final target location effort (Woodworth 1899), respectively. In multidirectional motion (e.g., Fig. 3), however, the relative excitation (reciprocal) pattern is not triphasic but rather, within each component of the movement, is biphasic. Function- ally these two epochs represent (i) an acceleration in a given direction followed by (ii) a braking (eccentric) and subsequent acceleration (concentric) in the opposite direction. Interestingly the two groups of subjects employed in this study adopted different strategies to attain the change in direction. Both sets of subjects increased the mean flexor resultant muscle torque with increases in load, but the skilled group also increased the duration of the net flexor activity while their less capable counterparts temporally decreased the flexor involvement. The result was an increase in the net flexor muscle torque with


Rz(J+I) Rx(J§ CSz(J+I) maz /

/ I #MT(J+,) CGx, CGz~max

R (d) ; ~ x

Free Body Mass-Acceleration Diagram Diagram

Fig. 5. The basis for deriving the equations of motion of a generalized segment. The x-z coordinates are cited in pairs while the forces and torques are associated with vectors. Consult the Appendix for an explanation of the symbols

load by the better subjects and a decrease by their colleagues.

Many variables influence the net torque that a muscle-set produces. Among these are the recruit- ment and activation rate and pattern of motor units, prior history (e.g., effects of warm-up, fatigue, potentiation) and the classic torque-velocity and length-torque relationships. Mechanically, one of the major differences between uni- and multidirectional movements lies within the realm of prior history. Specifically, within the framework of the storage and utilization of elastic energy it is known that a muscle can perform more work upon shortening if it has been previously stretched (Cavagna 1977). Further, the extent of this enhancement has been demon- strated to depend on the time delay between the lengthening and shortening (Cavagna et al. 1974), the velocity of the stretch (Rack and Westbury 1970) and the amplitude of the stretch (Cavagna et al. 1972). The DKB is precisely the type of movement which maximizes the elastic energy transfer from the lengthening to the shortening phase (Alexander and Benet-Clark 1977; Asmussen and Sorensson 1971; Bosco and Komi 1979). Thus, multidirectional movements contain at least one additional factor that the system must consider and it would appear, therefore, that the control of multidirectional learned movements is more involved than the mere specification of an average movement speed.

Appendix

In the analysis of the DKB in Olympic weightliffing, the lifter- barbell system was considered to comprise eight rigid links;

namely, feet, legs, thighs, torso, head, (upper) arms, forearms, and hands-barbell. The equations of motion for each segment were derived by progressing sequentially through the model from a known external condition, the ground reaction force, utilizing the Newtonian approach. In this procedure a free body diagram of a segment is equated to an appropriate mass-acceleration diagram (e.g., Andrews 1982; Crowninshield and Brand 1981; Miller and Nelson 1973).

Figure 5 represents such a configuration for a generalized segment. Essentially the equations are derived by setting the external forces, and the torques they produce about the center of gravity (CG), equivalent to the inertia forces (ma) and torques (Ia), respectively. In a planar situation the external forces (F) can be resolved into a weight (W) vector, vertical (R~) and horizontal (Rx) joint reaction forces acting on the proximal (J+l) and distal (J) segment limits and resultant muscle torques (RMT) about the proximal and distal locations, In a similar vein, the inertia forces and torques can be expressed in vertical (maz), horizontal (max) and angular (Igct) terms as the product of mass (m) and acceleration (a) for the finear components and the moment of inertia (Ig) with respect to a transverse axis through the CG (g) and angular acceleration (a) for the angular contribution. In vector notation these relationships can be stated as:

and ZF = mag

ZMg = IgOr

In two dimensional space, these statements produce three scalar equations of motion. Specifically, with respect to the generalized segment in Fig. 5, where CS (J+I) and CS (J) represent the proximal and distal segment limits, respectively:

YFx = max -Rx(J) + Rx(J+l) = max [1] YFz = ma~ -R~(J)-W + R~(J+I) = max [2] ZMg = Iga -(R~(J)* (CSx(J) - CGx(S))) -(Rx(J)* (CSz(J) - CGz(J))) -RMT (J) + RMT (J+l) -Rz(J+l)* (CSx(S+l) - CGx(J+I)) ) -Rx(J+ 1)* (csz(J+ 1) - CGz(J + 1))) = Ig c~ [3]

In equation [3] the moment arms (e.g., CSx (J) - CGx (J)) refer to absolute distances.

The acceleration information was determined from the cinematographic records, the body segment parameters were estimated from cadaver data (Chandler et al. 1975) and the ground reaction force, which provided the initial Rx (J) and Rz (J), were measured by the force platform. With regard to this external condition, the force platform output also provided information on the point of application (Ax) of Rx (1) and ILL (1) and since no RMT existed between the distal end of the foot and the floor, RMT (1) was set to zero. Thus, as the analysis was performed from the ground reaction force upward through the system, the only unknowns in equations [1], [2] and [3] were the forces and torques acting at the proximal end of the segment. The equations were, therefore, reorganized to solve for the unknowns:

Rx(J+l) = Rx(J) + max [4] Rz(J+l) = Rz(J) + W + max [51 RMT (J+l) = RMT(J) + (R~(J)* (CSx(J) - CGx(J))) + (Rx(S)* (CSz(J) - CGz(J))) +(Rz(J+l)* (CSx(J+I) - CGx(J+l))) +(Rx(J+l)* (CSz(J+I)- CGz(J+I))) + Iga [6]


Acknowledgements. I am grateful to Drs. R.S. Hutton, D.I. Miller, and R.W. Schutz for their assistance during the course of the investigation, to Drs. T.M. Hamm, Z. Hasan, W. Koehler, D.G. Stuart, and M.C. Wetzel for constructive criticism during the preparation of the manuscript, and to Mrs. P. Pierce for help with the figures.

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Received August 17, 1982

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