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Exp Brain Res (1983) 51:135-145
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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, A Z 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 Olympic 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 P h . D . dissertation 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 - Weightlifting
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; Stetson 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 agonistantagonist 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
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 m o v e m e n t 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; W a d m a n 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 p a r a m e t e r 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 B o u m a n 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 exhibiting 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
R.M. Enoka: Control of a Learned Movement
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 l o a d 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 conventionalcontingencies
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 typicallytermed
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-backwardtrunk rotation is the realignment of the lifter relative to the barbell such that the maximum
contribution from the back and hip extensors, which occurs postSKB, 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 cinematographicrecord 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 approximately0.46 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
,80[
Extension
KNEE
ANGLE
(dog)
137
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.
160[
140[
120[
The Protocol
Flexion
0
Forward ~
rotation
TRUNK ANGLE----z~-Backward
(dog)
rotation
Fig. 1. Temporal relationship between the vertical and forwardbackward 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
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
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), sideto-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
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 conversion 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
138
R.M. Enoka: Control of a Learned Movement
A
Flexor
8o%
90%
200T'~ " ~ ' ~ ' ~ " ~ ' ~ ' ~
"~ )
~'l
100
TORQUE
(N. m)
.....
......... ~ : : ~ . - " . . . . . . . ~ . . . . ~
0
Ext|sore~n 200
1 0 I0 ~
6
6,
3
t
'"................' .......
V "
.......................... .......
"
20
40
60
8096
t
loo t
TORQUE
/-.
(rad)
"....... ~
~
?
t
~
9....
....
.
""-_.3"
i
.'
B
-Flexor 200~
Exte!sor
(N-m)
......... ;
~
"
3
2
"
....~
~....-
_61
0
100%
200
I UuI
_l G , ~
80
100
40 60 80
TIME (%)
20 40 60 80 100
100
90%
100%
I
t
~
......
I
" ..........
,~
2
iiiil
1
e
0 1 - -20 ' 40'
20
60
' : - - ' 80 " O0
" ~ ~
20
~.!!iiii~! ......
40 60 80
TIME (%)
100
........
~
'
............
....... ~
20
40
....
'
60'80'100
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-massacceleration method by proceeding from a known boundary
R.M. Enoka: Control of a Learned Movement
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-differentiation 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 differentiation, 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 positiontime 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 computed, 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 deviations of temporally standardized angular position,
angular velocity and resultant muscle torque histories
about the knee joint for both groups of subjects.
A t 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 m o v e m e n t , 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 p e a k 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) e m p l o y m e n t of the
knee extensors that lasted for 37% of the total pull
and reached m a x i m u m 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
139
Flexor
TORQUE
(N.m)
I
400[
200 ~
o/
i-........... .~
9
,
.
H
".~
..."
Ext!nsor
(tad/s-)
::[
V
9
3
9
(rad)
,
I
0
0
ZO
I
lOOms
40
60
80
TIME (%)
I00
Fig. 3. Mean (solidline) 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. R a t h e r 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 majority (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 p e a k values of 80 N . m as the net
contraction type changed from eccentric to concentric. For the final 6% of the time-frame the resultant
activity represented a braking of the second period of
knee extension as the athletes p r e p a r e d to m o v e
under the bar.
140
R.M. Enoka: Control of a Learned Movement
A
C
B
9
/
Jt
3o
40
.o[
" "
t
1,5o F,.0r
1
20
.,,~o
EMG
(%)
o
60
o..
9O
0
.or
. ~4
.2o
TIME (s)
.27
.34
ol . . . .
t:01
o
2o
I ul
4~
so
TIME (%)
eo
~oo
.:" , , : , , : I oTORQU.E
~
." j
f2.
L
4o
/
0
,vv mz
20
T!
40
60
80
1
(N mJ
Extensor
J| 50
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) E M G 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 E M G 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 takeoff 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 (sessionpercentage) effects for either the extensor or flexor
durations (all p values >0.15), the data were collapsed across sessions.
R.M. Enoka: Control of a Learned Movement
141
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"
Skilled
Less skilled
Combined
Extensor
Flexor
80
90
100
80
90
100
0.313+0.102 b
(5) c
0.322+0.007
(2)
0.301 _+0.075
(7)
0.327_+0.117
(6)
0.295_+0.083
(4)
0.309_+0.101
(10)
0.299_+0.053
(15)
0.322+0.089
(16)
0.319_+0.059
(31)
0.172_+0.031
(5)
0.123+0
(2)
0.160_+0.030
(7)
0.239_+0.045
(6)
0.212+0.051
(4)
0.220 _+0.039
(10)
0.287_+0.029
(15)
0.168_+0.070
(16)
0.221 +0.086
(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) A N O V A
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 lifters
(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
Skilled
Less skilled
Combined
a Mean + SD
Extensor
Flexor
80
90
100
80
90
100
53.9+-4.9 a
41.3+6.7
52.5+8.3
53.9+ 4.9
50.9+15.7
53.7+11.0
59.7+11.2
61.3+11.1
60.0+ 4.9
17.8+6.6
9.5+1.1
15.7+4.7
27.6+8.2
20.4+2.4
24.1+6.1
33.8+10.0
19.6+ 9.2
25.0+11.8
142
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 flexors
(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-
R.M. Enoka: Control of a Learned Movement
rence in the weightlifting event of movement about
joints other than that being analyzed. Such movement, however, should not be construed as invalidating 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 goaldirected 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. Functionally 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
R.M. Enoka: Control of a Learned Movement
143
Rz(J+I)
Rx(J§
CSz(J+I)maz /
/I#MT(J+,) CGx,CGz~max
R (d)
Free Body
Diagram
;~x
Mass-Acceleration
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
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:
ZF = mag
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 recruitment 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 demonstrated 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 lifterbarbell system was considered to comprise eight rigid links;
and
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
YFz = ma~
-R~(J)-W + R~(J+I) = max
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~
[1]
[2]
[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
Rz(J+l) = Rz(J) + W + max
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
[4]
[51
[6]
144
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