Spatial topological constraints in a bimanual task

Spatial topological constraints in a bimanual task

Acta Psychologica North-Holland 77 (1991) 137-151 137 Spatial topological constraints in a bimanual task * Elizabeth A. Franz, Howard Piudue Uni...

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Acta Psychologica North-Holland

77 (1991) 137-151


Spatial topological constraints in a bimanual task * Elizabeth

A. Franz,


Piudue Uniuersify, West Lafayette, Accepted


N. Zelaznik






Previous research has shown that the concurrent performance of two manual tasks results in a tight temporal coupling of the limbs. The intent of the present experiment was to investigate whether a similar coupling exists in the spatial domain. Subjects produced continuous drawing of circles and lines, one task at a time or bimanually, for a 20 s trial. In bimanual conditions in which subjects produced the circle task with one hand and the line task with the other, there was a clear tendency for the movement path of the circle task to become more line-like and the movement path of the line task to become more circle-like, i.e., a spatial magnet effect. A bimanual circle task and a bimanual line task did not exhibit changes in the movement path when compared to single-hand controls, In all bimanual conditions, the hands were tightly temporally locked. The evidence of temporal coupling and concomitant accommodation in the movement path for the conditions in which the hands were producing different shapes suggests that spatial constraints play a role in the governance of bimanual coordinated actions.

A recent approach human motor actions appear to be controlled and those which are aspects (Heuer 1985).

toward examining the nature of constraints in has been to identify the characteristics that jointly for the two limbs, i.e. global aspects, controlled separately for each limb, i.e. local Identifying the global aspects of coordination

* Special thanks to J. Hultsman for many helpful comments on earlier drafts of this paper and to S. Wootton for help in debugging the algorithm used to quantify the results. We are also indebted to the members of R. Melara’s lab for their contributions and helpful questions. This project was a continuation of master’s thesis work done by E. Franz under the advisement of H. Zelaznik. During the initial stages of the project E. Franz was funded by a David Ross XR Grant awarded to H.N. Zelamik and a NIH Grant No. 510-1353-2578 awarded to A. Smith, H.N. Zelaznik and C. McGillum. Requests for reprints should be sent to E.A. Franz, c/o H. Zelaznik, Motor Behavior Laboratory, PEHRS, Purdue University, West Lafayette, IN 47907, USA.


0 1991 - Elsevier Science Publishers

B.V. All rights reserved


E.A. Franz et al, / Spatial constraints

provides insights into the central nervous system constraints that govern movement control. An abundance of empirical support has indicated that the timing properties of movements are powerful global constraints. Studies involving bimanual tapping (Klapp 1979; Peters 1977; Yamanishi et al. 1980) and timing tasks of anatomically distinct systems (Chang and Hammond, 1987; Klapp 1981; Muzii et al. 1984; Smith et al. 1986) have demonstrated the difficulty people encounter when attempting to produce two or more timing patterns that are not related by a simple harmonic. Movements that require advance planning also have shown strong evidence of temporal constraints (Heuer 1985; Konzem 1987, cited in Schmidt 1988). Performance of both discrete (Konzem 1987, cited in Schmidt 1988) and continuous (Heuer 1985) bimanual movement tasks is difficult when the production of different movements is required by the two hands. From these findings it is inferred that the spatio-temporal form of movements is a constraint controlled jointly for the two hands. The treatment of dual-task motor constraints can be conceptualized according to two prevailing views - the motor program and dynamic pattern perspectives. Motor program theorists assert that the global aspects of an action (relative motion patterns) are abstractly represented in a program, and the details of the action are prescribed as mutable parameters. Accordingly, a topological representation guides the movement but a number of variations in the details of the program may occur. The assumption based on traditional bottleneck theories of response execution (Keele 1973; Welford 1967) is that two different motor programs cannot be executed concurrently. On the other hand (no pun intended), proponents of the dynamic pattern perspective assert that actions result from self-organizing properties of biological systems. This view, put forth by Bernstein (1967) and rekindled by Turvey (1977) is consistent with the notion that the temporal and topological characteristics of movements are emergent properties of the dynamical structure of organisms. The notion of oscillators, as extended by the seminal work of von Holst (cited in Gallistel 1980) provides a basis for understanding this perspective. Out of von Holst’s work on the fin movements of fish emerged concepts such as the magnet effect and relative coordination. The former refers to the effect one oscillator imposes on another which results in the sustainment of a mutual phase relationship. The latter occurs when the slowing down or speeding up of one oscillator influences the magnitude

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of response of another oscillator, even though a 1 : 1 frequency ratio is not necessarily maintained. In other words, certain effecters may speed up and slow down because of the influence of other effecters. The work of Kelso et al. (1979) has been interpreted in light of the dynamic pattern perspective. It was demonstrated in a bimanual Fitts aiming task that each hand did not obey Fitts’ Law when a high index of difficulty movement assigned to one hand was combined with a low index of difficulty movement assigned to the other. The low index of difficulty hand produced a larger movement time than would be expected based on its single hand movement time, in an attempt to accommodate the movement time of the high difficulty hand (but see Corcos (1984) and Marteniuk et al. (1984) for slightly different interpretations). It is apparent from the abundance of literature on timing that the examination of temporal constraints has been the dominant approach used to investigate coordinated movements. An investigation of the contributions of spatial topological constraints in the control of such tasks, therefore, seems worthwhile. Recent evidence has, in fact, suggested that spatial constraints may play a significant role in coordination. In a bimanual Fitts aiming task, Kelso et al. (1983) placed an obstacle in the movement path of one limb but not the other. The limb that did not go over the obstacle produced a movement trajectory similar in form to that produced by the limb that ‘hurdled’ over the real obstacle. Kelso et al. (1983) claimed that the limb that jumped over the phantom obstacle produced this trajectory in an attempt to maintain temporal synchrony. An equally valid interpretation of these findings would be that the limbs were constrained spatially to move with similar trajectories. Additional evidence (Swinnen et al. 1988; 1990) suggests that deviations from temporal synchrony occur when the required limb movements are dissimilar in their spatio-temporal trajectories. In these experiments, one limb was required to produce an elbow flexion (unidirectional) movement, and the other limb was required to produce an elbow flexion-extension-flexion (reversal) movement. Initial performance of the bimanual task revealed a strong tendency for the reversal movement to impose its spatio-temporal pattern on the movement of the limb producing the unidirectional movement. The extant literature includes numerous examples of tasks whose


E.A. Franz et al. / Spatial constramts

temporal characteristics have been emphasized over the spatial characteristics. In tasks in which the spatio-temporal patterns of the movements were complex (e.g. Swinnen et al. 1988) the precise timing of the flexion-extension movements was required for their successful execution. Thus, it is clear that the timing control has been the dominant feature of these tasks. Most theorists in motor control postulate that the spatio-temporal form, i.e. pattern, of movements is the determinant of control in coordinated activity despite the lack of knowledge of how spatial constraints contribute to such actions. The present experiment is our initial attempt to examine the spatial rules of coordination. Because of the distinction that has been made in the neuromotor science literature concerning the fundamental nature of straight line versus curved line trajectory formation (Hollerbach 1981; Hollerbach and Flash 1982; Morass0 1981) we chose to employ tasks of these two forms, lines and circles. Specifically, we assumed, a priori, that a line movement is of a different spatial form than a circle movement . To apply a spatial analog of the temporally-based notions extended by von Holst, we attempted to determine whether absolute or relative spatial coordination would be observed in the concurrent production of circle movements by one hand and line movements by the other hand. One might think of absolute spatial coordination as the effect of one spatial form taking on the form of the other, i.e. a line becomes a circle. The term relative spatial coordination might be applied if the shapes of both tasks take on characteristics that are common, yet the line remains line-like and the circle circle-like. Continuous circle drawing movements and line drawing movements were performed in three types of experimental conditions: (1) producing circles or lines with one hand alone (single), (2) producing circles or lines with both hands (dual-same), or (3) producing circles with one hand and lines with the other (dual-different).

Method Subjects The subjects were four male and four female right-handed graduate and undergraduate volunteers from Purdue University. All subjects were naive to the purpose of the study.

E.A. Franz er al. / Spatial constraints


The apparatus consisted of a standard rectangular desk (90.0 cm long, 65.0 cm wide, 72.0 cm high) covered by black posterboard. Two white sheets of paper (28.0 cm x 36.0 cm) were placed on the desk. An audio amplifier was interfaced via a Scientific Solutions 12 bit Digital to Analog converter, with a Zenith ZW-248 computer. A mallory Sonalert 1800 Hz buzzer also was interfaced with the Zenith computer via a digital output board. Infrared light emitting diodes (IREDS) were mounted just above the writing tip of each of two 0.9 mm mechanical pencils. Ireds were also placed at each of three joints shoulder, elbow, and wrist - of each limb. ’ All ireds were sampled at 250 Hz via a Watsmart infrared recording system which was interfaced with a Compaq 386/16 computer. The static calibrations for each session ranged from 2.1-3.0 mm of RMSE. Task Two tasks were performed: a line task and a circle task. The line task consisted of drawing reciprocal lines in rhythm for a 20 s trial along the Y-dimension. The circle task consisted of drawing circles in rhythm (the direction of motion was not specified). Each task was to be drawn the approximate size indicated by templates which were presented to the subject at the beginning of the testing session. The line template was 27.0 cm long and the circle template was 54.0 cm in circumference. Both tasks were to be performed with a ‘stiff wrist and only the point of the pencil was to touch the drawing surface. Tasks were to be performed in pace with a metronome (600 ms per cycle). The metronome pace was terminated midway through each 20 s trial and the subject was to self-pace the remainder at the 600 ms cycle duration. Conditions and design Subjects performed four single-hand conditions (each hand performed lines or circles alone) and four dual-hand conditions (two tasks by two hands). The dual task conditions will be referred to as dual-same (both hands attempted to produce the same shape) or dual-different (one hand attempted to draw circles and the other attempted to draw lines). There were eight trials per condition. Subjects performed single-hand conditions first (with those conditions randomized across subjects) followed by dualhand conditions (also randomized). Procedure Upon entering the laboratory, the task requirements were explained after which each subject was asked to read and sign an informed document. A template of a line, i The purpose of this paper was not concerned with the joint angle kinematics. Before each testing session, we measured the subject’s limbs in order to use anthropometric measures in our analyses at a later date. We are fully aware of the importance in analyzing these data but at the present time our software programs are in their preparatory stages of development.


E.A. Franz et al. / Spatial constraints

27.0 cm in length, oriented along the Y-axis and another template of a circle, 17.2 cm in diameter (54.0 cm in circumference), were placed on the desk to indicate to the subject the shape and size for each task. The subject was informed that the templates were to be used only to indicate the approximate size task to draw, and that the shape of the movement was more important than the exact size. A trial began by a verbal ‘ready’ signal from the experimenter. The metronome then began and the subject performed the assigned task(s) in pace with the metronome. After 10 seconds the metronome terminated and the subject was instructed to continue performing the task(s) for another 10 seconds when a signal to stop occurred.

Results Data reduction The kinematic displacement data were filtered digitally, forward and backward, at a cut-off frequency of 10 Hz. A three-point difference technique was utilized to generate velocity measures. Numerical algorithms were used to ascertain kinematic landmarks. The first and last seconds of each trial were omitted, resulting in 3 equal time intervals each lasting 6 s. Spatial effects The line trajectory of a typical dual-different trial is depicted in fig. 1. The trajectory of lines became elliptical when the other hand produced circles concurrently



dual-hand SQrne

dual-hand different

Fig. 1. Typical displacement in mm in the X and Y dimensions of the line task performed alone (single), when the other hand also produced lines (dual-same) and when the other hand produced circles (dual-different), for a 20 s trial.


E.A. Franz et al. / Spatial constraints



I tingle-hand

dual-hcnd same

dual-hand different

Fig. 2. Typical displacement in mm in the X and Y dimensions of circles when performed alone (single), when the other hand also produced circles (dual-same) and when the other hand produced lines (dual-different), for a 20 s trial.

(dual-different) but not when the other hand produced a line (dual-same) or in the single hand condition (single). When the circle task was combined with the line task the circle topologies tended to take one of two forms. Either they became elliptical or they produced lines intermittently with the circles. The majority of cases were like those depicted in fig. 2 which illustrates that the path of the pencil became less circular and more elliptical when paired with the lines. Very little spatial disruption was observed when two circles were paired (dual-same) or when circles were performed alone (single). In order to quantify the shape of the two tasks, an index of circularity was computed1 for each period of these repetitive movements. If a subject produced a perfect circle, then the ratio of the two diameters should be one. On the other hand, if the X axis diameter is divided by the Y axis diameter of a movement that is approaching a perfect line, then the ratio should be equal to zero. This ratio measure was devised as an index for the shape of the circle and line tasks produced. The index of circularity measure was based on four points from the Y-dimension velocity profile that comprised one cycle of movement. The four points were the first zero cross, peak positive velocity, the second zero cross, and peak negative velocity. The X and Y position coordinates at each of these velocity landmarks were used to compute distances joining the points at the zero crossings and the points at the peak velocities. The ratio of these two distances was computed with the larger of the two numbers as the denominator. Thus, the index of circularity was within the range of 0 (most linear) to 1 (most circular). Fig. 3 depicts the index of circularity for the three conditions, (1) single-hand, (2) dual-same, and (3) dual-different, for the line and circle tasks across the 8 trials. As


E.A. Franz et al. / Spatial constraints


x .E D z









.*. .*

.* ” a ” a

0.5 -




v D &




Lines 0..




‘D Et ~+-a-_&q-+, B





43 .D



.a ’



Fig. 3. Mean index of circularity for lines and circles under the 3 conditions, single (dashed), dual-same (solid) and dual-different (dotted) for the 8 trials. Data are collapsed across left and right hands. Circle data are depicted as filled dots and line data are depicted as open squares. A perfect circle would be an index of 1.0 and a perfect line would be an index of 0.0.

depicted in the figure, these measures for lines and circles do not overlap, F(1,7) = 762.68, p < 0.001, which indicates that circle tasks could be distinguished from line tasks even under the conditions that are presumably most difficult (dual-different). As seen in fig. 3, the magnitude of change in the index of circularity for all circles was greater than that for all lines. The interaction of condition and task (circle or line) was significant, F(2,14) = 26.74, p < 0.001. Planned comparisons of the mean index of circularity produced in the single and dual-same conditions versus those produced in the dual-different condition were significant for both the line and the circle tasks, respectively, F(l,14) = 17,13 and F(1,14) = 60.66, p’s < 0.001 in both cases. This is depicted in fig. 3 by the decrease in the ratio metric for circles in the dual-different conditions and the increase in the ratio metric for lines in the dual-different conditions. ’ The main effect of hand was not significant, F(1,7) = 5.13, p > 0.05, which suggests that the disruption in spatial trajectories was not markedly different for the two hands. A trial b,y task interaction, F(7,49) = 5.58, p < 0.001, and a three-way interaction between trial, condition and task, F(14,98) = 5.52, p < 0.001, also were found. As indicated in fig. 3, the index of circularity for the first trial most likely produced these relatively small interactions (see the Appendix for a table of means and standard deviations for the spatial data). The main findings from the spatial analysis indicated that the index of circularity of the line task increased and the index of circularity of the circle task decreased in

2 All interactions that occurred across both tasks together will not be reported because, due to the directional nature of the index of circularity, circle ratios get smaller and line ratios get larger as more accommodation in the tasks occurs.


E.A. Franz et al. / Spatial constraints

Table 1 Means and standard deviations of half period and VE for lines and circles across the three conditions. Condition

Lines M VE Circles M VE


Dual-hand same

Dual-hand different

284 (33) 43 (18)

296 (63) 38 (21)

292 (09) 35 (10)

287 (21) 34 (11)

290 (10) 33 (16)

289 (24) 28 (08)

Note: Means and (standard deviations) are represented in ms.

conditions in which line tasks were combined with circle tasks. These results evidence for relative spatial coordination, i.e. a spatial magnet effect.


Temporal effects

The temporal measures of interest were the average time between successive velocity peaks, i.e. the half period, and its within-subject standard deviation, commonly called variable error, VE. Half periods were measured as the time between two successive peaks in the velocity profile (scalar absolute values) in the Y-dimension of motion. With respect to the dependent measure, half period, a main effect of time interval, F(2,14) = 8.88, p -C 0.01, indicated that the first 6 seconds of all trials averaged together were slightly faster than the subsequent 12 seconds. The mean cycle times for intervals 1, 2, and 3, were 285 ms, 291 ms, and 292 ms, respectively which indicates that subjects slowed down only 7 ms on average during each trial, across all conditions. An interaction between condition and interval, F(4,28) = 4.91, p < 0.01, indicated that single and dual-same conditions slowed down by approximately 10 ms and 5 ms, respectively, while dual-different conditions maintained the same average speed throughout the trial. Of primary importance with respect to the temporal data was the lack of an interaction between task and condition, F(2,14) < 1, which indicates that all tasks were produced at the same average speed under single- and dual-hand conditions (see table 1). The absence of such an interaction suggests that our temporal manipulation (metronome pace) was successful and that subjects were able to maintain the same average temporal metric even after the metronome was turned off. For VE in half period a main effect of interval was found, F(2,14) = 12.89, p < 0.01, indicating a larger VE for the first 6 s of the trial than for the remaining 12 s (38 ms compared to 35 ms). A significant interaction of hand and trial also was found, F(7,49) = 4.19, p < 0.01, wherein the VE became slightly smaller for the left hand across trials while the VE for the right hand remained the same.


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In sum, the lack of robust, and in our minds meaningful, temporal effects for the interaction of task and condition holds considerable importance. The lack of such effects indicates that the hands remained tightly temporally locked regardless of whether they produced the same tasks or two different tasks, circles and lines.

Discussion The present study examined the possible influence of spatial constraints in the coordination and control of bimanual movements. Subjects when asked to produce two movements of different spatial forms, circles and lines, tended to exhibit spatial accommodation in the performances of both tasks. In most cases this was manifest in a tendency for each task to look more like the task being performed by the other hand. These effects in the spatial domain occurred despite a tight temporal coupling of the limbs which suggests that a simple temporal explanation would not apply. It appears that a spatial magnet effect may be operating and it is the nature of that presumed effect that remains to be explained. It seems a parallel can be drawn between previous findings in the temporal domain of bimanual movement tasks and our present findings in the spatial domain. The majority of previous work has required subjects to perform two different movements as quickly as possible (i.e., Kelso et al. 1979; 1983; Konzem 1987, cited in Schmidt 1988), or two different movements in a discrete fashion where the precise timing of flexions and extensions of the limbs formed the basis of the temporal structure of the movement (Swinnen et al. 1988). These movement tasks all involved strict temporal requirements and minimal spatial demands. In such tasks the typical finding is a tendency of one hand to influence the temporal structure of the other hand’s movement. Simultaneity in the initiation and termination of movements has been reported (Kelso et al. 1979) albeit departures from simultaneity appear to be the rule rather than the exception (Corcos 1984; Martenuik et al. 1984; Swinnen et al. 1988). These findings provide strong evidence of relative coordination in timing, i.e. a magnet effect. In the present approach the opportunity for spatial deviations in the trajectories was maximized. Unlike previous work, any number of possible trajectories could have been produced because the movements were virtually unaffected by external physical constraints (other than

E.A. Franz et al. / Spatial constraints


the desktop surface). A relaxed temporal metric was employed so that the average speed of movement production would be maintained throughout the different task conditions. Our findings indicate that the two tasks did not become identical, rather the spatial topology of one task tended to influence that of the other. These findings provide evidence of relative spatial coordination, i.e. a spatial magnet effect. As in the temporal domain of movements, the effect of coupling in space is not absolute but relative (see Smith and Zelaznik (1991) for a review of coupling effects). It is reasonable to assume that the same processes are operating whether the basis of the observed magnet effect is temporal or spatial. One possible explanation for the results of the present experiment might be that movement organization is based on the minimization of one or several control parameters. The optimization of certain dynamic variables has been postulated as a possible mechanism in the formation of smooth single limb trajectories (Abend et al. 1982; Flash and Hogan 1985). The minimum jerk model explains trajectory formation by positing that a smooth trajectory is a desired one. Smoothness is maximized by minimizing the sum of the mean square jerk, i.e., the transient changes in acceleration. If a minimum jerk model could be applied to bimanual movements it would be expected that the two limbs operate by minimizing total jerk. Because the smallest magnitude of jerk results in a straight line trajectory, the prediction for the tasks employed in the present study would be that circles become more line-like while lines remain as straight lines. The observation that lines in the present study became more circle-like suggests that a strict version of this minimization model would not apply. An important feature of the minimum jerk model, relevant to our understanding of trajectory formation, is that predictions are based solely on hand trajectories without regard to specific neuromuscular variables. However, while it is generally believed that movement representation can occur either in joint coordinate space (Abend et al. 1982; Hollerbach and Atkeson 1986; Soechting and Lacquaniti 1981; Viviani and Terzuolo 1982) or in endpoint trajectory space (Hollerbach and Flash 1982; Merton 1972; Morass0 1981; Viviani and Terzuolo 1980), the rejection of a strong version of the minimum jerk model does not necessarily exclude either of these possibilities. Although the minimum jerk model is based on the kinematics of the hand movement in extracorporeal space, it is possible that the smoothness of hand trajec-


E.A. Franz et al. / Spatial constraints

tories would result from the internal mechanics of the neuromuscular system. An intimate relationship exists between torque and joint angle movement because torque must be generated by the musculature to produce changes in joint angles (Hogan 1984). Thus, another likely candidate for minimization may be the rate of change in torque. Accordingly, the minimum torque change model, proposed by Kawato and colleagues (Kawato et al. 1990; Uno et al. 1989), purports that limb movements find a unique trajectory by minimizing torque change. Unlike the minimum jerk model, this model depends on the dynamics of the musculoskeletal system. The model involves minimizing the sum of the square of the first derivative of torque. Because the torque produced by the components of the musculoskeletal system and the objective amount of force produced by the movement are not isomorphic, exact predictions based on this model involve elaborate measurements of neuromuscular variables. Thus, although the model would be difficult to implement for bimanual movements, it seems reasonable to conjecture that the change in torque is a plausible control variable minimized for the two limbs combined. We are suggesting that the way in which the bimanual movement system circumvents some of the problems that arise in controlling its vast number of degrees of freedom is by a single minimization principle. We believe that this attempt toward minimization forms the basis of the spatial magnet effect like that observed in the present work. Specifically, we are postulating that the minimization of relevant control parameters provides a constraint that operates by the two limbs combined in order to reduce the many degrees of freedom in producing coordinated movements. The present findings suggest that spatial effects hold considerable importance in bimanual movement control. At least two main issues for future work remain. One is concerned with representation, and the other is concerned with spatio-temporal constraints in the neuromuscular system. The minimization models put forth as possible mechanisms of control in bimanual movements address each of these issues. Whether the spatio-temporal constraints are emergent characteristics of the neuromuscular dynamics or whether they are prescribed by higher-order cognitive mechanisms, are issues that are difficult to resolve. Insight regarding the relative contributions of higher-order processes and lower levels of constraint and the way the two levels interact, might

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be gained if the appropriate manipulations are applied. It is possible, for example, given an appropriate higher-order organizational framework, that one might be able to produce circles and lines concurrently without producing spatial accommodation effects. Such evidence would suggest that higher-order constraints may be able to override the spatio-temporal constraints that occur at the lower levels of the system. This possibility is currently under investigation in our laboratory. Our laboratory is also investigating the effects of practice in these tasks to ascertain whether the inherent constraints can be altered through the development of new coordination strategies. In sum, the present study provides strong evidence that spatial constraints play an important role in the coordination of bimanual movement control. Circles, when performed concurrently with lines, became more line-like and lines became more circle-like. These spatial effects occurred despite a tight temporal coupling. Such findings may be interpreted as support for a spatial magnet effect which occurs in the coordination of bimanual movements that require different spatial patterns. The nature of this accommodation may be in a minimization principle that operates for the combined efforts of the two limbs.


Table A.1 Index of circularity means collapsed across trials.

and standard


for lines and circles

for the three conditions

Condition Single-hand


M SD Circles

0.104 0.072

0.086 0.028

0.164 0.078


0.852 0.072

0.819 0.117

0.598 0.129






E.A. Franz et al. / Spatial constratnts

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