ELSWIER Human Movement Science 15 (1996) 101-I 14

The effects of practice on movement reproduction: Implications for models of motor control

D.B. Ilic a, Daniel M. Corcos bqc, Gerald L. Gottlieb c*d, Mark L. Latash e, * , Slobodan Jaric a3f

a Faculty for Physical Culture, University of Belgrade, Belgrade 11000, Yugoslatiia b College of Kinesiology (M/C 194), University of Illinois at Chicago, 901, West Rooserelt Road, Chicago.

IL 60680, USA ’ Department of Neurological Sciences. Rush Medical College. Chicago, IL 60612, USA

’ Department of Physiology, Rush Medical College, Chicago, IL 60612, USA ’ Department of Exercise and Sport Science, Biomechanics Laboratory, Pennsylvania State Unioersity,

Unicersity Park, PA 16802, USA f Institute for Medical Research, University of Belgrade, Belgrade 11000, Yugoslaria

Abstract

This study investigated how consistently and accurately subjects could reproduce final move- ment position when performing three different movement tasks over four experimental sessions. Task 1 involved moving five different inertial loads over one movement distance. Task 2 involved

performing movements over five different distances against a constant inertial load. Task 3 involved moving five distances against five inertial loads that were adjusted to keep movement time relatively constant. Subjects who had practised Task 1 demonstrated the largest decrease in variable error over experimental sessions but little change in constant error. Subjects who had practised Task 2 showed a smaller improvement in variable error and no improvement in constant error. Subjects who had practised Task 3 demonstrated a small change in variable error and an improvement in constant error. The largest reduction in variable error in the first group is consistent with the equilibrium-point hypothesis of motor control but not with force-control models. The improvement in constant error in the third group is discussed with respect to a possible role of noise in practising simple movements.

* Corresponding author. E-mail: ml11 1 @psu.edu, Fax: + 1 814 865-2440, Tel: + 1 814 863-5374.

0167-9457/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved

SSDI 0167-9457(95)00042-9

102 D.B. Ilic et al/Human Mouemenr Science 15 (19961 101-114

PsyclNFO class#cation: 2330

Keywords: Movement; Practice; Equilibrium point; Error; Human

1. Introduction

Two competing approaches to single-joint motor control may be termed force-control and equilibrium-point (EP) control. According to the first ap- proach, the central nervous system calculates required time patterns of muscle forces and controls the movement by sending signals to the muscles that give rise to these force patterns (Atkeson, 1989; Bock and E&miller, 1986; Bock et al., 1990; Wallace, 1981). According to the second approach, the central nervous system manipulates equilibrium states of the joint while muscle forces (as well as electromyograms) emerge during the movement and depend on both control signals and actual movement kinematics (Feldman, 1986; Feldman et al., 1990).

Earlier, we performed two studies (Jaric et al., 1992, Jaric et al., 1994) the results of which can be interpreted in the framework of EP-control but not force-control. These studies assumed that learning a control pattern should lead to improved movement reproducibility. If a force pattern is learned, one may expect lower indices of variability in tasks that require reproduction of the learned force pattern, e.g., during movements over the same distance when starting from different initial positions. On the other hand, if an equilibrium point is learned, one may expect lower indices of variability during movements to the same final position when starting from different initial positions. Jaric et al. (1994) have shown better reproduction of final position, even in the group that was specifically instructed to learn movement distance during extensive practice. This finding is consistent with the EP-control approach but not with the force-control approach.

According to the EP-control approach, if a subject is practising an isotonic movement ‘as fast as possible’ to a fixed final position, the central nervous system shifts at a close to maximal rate a variable associated with joint equilibrium position (r) to a final value (Feldman, 1986). The final value of r is the only parameter that needs to be learned by the hypothetical controller in order to successfully reproduce the practised movement. Note that EP-control is rather insensitive to transient force changes during the movement (cf. equifinal- ity of perturbed movements, Bizzi et al., 1976; Kelso and Holt, 1980; Schmidt and McGown, 1980; Latash and Gottlieb, 1990). In particular, an increase in

D.B. Ilic et al./Human Mouement Science 15 (1996) 101-114 103

inertial load should not require the controller to use a different control pattern. Therefore, if one practises movements against different inertial loads to the same final position, EP-control predicts a high level of success and correspondingly low indices of variability because only a single parameter (final r> needs to be learned. On the other hand, movements against the same inertial load over different distances pose a much harder task for EP-control. The controller needs

to learn as many final values of r as the number of distances used during practice.

According to force-control approach, changes in inertial load and in move- ment distance are equivalent in the sense that they require comparable changes in force patterns generated by the agonist and antagonist muscles (Gottlieb, 1993). This approach predicts comparable indices of variability in subjects practising movements over different distances and those practising movements against different inertial loads. One may also co-vary distance and load in such a way, that movement time remains approximately constant (e.g., when move- ments over larger distances are performed against smaller loads). In this situation, the subject might use approximately the same force patterns in different trials, and therefore, might be expected to demonstrate lower indices of variability. Note, that from the EP-control standpoint, adding or subtracting inertial loads should not help or hinder the control system. As such, movements over different distances should have similar indices of variability despite changes in inertial load.

The following series of experiments were designed to test the predictions of the EP-control and force-control approaches and thus to provide support for one of these two competing views. The subjects practised movements over the same distance against different inertial loads (load group - LG), over different distances against the same inertial load (distance group - DG), and under a covariation of load and distance that approximately preserved movement time (load-distance group - LDG). Table 1 summarizes the predictions of the EP-control and force-control approaches in these three conditions under the

Table 1 Predictions from the equilibrium-point and force-control models for variable error

LG DC LDG

EP-control Best Poor Poor

Force-control Poor Poor Best

Three groups of subjects practiced movements against different loads (LG), over different distances (DG) and

over different distances with a load subtracted as distance increased (LDG).

104 D.B. Ilic et al./Human Moaement Science 15 (1996) 101-114

assumption that the best performance will be achieved on tasks that require learning the fewest values of the control variables.

2. Materials and methods

2.1. Subjects

Eighteen healthy male subjects were tested in these experiments. All the subjects were between the ages of 18 and 24 years and without any previous experience in the laboratory.

2.2. Experimental setup

Subjects sat in a rigid chair with their right arm abducted 90”. The forearm was placed on a light and almost frictionless rigid manipulandum which permitted rotation about the elbow joint in a horizontal plane. Joint angle was measured by a linear potentiometer. Subjects viewed a rigid arrow at the distal end of the manipulandum, and fixed narrow markers displaying large numbers, + 2, + 1, 0, - 1, and - 2 indicating different final elbow positions. Prior to each movement, the experimenter identified the target for the subject.

2.3. Instructions

Each subject was instructed to keep his arm muscles relaxed at the starting position. He heard three computer generated tones in sequence, two seconds apart. On the first tone he was instructed to close his eyes. When the second computer-generated tone sounded, he was instructed:

“Move your forearm into the target as fast as possible. I know that you will almost always miss the target. You may adjust your next movement on the basis of the previous undershoot or overshoot, but only under the condition that you not slow down. Do not adjust your final position.” On the third tone he was instructed to open his eyes, observe and remember

his overshoot or undershoot, if any, and return to the starting position. Prior to each trial he was told the location of the target for the next movement.

2.4. Experimental groups

The subjects were assigned to three experimental groups depending of the movements they were instructed to learn. Each of the three groups had six subjects and performed five different movements.

D.B. Ilic et al./Human Mouemenr Science 15 (1996) 101-114 105

(1) Load group (LG) subjects were instructed to perform 36” movements from an initial position of 125” to a final position of 89” with five inertial loads. The total loads (forearm + manipulandum + additional weights) were 0.2 kg . m*, 0.25 kg. m*, 0.3 kg * m*, 0.35 kg. m* and 0.4 kg. m*.

(2) Distance group (DG) subjects were instructed to perform elbow flexion movements with a fixed inertial load of 0.3 kg . m* (including the forearm and manipulandum) over five movement distances. Initial position was 125”, while final positions were 103”, 96’, 89”, 82” and 75” of elbow angle. Therefore, movement distances were 22”, 29”, 36”, 43” and 50”.

(3) Load-distance group (LDG) subjects were instructed to perform move- ments over five different distances with a different load at each distance. Distance and load covaried such that the longer movement was performed with the lighter load. The following combinations of load and distance were applied: 0.2 kg. m* and 50”, 0.25 kg. m* and 43”, 0.3 kg. m* and 36’, 0.35 kg. m* and 29” and 0.4 kg . m* and 22”.

The combinations of loads and distances for the LDG were selected on the basis of pilot measurements on two representative subjects. These subjects performed movements over five distances against different inertial loads. Lighter loads were selected for longer distances keeping movement duration approxi- mately constant.

2.5. Experimental procedure

During the learning procedure, each subject performed 500 movements ‘as fast as possible’ over approximately a one week period (three sessions of 155 movements each and a fourth session of 35 movements, every other day). The first three sessions had five practice movements and five blocks of 30 move- ments each. The fourth session had five practice movements and one block of 30 movements. The intervals between two consecutive movements within a block were 10 s; the intervals between two consecutive blocks were 2 min. Only the first movement block of each session was recorded. Within a block, each particular distance and/or each particular load were repeated six times. Within each group, the order of presentation of different distances and/or different loads was randomized; the subjects always knew, prior to each trial, over which distance and/or against which load they were going to move.

2.6. Data acquisition and procession

Position data were digitized at a sampling rate of 250/s and digitally low-pass filtered with a 20 ms moving average window. Final position was

106 D.B. Ilic et al./Humn Mol,ement Science 15 (1996) 101-114

1.5 L

1 2 3 4

SESSION

Fig. 1. Variable error + s.e. is plotted versus experimental session for movements performed over one

movement distance against five inertial loads (LG), five movement distances (DG) and five movement

distances with the load adjusted to keep movement time approximately constant (LDG). Each set of data is

averaged over six subjects.

measured 500 ms after movement initiation. Since the subjects performed very fast movements, were told not to correct them, and had their eyes closed, the limb was virtually motionless at the time of measurement. Variable error was assessed by the standard deviation of final position, while constant error was calculated as difference between averaged final position and the middle of actual target location. The data were analyzed by one-, two-, and three-way analyses of variance (ANOVA); the main factors included session number, group, and task (amplitude, load, or amplitude/load combination). A post-hoc Scheffe test was also used.

3. Results

Practice led to a reduction in variable error that was dependent on which of the three movements tasks were performed (Fig. 1). A two way analysis of variance was performed on the variable error data. The first factor was experi-

Fig. 2. Constant error is plotted versus experimental session for movements performed over one movement

distance against five inertial loads (LG. part A), five movement distances (DC, part B) and five movement

distances with the load adjusted to keep movement time approximately constant (LDG, part C). Each set of data is averaged over six subjects. Vertical bars show standard errors.

D.B. Ilic et al/Human Movement Science 15 (1996) 101-114 107

A

4-

2 -

O-

-2 -

-4 -

+ load .2 -_i.* - 1306 .25 + load .3

0 i$3::.:is - load.4

0 1 2 3 4 5

SESSION

B

1 2 3

SESSION

4 5

I I I I I I 0 1 2 3 4 5

SESSION

108 D.B. Ilic et al./ Human Movement Science 15 (1996) 101-114

mental group (load, distance, and distance/load) and the second factor was experimental session (four sessions), which was a repeated factor. There was a group by session interaction (F(3,45) = 4.90, p = 0.0006). There was also a main effect of experimental group ( F(2,15) = 17.09, p = 0.001) and a main effect of experimental session (F(3,45) = 15.44, p = 0.001). Three separate one way repeated measures analyses of variance were performed on the three groups. Each group improved over the four experimental sessions (LG, F(3,15) = 14.5, p = 0.0001; DLG, F(3,15) = 8.796, p = 0.001; DG, F(3,15) = 3.69,

p = 0.03). We also performed one way analysis of variance on the variable error data for

session 1 and session 4 separately. There was no effect of experimental group (load, distance and distance/load) for session 1 (F(2,15) = 1.032, p = 0.3803). For session 4, there was a significant effect of group ( F(2,15) = 13.29, p =

0.0005) reflecting the larger improvement in performance by LG (cf. Fig. 1). Scheffe post hoc tests showed that the distance group and load group were not significantly different from each other. In contrast the load group was signifi- cantly different from both the distance group and the load group (cf. the prediction of EP-control in Table 1 of the biggest improvement in performance for the LG group).

The data in Fig. 2 show changes in constant error for the LG (part A), the DG (part B) and the LDG (part C> with practice sessions. The vertical bars show standard errors. Two way analyses of variance were performed on the data for each group. The first factor was experimental condition (either five loads, five distances or five distance/load combinations). The second factor, four experi- mental sessions, was a repeated factor. Fig. 3 shows the same data organized differently so that some of the interaction effects are better seen. The data in Fig. 2A and Fig. 3A show that there was an interaction between load and experimental session F( 12,601 = 8.07, p = 0.0001. For the first three sessions, the effect of inertial load was similar. By session 4, the movements with the heavier loads slightly overshot the target. These data also show that there was a small shift in constant error as inertial load increased F(4,20) = 3.79, p = 0.018. Light loads overshot the target and heavy loads undershot the target with the exception of session 4. There was no main effect of experimental session F(3,15) = 2.08, p = 0.14.

Fig. 3. Constant error is plotted versus inertial load (LG, part A), movement distances (DG, Pati B). and

movement distances with the load adjusted to Each set of data is averaged over six subjects.

movement approximately constant (LDG, part Cl

D.B. Ilk- et al./Human Mooement Science 15 (1996) 101-114 109

A 4

+SESSION 1

3- -D-SESSION 2 +SFSSION 3 -0 -SESSION 4

2

_t !.-___

‘0

1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

INERTIAL LOAD (kS.m’)

B

4’ I I I I f I I

IS 20 25 30 35 40 45 50 55

MOVEMENT DISTANCE (deg)

-4 1 I I 1 I I I I I

15 20 25 30 35 40 45 50 55

MOVEMENT DISTANCE (dcg)

110 D.B. Ilic et d/Human Mooement Science 15 (IYY51 101-114

The data for the DG in part B of Fig. 3 only showed an effect for distance F(4,20) = 38.24, p = 0.0001. The DG overshot the shorter distances and under- shot the longer distances. There was no main effect of session F(3,15) = 1.04, p = 0.39 and no interaction, F( 12,60) = 1.65, p = 0.09.

The data for the LDG group had a session by distance/load interaction F(12,60) = 5.717, p = 0.0001 most clearly seen in part C of Fig. 3. For session 1, subjects overshot the shorter movements and undershot the longer distances as in the distance condition but learned to compensate for this tendency by session 4. There was a main effect of distance/load F(4,20) = 5.64, p = 0.003 but no effect of experimental session F(3,15) = 0.52, p = 0.67.

4. Discussion

4. I. Changes across sessions

The data that we have presented demonstrate that movement location be- comes very consistently reproduced when movements are practised against different sets of inertial loads (Fig. 1, LG condition). With practice, the variable error of LG decreases two-fold, from about 3” to 1.5”. This decrease in the variability of final position is similar to that previously reported for movements practised at one movement distance against a single inertial load (see Figure 5B in Corcos et al., 1993). Movements performed over different distances from different starting positions and movements performed over different distances with loads reduced as distance increased also showed improved performance although the improvement was modest and much smaller than for LG. In particular, DG showed a decrease in the variable error from about 3.2” to 2.7”, while LDG decreased the variable error from 3.6” to 2.9”.

In terms of constant error, practising movements over one distance caused the movements against larger loads to slightly overshoot the target on average while the movements against lighter loads tended to undershoot the target. This effect was small, however, since the constant error varied by only about + 1” with respect to perfect movement reproduction. It is clear that reproducing several movement distances was a more difficult task since the absolute values of the constant error were two- to three-fold higher than for LG and no improvement in constant error took place even after four sessions of practice. The observation that movement distance is not as well reproduced as location has been reported previously (Jaric et al., 1992) and is consistent with the range effect or contraction bias (Poulton, 1988). The ‘range effect’, ‘contraction bias’ or

D. B. llic et al. / Human Mol,ement Science 15 ( 1996) IOI- 114 111

‘regression effect’ refers to the fact that short distances are overestimated and long distances are underestimated. This difficulty in reproducing movement distance extends previous results by showing that practice does not lead to a considerable improvement in the reproduction of movement distance. This observation may be related to more difficulties experienced by subjects in memorising movement amplitude as compared to memorising final position, and is consistent with findings that distance information decays over time and as such would be less well retained at subsequent testing sessions (Posner, 1967). In a previous study (Jaric et al., 1992), we argued that, within the framework of the EP-hypothesis, reproducing final position requires memorising a value of only one variable at a hypothetical control level, while reproducing movement distance requires adjustment in values of two control variables. The present study extends these arguments to movements performed over one distance against different inertial loads.

What is most intriguing in this data set is the finding that subtracting a load proportional to distance facilitates the reproduction of movement distance which is reflected in the decrease in the constant error although without a change in the variable error. If we compare the data for the shortest movements in Fig. 2B and Fig. 2C for session 1, we can see that the movements were about 1” more accurate in Fig. 2C even on the first session. In addition, the movements with the distance adjusted loads increased in accuracy over the four experimental sessions. Conversely, if we consider the data for the longest movement distance, the movements overshot in session 1 but were almost perfectly accurate by session 4. The progressive subtraction of the load enabled individuals to learn a more accurate reproduction of movement distance and by session 4, movement distance was reproduced almost perfectly for all five distances. The effect of subtracting load will be considered in the next sections in which we discuss predictions of different models of motor control.

For behavioral changes to be considered learned, they need to meet at least one of three criteria (Brooks and Watts, 1988; Ito, 1976): 1. Repetition of behavior leads to change. 2. Improvements is retained over time even in the absence of performance. 3. The behaviors become less variable.

According to these criteria, the LG satisfied criterion 3 and was the least variable of all three groups. The LDG learned to more accurately reproduce movement distance. In order to understand why learning the load task produces the most consistent performance (Fig. 1) and why covarying distance and load leads to a reduction in constant error as a result of practice (Fig. 2C), we will consider two models of motor control. The first is the EP-hypothesis. The

112 D.B. Ilic et al./Human Mor’ement Science 15 (lY%I 101-114

second is a force based model in which final position is determined by the forces generated during the dynamic phase of the movement; within this model, errors in final position are due to errors in the force time profile.

4.2. Errors explained in terms of EP-hypothesis

In the Introduction, we made a point that the EP-hypothesis predicts the best reproduction of movements to a fixed final position independently of possible variations in inertial load (Table 1). At a first approximation, these movements require the subject to learn only one value, a final value of a central control variable r corresponding to the required final position. Therefore, greater reduction in variability by the group that performed 500 movements to the same final position (compared to the groups that had multiple final positions) fits the predictions of the EP-hypothesis. These findings extend previous results that location is well reproduced (Posner, 1967; Walsh and Russell, 1980; Wrisberg and Winter, 1985; Latash and Gutman, 1993).

One finding is unexplained, namely the lower constant errors after practice in LDG as compared to DG (Fig. 2, parts B and C>. Note that the lower constant errors in LDG were accompanied by variable errors that were as high as in DG. From the standpoint of EP-control, these two conditions are equivalent since changes in the inertial load do not require changes in the hypothetical control patterns. Some studies of learning the control patterns in non-equilibrium, dynamic systems have suggested that noise can actually help learning (Kelso and Schoner, 1988; Schiiner and Kelso, 1988). Burton and Mpitsos (1992) have shown that noise may accelerate learning in neural networks simulating a non-equilibrium, dynamic system. So, it is possible that covariations of inertial load in our LDG played the role of noise and helped the subjects to learn a relatively complex task, i.e., how to reproduce movements over different distances.

4.3. Errors in terms of force time profiles

An alternative approach to considering these results is from the perspective of a purely force based model in which force time profiles are scaled to perform a movement task (Meyer et al., 1988; Schmidt et al., 1979). In such models, the inertial load task requires that individuals learn to generate five such different force time profiles to cover the appropriate distance. The distance task requires that the individual also generates five different force time profiles to five different positions in space. The distance/load task requires a very similar force

D.B. Ilic et al./Human Movement Science 15 (1996) 101-114 113

time profile for all five movement conditions and to five different positions in space. Such a model suggests that the LDG task should be learned the best and does not distinguish between the other two tasks. This prediction is not supported by the variable error data of Fig. 1. This approach is consistent with the improvement in constant error shown in Fig. 2C but not with the constant errors shown in Fig. 2A and Fig. 2B since it predicts similar results for these data.

The presumption that, in isotonic conditions, the final position of a limb is an essential property of the central command (equilibrium-point control) has lead us to predict that tasks which require subjects to learn only a single final position will be learned better and/or faster than tasks with multiple final positions. Our experimental findings support the presumption. The control of muscle forces, to the extent that it fails to explicitly include compliant properties of the neuromuscular apparatus that produces limb movements, fails to predict the outcomes of these experiments. The equilibrium-point model unites ‘force control’ and ‘position control’ into one scheme based on control of equilibrium states of the system. Schmidt and McGown (1980) have shown that final position is accurately reproduced despite changes in load in the horizontal plane. They also demonstrated that movements against a load in the vertical plane undershoot the target by an amount due to forces provided by gravity. These findings are in a good correspondence with the EP-control of movements. Our study extends the arguments in favor of EP-control based on the investigation of the dynamics of positional errors during prolonged practice.

Acknowledgements

This study was supported in part by HHS grant JF-012 through the US- Yugoslav board of scientific cooperation, a grant from the Serbian Research Foundation, National Institute of Neurological and Communicative Disorders and Stroke Grants K06NS 01509, ROl-NS 28127, ROl-NS 28176, National Institute of Arthritis and Musculoskeletal and Skin Diseases Grant ROl-AR 33189, and National Center for Medical Rehabilitation Research at the National Institute of Child Health and Human Development R29-HD 30128.

References

Atkeson, C.G., 1989. Learning arm kinematics and dynamics. Annual Reviews in Neuroscience 12, 157-183.

Bizzi, E., A. Polit, and P. Morasso, 1976. Mechanisms underlying achievement of final head position. Journal

of Neurophysiology 39, 434-444.

114 D.B. llic et al. / Human Movement Science 15 (19%) 101-l 14

Bock, 0. and R. Eckmiller. 1986. Goal-directed arm movements in absence of visual guidance: Evidence for

amplitude rather than position control. Experimental Brain Research 62, 45 l-458.

Bock, 0.. D. Michael, D. Ott, and R. Eckmiller, 1990. Control of arm movements in a 2-dimensional pointing

task. Behavioral and Brain Research 40, 237-250.

Brooks V.B. and S.L. Watts, 1988. Adaptive programming of arm movements. Journal of Motor Behavior 20,

117-132. Burton R.M. and G.J. Mpitsos, 1992. Event-dependent control of noise enhances learning in neural networks.

Neural Networks 5. 627-637.

Corcoa, D.M., S. Jaric, G.C. Agarwal, and G.L. Gottlieb, 1993. Principles for learning single-joint movements

I. Enhanced performance by practice. Experimental Brain Research 94, 499-5 13.

Feldman, A.G., 1986. Once more on the equilibrium-point hypothesis (I model) for motor control. Journal of

Motor Behavior 18, 17-54.

Feldman, A.G.. S.V. Adamovitch, D.J. Ostry, and J.R. Flanagan, 1990. ‘The origin of electromyograms -

Explanations based on the equilibrium point hypothesis’. In: J.M. Winters and S.L.-Y. Woo (eds.1,

Multiple muscle systems. Biomechanics and movement organization (pp. 195-2131, New York e.a.:

Springer-Verlag.

Gottlieb, G.L.. 1993. A computational model of the simplest motor program. Journal of Motor Behavior 25,

153-161.

Ito, M., 1976. Adaptive control of reflexes by the cerebellum. Progress in Brain Research 44, 435-443.

Jaric. S., D.M. Corcoa, G.L. Gottlieb, D.B. Ilic. and M.L. Latash, 1994. The effects of practice on movement

distance and final position reproduction: Implications for the equilibrium-point control of movements.

Experimental Brain Research 100, 353-359.

Jaric, S.. D.M. Corcos, and M.L. Latash. 1992. Effects of practice on final position reproduction. Experimental

Brain Research 9 I, 129- 134.

Kelso, J.A.S. and K.G. Holt, 1980. Exploring a vibratory systems analysis of human movement production.

Journal of Neurophysiology 43, 1183-l 196.

Kelso, J.A.S. and G. Schiiner, 1988. Self-organization of coordinative movement patterns. Human Movement

Science 7, 27-46.

Latash, M. and G.L. Gottlieb, 1990. Compliant characteristics of single joints: Preservation of equifinality with

phasic reactions. Biological Cybernetics 62. 33 l-336.

Latash, M.L. and S.R. Gutman, 1993. ‘Variability of fast single-joint movements and equilibrium-point

hypothesis’. In: K.M. Newell and D.M. Corcos (edsl. Variability in motor control (pp. 157-1821. Human Kinetics, Urbana, IL.

Meyer. D.E.. R.A. Abrams, S. Kornblum, C.E. Wright, and J.E.K. Smith, 1988. Optimality in human motor

performance: Ideal control of rapid aimed movements. Psychological Reviews 95, 340-370.

Posner, M.I.. 1967. Characteristics of visual and kinesthetic memory codes. Journal of Experimental

Psychology 75. 103-107.

Poulton, E.C., 1988. The journal of motor behavior in the 1960s and 1980s. Journal of Motor Behavior 20,

75-78.

Schmidt, R.A. and C. M&own, 1980. Terminal accuracy of unexpected loaded rapid movements: Evidence

for a mass-spring mechanism in programming. Journal of Motor Behavior 12, 149-161.

Schmidt, R.A., H. Zelaznik. B. Hawkins, J.S. Frank, and J.T. Quinn. 1979. Motor-output variability: A theory for the accuracy of rapid motor acts. Psychological Reviews 86, 415-45 I,

Schiiner. G. and J.A.S. Kelso, 1988. Dynamic pattern generation in behavioral and neural systems. Science 239. 1513-1520.

Walsh. W.D. and D.G. Russell, 1980. Memory for preselected slow movements: Evidence for integration of

location and distance. Journal of Human Movement Studies 6. 95-105.

Wallace, S.A.. 1981. An impulse-timing theory for reciprocal control of muscular activity in rapid. discrete movements. Journal of Motor Behavior 13, 144- 160.

Wrisberg. C.A. and T.P. Winter, 1985. Reproducing the end location of a positioning movement: The long and short of it. Journal of Motor Behavior 17, 242-254.