Limb-segment Selection in Drawing Behaviour

THE QUARTERLEY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 1993.46A (2) 273-299

Limb-segment Selection in Drawing Behaviour Ruud G.J. Meulenbroek

Downloaded By: [Radboud Universiteit Nijmegen] At: 06:25 25 February 2009

Nijmegen Institute for Cognition and Information, Nijmegen, The Netherlands

David A. Rosenbaum University of Massachusetts, Amherst, Massachusetts, U .S. A

Arnold J.W.M. Thomassen and Lambert R.B. Schomaker Nijmegen Institute for Cognition and Information, Nijmegen, The Netherlands How do we select combinations of limb segments to carry out physical tasks? Three possible determinants of limb-segment selection are hypothesized here: (1) optimal amplitudes and frequencies of motion for the effectors; (2) preferred movement axes for the effectors; and (3) a tendency to continue using already-recruited limb-segments. We tested these factors in a graphic production task. Seven subjects produced back-and-forth drawing movements of gradually changing amplitude. The largest amplitude to be covered, trial duration, movement axis, and direction of amplitude change (from small to large or vice versa) were varied between trials. Selspot recordings were used to study the relative contributions of the fingers, hand, and arm to displacements of the pen. The temporal order of limb-segment involvement was also studied. The results confirmed the predicted effects of the three limb-segment selection factors. We conclude that limb-segment coordination is adaptively related to biomechanical features of the motor system and to the computational demands of movement selection itself. Requests for reprints should be sent to Ruud G. Meulenbroek, NICI, PO Box 9104, HE Nijmegen, The Netherlands. Email: [email protected]. The research was supported by the Netherlands Organization for Scientific Research (NWO) Project 560-259-035 and the European Strategic Programme for Research and Development in Information Technology (ESPRIT) Project 419. The contribution of the second author was supported by Grants BNS 87-10933 and BNS 90-08665 from the National Science Foundation (USA), a Research Career Development Award from the National Institutes of Health (USA), and a Research Scientist Development Award from the National Institute of Mental Health. The research was initiated while the second and third authors were fellows at the Netherlands Institute for Advanced Study (NIAS), Wassenaar, The Netherlands. The authors thank two anonymous reviewers for valuable feedback on an earlier version of the paper.

01993 The Experimental

Psychology Society


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Moving is the result of decision-making. Even for mundane tasks, such as picking up a stick or drawing a line, decisions must be made about the means by which the task should be achieved. In the case of picking up a stick, the actor must determine whether the stick should be picked up with the right hand or the left, with the thumb pointing towards one side of the stick or the other, and so on. In the case of drawing a line, the actor must decide whether the pen should be moved by the fingers, hand, or arm, how quickly the line should be drawn, and so on. Although these sorts of decisions are rarely made consciously, they must be made nonetheless. If one hopes to understand the adaptive character of action-the capacity of people and animals to choose movements in a flexible manner in response to, or in anticipation of, environmental demands-one must identify the factors that are taken into account during movement selection. This paper is concerned with an aspect of movement selection that has so far received relatively little attention-namely , determining which limb segments should be used to complete tasks that can be achieved with different limb-segment configurations. In the past, most studies of movement selection have concentrated either on the selection of one instrumental response or another (e.g. which of two button presses to make in a choice reaction-time situation) or on the kinematics of single points affixed to, or viewed as equivalent to, a single moving effector (e.g. studies of the time-varying position of the hand during rapid aiming movements). The focus of the present investigation, by contrast, is on the body itself. We concentrate on the spontaneously adopted contribution of the fingers, hand, and arm in transporting a pen back and forth to draw line segments of steadily increasing or decreasing amplitude. We investigate this task because some (but not all) of the amplitudes can be achieved with a variety of limb-segment combinations. We wish to understand how the actor chooses the limb-segment combinations that are used. Our reason for focusing on the production of line segments of steadily increasing or decreasing amplitude is to explore sequential dependencies in the limb-segment selection process. Such dependencies can shed light on psychological determinants of limb-segment selection. Because our task can be achieved with different limb-segment combinations, subjects in our experiment face Bernstein’s (1967) degrees offreedom problem. This problem arises when more degrees of freedom are available for task completion than are required for task description. In our linedrawing task, the line might be drawn with the fingers alone, with the hand alone, with the arm alone, or with various combinations of these effectors. Although the final product is likely to be the same in all these cases-a remarkable result in itself (Raibert, 1977)-it is no less challenging and important to understand how the observed means of performing the task is actually determined.


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Classically, the degrees-of-freedom problem has been approached by seeking dependencies between or among limb segments (Turvey, 1990). The rationale for seeking such dependencies is that they can serve to reduce the number of degrees of freedom that must be considered. Many dependencies have been found. For example, the frequency with which one hand swings a pendulum of given length and mass depends on the length and mass of the pendulum swung by the other hand (see Turvey, 1990). In the domain of graphic behaviour, coupling of the elbow and shoulder has been observed in circular drawing movements (Soechting, Lacquaniti, & Terzuolo, 1986). Such coupling depends on the size of the circle being drawn (large circles have stronger coupling than small circles), the orientation of the circle (vertical circles have stronger coupling than horizontal circles), and the dominance of the hand used for drawing (the nondominant hand has stronger coupling than the dominant hand) (Van Emmerik & Newell, 1990). Another approach to the degrees of freedom problem has been to emphasize the mechanical properties of the body as well as the mechanical properties of the body’s interaction with the external environment. The idea is that if the physical characteristics of the actor-environment system limit the range of possible behaviours, then it is unnecessary to postulate explicit elimination of impossible behaviours. Recognizing such limitations helps reduce the number of behavioural options that must be considered (Thelen, Kelso, & Fogel, 1987). A third approach to the degrees of freedom problem is based on the observation that dependencies between effectors are not so strong, nor are physical constraints so powerful, that behavioural options narrow to one. In general, even after dependencies and physical constraints are considered, many methods still exist to achieve a task. For example, drawing an arc longer than the range of motion of the fingers requires the use of the hand or arm. Still, it is not obvious how or whether the fingers should act when such arcs are drawn (apart from holding the writing implement). Similarly, though small arcs can be produced with the fingers, hand, or arm, which combinations of effectors should be used is again unclear. Our central hypothesis is that the choice of method for these and similar tasks depends on efficiency constraints as well as coupling and mechanical limitations. We propose that three efficiency constraints are taken into account in selecting limb segments for drawing behaviour. Two are biomechanical; the other is psychological. We describe the constraints below and then present an experiment to evaluate them. At the end of the paper, we consider the implications of our study both for the understanding of graphic behaviour and for the role of efficiency constraints in the analysis of motor control writ large.

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EFFICIENCY CONSTRAINTS FOR LIMB-SEG MENT SELECT10 N


Optimal Amplitudes and Frequencies of Motion The first constraint we propose is the optimal amplitude and frequency of motion of each limb segment. It has been shown that the index finger, hand, and forearm have different optimal amplitudes and frequencies of motion (Rosenbaum, Slotta, Vaughan, & Plamondon, 1991). For the finger, a high frequency and large angle of rotation about the axis of rotation (i.e. about the metacarpophalangeal joint) is optimal. For the hand, a medium frequency and medium angle of rotation about the axis of rotation (the wrist) is optimal. For the forearm, a low frequency and small angle of rotation about the axis of rotation (the elbow) is optimal.' To investigate whether these ordinal relations apply to the task studied here, we varied the rates as well as the amplitudes of the pen-tip displacements that subjects were asked to produce. We analysed the relative contribution of the fingers, hand, and arm to the pen-tip displacements to determine whether the patterns of relative contributions corresponded to those expected from the optimal movement patterns described above.

Movement Axis A second factor that is likely to affect the selection of limb segments in the present task is movement axis. The axis in which a limb segment can be moved depends on the positions of the surrounding limb segments and on the characteristics of the surrounding joints. For right-handed subjects producing graphic movements in the horizontal plane at elbow height, movements along the line between the top right and bottom left are realized primarily by the hand (provided the amplitude of movement is not too large), movements along the line between the top left and bottom right are realized primarily by the fingers (again, provided the amplitude of movement is not too large), and movements in the vertical and horizontal directions are realized primarily by simultaneous hand and finger movements (Muelenbroek & Thomassen, 1991). Note that the latter description does not include an account of the arm's capabilities, because 'Due to the anatomical relationships and the size differences of the three segments, these rotation angles translate into large fingertip displacements for arm-driven movements, medium fingertip displacements for hand-driven movements, and small fingertip displacements for finger-driven movements. The observed optimal amplitude-frequency combinations for the finger, hand, and forearm can be attributed to the length and mass (or moment of inertia) of these limb segments. If each limb segment is viewed as a linear damped oscillator, it can be shown, based on principles of physical mechanics (French, 1971), that the amplitude-frequency optima for the finger, hand, and arm should follow the ordinal relations described above (see Rosenbaum et al., 1991).


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in the study of Meulenbroek and Thomassen (1991) the forearm was stabilized. In the present task, we expected the established preferences of the fingers and hand to be replicated, and we expected the forearm either to be translated (along its major axis) when large amplitudes were required along the top-lefthottom-right axis, or to be rotated (about the elbow) when large amplitudes were required along the top-righthottom-left axis. Motions along other axes were expected to elicit weighted combinations of forearm translation and rotation, where the weights would depend on how close the axis came to the axis optimally suited for forearm translation or rotation.

Hysteresis A third factor that we predict should affect limb-segment selection is the tendency to persist in the use of a limb-segment pattern even when that pattern would not otherwise be preferred. Such persistence should be reflected in hysteresis effects. A familiar example of hysteresis is the tendency of subjects in bimanual coordination tasks to switch from anti-phase movements to in-phase movements as frequencies increase, contrasted with the absence of a switch from in-phase movements to anti-phase movements as frequencies decrease (see Haken, Kelso, & Bunz, 1985). Such an asymmetry is the defining characteristic of hysteresis. Another example of hysteresis is the tendency of subjects to persist in the way they grab an object that is to be moved from one location to another (Rosenbaum & Jorgensen , 1992). This persistence phenomenon was found in a study concerned with the fact that people display an endstate comfort effect when grabbing a cylinder to be moved from one location to another. When grabbing the cylinder, people generally oriented the hand so that, at the end of the transport task (at the target position), the hand would occupy a comfortable position4.e. a position that allowed the arm to be at or near the middle of its range of motion about the shoulder (Rosenbaum, Marchak, Barnes, Vaughan, Slotta, & Jorgenson, 1990; Rosenbaum, Vaughan, Jorgensen, Barnes, & Stewart, 1992). Subjects in the study of Rosenbaum and Jorgensen (1992) tended to grab the cylinder one way (e.g. with an underhand grip) when transporting it to high target locations and tended to grab it the other way (e.g. with an overhand grip) when transporting it to low target locations. The transition from grabbing the cylinder one way to grabbing it the other way depended on whether the target heights steadily increased or decreased. A simple way of describing the observed effect was that subjects persevered in using the grip with which they started. This observed hysteresis effect was attributed to a cost associated with selecting a new movement pattern. The cost could be avoided if the prevailing movement pattern was acceptable.

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In the present experiment we explored hysteresis by asking subjects to produce pen-tip displacements of either gradually increasing or gradually decreasing amplitudes. We expected hysteresis to be reflected in asymmetries of limb-segment involvement in the increasing and decreasing cases. No previous studies have reported hysteresis effects in limb-segment recruitment. as far as we know.


THE EXPERIMENT We evaluated the three hypothesized limb-segment selection factors in a task requiring subjects to make back-and-forth drawing movements, where the amplitudes of the lines to be drawn either increased steadily or decreased steadily. The following between-trial task factors were varied: (1) the Largest Amplitude of the line to be drawn ( 5 , 10, or 20 cm); (2) Trial Duration (4,7, or 10 sec); (3) Movement Axis (horizontal, top-right/ bottom-left, top-left/bottom-right, or vertical); and (4) Direction of Amplitude Change (incremental or decremental). Notice that the names of the task variables are capitalized. This convention will be used throughout this paper. The predictions were as follows. First, with respect to Largest Amplitude, if the ordinal relations involving the optimal amplitudes of fingers, hand, and arm described above apply to the present task, finger movements should be favoured in the 5-cm Largest-Amplitude condition, hand movements should be favoured in the 10-cm Largest-Amplitude condition, and arm movements should be favoured in the 20-cm LargestAmplitude condition. With respect to Trial Duration, we expected the relative contribution of the limb segments to depend on the pace of performance, because short-duration trials required high-frequency motion whereas long-duration trials required low-frequency motion. Assuming that finger movements are favoured at high frequencies, that hand movements are favoured at medium frequencies, and that arm movements are favoured at low frequencies (Rosenbaum et al., 1991), finger movements were expected to prevail in the 4-sec trials, hand movements were expected to prevail in the 7-sec trials, and arm movements were expected to prevail in the 10-sec trials. Concerning Movement Axis, we predicted that for the horizontal and vertical axes, fingers, hand, and arm would all be involved, but that for the diagonal axes the hand and forearm would be used for the top-right/ bottom-left axis, and that the fingers and upper arm would be used for the top-left/bottom-right axis. (As can be demonstrated informally, the fingers can bring about short movements along the top-left/bottom-right axis, but the upper arm is needed to bring about longer movements along this axis. Note that the upper arm achieves the forearm translation mentioned above.)



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Finally, as concerns Direction of Amplitude Change, we expected this factor to induce different patterns of limb-segment involvement in the incremental and decremental conditions. We expected subjects to start with finger movements at the beginning of incremental trials (all of which started with short movements) and to maintain the use of the fingers for as long as possible. However, in decremental trials (all of which started with long movements), we expected subjects to start with arm movements and to maintain the use of the arm for as long as possible. In other words, we predicted hysteresis effects: the amplitudes at which subjects would switch from the finger to the arm in incremental trials would differ from the amplitudes at which subjects would switch from the arm to the finger in decremental trials.

Method Subjects

Seven adult right-handed subjects participated either for academic course credit or payment of Dfl. 20.00. The subjects were not informed about the purpose of the experiment. Apparatus and Data Collection

Drawing was done on a Calcomp-9240 digitizer with a pressure-sensitive pen connected to the digitizer by means of a thin wire. The digitizer was connected to a VAX-2000 workstation from which the experiment was controlled. Pen-tip displacements were recorded and displayed in real time on a computer screen viewed by the experimenter to allow him to verify that the task instructions were followed. A stimulus sheet (format A4) with three preprinted concentric circles, 5,10, and 20 cm in diameter (see Figure 1) was taped on the digitizer (and replaced after every 12 trials). Circles were used to indicate the largest amplitudes. The stimulus sheet also contained four preprinted straight lines (a horizontal line, a vertical line, and two diagonal lines, each 20 cm long, crossing at the centre of the circles), indicating the four movement axes along which the back-and-forth movements were to be produced. Pen-tip displacements were recorded at a sampling rate of 100 Hz and with a spatial accuracy of 0.2 mm. A Selspot system consisting of one camera and four light-emitting diodes (LEDs) was used to record finger, hand, and arm movements. The camera was placed 150 cm above the digitizer, so that movements were recorded from above. The four LEDs were taped on (1) the most distal joint of the index finger, (2) the first metacarpophalangeal joint (where the index finger joins the hand), (3) the wrist joint, and (4) the forearm (at a distance of approximately 15 cm from the wrist joint). The Selspot data were recorded on the IBM-AT microcomputer at a sampling rate of 320 Hz and with a spatial


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FIG. 1. Stimulus sheet with preprinted concentric circles indicating the Largest Amplitudes (5, 10, and 20 cm) and horizontal, vertical, and diagonal lines indicating the movement axes along which the back-and-forth drawing movements of gradually changing amplitude had to be produced.

accuracy of approximately 0.5 mm. The data collection of the Selspot and Calcomp was synchronized by means of a single pulse transmitted from the VAX workstation to the IBM-AT at the start of each sampling period. Procedure

After explaining the task, the experimenter asked the subject to write his or her name on a blank sheet of paper. The purpose of this exercise was to determine whether the subject’s habitual pen grip allowed the Selspot to record the positions of the index finger, hand, and arm. It was crucial that the hypothenar (the part of the hand at the base of the little finger) remain in contact with the drawing surface to ensure that the LED on the most distal joint of the index finger would be recorded. A second requirement concerned the stylus; it was essential that the stylus should not obstruct the view of any of the LEDs. Provided that these conditions were met, the four LEDs were taped to the four positions indicated. The subject was next instructed to perform the task without moving the trunk. Prior to formal data acquisition, a few (fewer than five) test recordings were made. If the positions of the four LEDs could not be tracked, their positions were adjusted accordingly.



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The experimental task consisted of three series of 24 trials each. A trial duration of 7 sec was used during the preliminary test recordings and during the first trial series. In the second and third series, trial durations were 10 sec and 4 sec, respectively. Subjects were instructed to adopt a comfortable working pace during the first series of trials, to slow down during the second series of trials, and to speed up during the third series of trials. A t the start of the second and third series, subjects were informed about the change in trial duration. Between trials, the experimenter checked the Selspot and Calcomp recordings and instructed the subject about the experimental conditions of the next trial. The intertrial interval was about 30 sec. In each trial, subjects were asked to produce back-and-forth movements of gradually changing amplitude along an indicated axis. Subjects were told to pass through the centre of the concentric circles in each drawing movement. In the incremental condition subjects were instructed to produce gradually larger strokes, and in the decremental condition they were instructed to produce gradually smaller strokes. The first stroke of the incremental trials and the last stroke of decremental trials had to be smaller than 1 cm. Subjects were urged to realize the amplitude change within the indicated trial duration and to produce a smooth stroke-by-stroke amplitude change during this interval. The position of the pen tip at the start of a trial was either at the centre of the stimulus circles (in the incremental condition) or at the intersection of one of the four direction indicators at the circumference of the appropriate stimulus circle (in the decremental condition). Within each trial series there was a fixed order of experimental conditions. Twelve trials with an incremental amplitude change were followed by twelve trials with a decremental amplitude change. Each of these two subsets consisted of four sets of three trials each, having a fixed order with respect to Movement Axis. Finally, within each set of three trials, Largest Amplitude varied from 5 to 10 to 20 cm. Subjects were instructed to start moving when a low-frequency tone was presented and to stop moving when a high-frequency tone was presented. Trial duration was held constant within each block of 24 trials. Subjects briefly practised in each condition before performing it. It was important for subjects to have an idea of the total trial duratioii because they were responsible for pacing the increases and decreases of their movement amplitudes. Data Analysis Pen-tip Displacement. An example of the pen-tip displacement signal is shown in Figure 2. The pen-tip displacement signal was filtered with a low-pass FIR filter containing a transition band from 8 to 16 Hz,with weights based on Rabiner and Gold (1975). The tangential velocity func-


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.-x

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FIG. 2. Example of data analysis of the pen-tip displacement signal from one trial. The filtered xy signal is displayed at the top. The tangential velocity of the pen tip as a function of time (7 sec) is given below. Circles indicate time indices of consecutive velocity minima.

tion was derived and segmented by means of an automatic search procedure that identified the time index of each velocity minimum. This time index was determined by means of a quadratic interpolation technique using the sample nearest to the velocity minimum and its two neighbouring samples (Teulings & Maarse, 1984). Two consecutive time indices were considered to represent the start and end of each stroke. Each stroke size was calculated by integrating the velocity function between its respective time indices. Strokes less than 0.2 cm long were regarded as noise and were discarded from the analysis. A linear regression of stroke number and stroke size within trials was conducted to test the smoothness of the realized amplitude changes. The number of strokes within a trial was then divided by the duration of the trial to determine the mean movement frequency. The full set of mean movement frequencies was then analysed with an ANOVA according to a 2 Directions of Amplitude Change x 3 Trial Durations X 3 Largest Amplitudes x 4 Movement Axes factorial design. Selspot Data. The Selspot data were corrected for outliers, lens-distortion effects (Woltring, 1975), and parallax effects2 and were then reduced by means of quadratic interpolation so each sample represented 10 msec. 'Outliers were detected by searching for successsive sample pairs for which the x or y data differed more than 50 bits (25 mm). These were eliminated and replaced by values interpolated from the data of the surrounding samples. Lens distortion artifacts were estimated on the basis of calibration recordings using stationary LED positions. The centre of


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Finally, the Selspot data were filtered with the same filter as that used for the pen-tip displacement signals. Several analyses of the Selspot data were completed. One was designed to characterize subjects’ movements. As shown in Figure 3, five movement functions were derived from the Selspot data: (1) end-effector displacement; (2) finger amplitude; (3) wrist angle; (4) arm rotation; and ( 5 ) arm translation. The derivation of these functions is explained in Appendix A. A second analysis was designed to identify drawing strokes. Strokes were identified by means of an automatic search procedure that identified

Time (s)

FIG. 3. An example of the analysis of limb-segment activity on the basis of a Selspot recording. From top to bottom, the five functions reflect the displacement of the end effector, the activity of the finger-thumb system, the wrist angle, the rotation of the forearm in the horizontal plane, and the translation of the forearm in the horizontal plane as a result of activity in the upper arm. The x-axis represents time (up to 4 sec). Circles indicate the time indices of consecutive extrema of the end-effector displacement function (i.e. the start and end of each back-and-forth movement).

this distribution corresponded to the centre of the camera lens. A pincushion artefact (Woltring, 1975) was observed which resulted in larger distortions (8% overshoots) at the periphery of the working field than at the centre. A quadratic function was used to correct this distortion effect; the parameters were based on the calibration recordings. Parallax effects were similarly corrected by means of calibration recordings using stationary LED positions and estimated levels of between-LED height differences. The LED on the first metacarpophalangeal joint was considered to be higher than the other three LEDs. Other height differences due to pronation and supination were considered negligible given the large distance (150 cm) between the digitizer and the camera and the use of a writing instrument that limited hand rotations.


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time indices of the upper and lower peaks of the end-effector displacement function (the circles in the top graph of Figure 3). Details concerning the stroke-estimation procedure are given in Appendix B. A third analysis of the Selspot data concerned the temporal order of limbsegment involvement. An iterative optimizing least-sum-of-squares algorithm was used to derive two time values from the Selspot data of each LED: t l , when the amplitude of the LED movement started to change, and t2, when the amplitude of the LED movement stopped changing. An example of the algorithm as applied to the data of one LED is shown in Figure 4. Details concerning tl and t2 estimation are provided in Appendix C. From the tl and t2 values of a trial, we extracted two time-differences, ATfh, the delay between finger and hand involvement, and ATha, the delay

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c, Y

Time (s) FIG. 4. An example of the analysis of a Selspot recording. The upper graph shows x displacement (dotted line) and y displacement (solid line) as a function of time (up to 7 sec). Displacement of one LED (LED 1) is depicted at the left side slightly above this graph. The middle graph shows the same functions after rotation of the xy data, such that y displacement reflects movements along the instructed Movement Axis and x displacement reflects movements perpendicular to the instructed Movement Axis. The bottom graph shows the absolute-difference function; fI and t2 denote the start and end of the transition phase.


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between hand and arm involvement. In the incremental condition ATfi was calculated by subtracting t2 of LED 1 from t l of LED 2, and ATha was obtained by subtracting tl of LED 2 from tl of LED 3. In the decremental condition ATfi was calculated by subtracting f2 of LED 2 from f2 of LED 1, and ATha was obtained by subtracting t2 of LED 3 from t2 of LED 2.


Results and Discussion The presentation of Results begins with the required aspects of performance. Then we turn to those aspects of performance that were up to the subjects. Required Aspects of Performance

Produced Directions. To check whether subjects moved along the indicated axes, we retrieved the pen-tip displacement records and determined the axis of each back-and-forth movement. We defined movement axis as the orientation of the straight line between the start and end of the movement. (See the Method section for how the beginning and end of movements was determined .) Then, we determined for each movement the difference between the obtained and instructed axis. This difference was defined as negative if the deviation was clockwise and positive if the deviation was counterclockwise. (Note that the horizontal axis corresponds to a movement direction of either 180"or 360".)We averaged the deviations across the movements of a trial before and after taking absolute values. The analysis showed that subjects moved along the required movement axes. The mean deviation from the instructed axis was 0.30" (standard deviation = 2.31"), showing that clockwise and counterclockwise deviations were about equally large and nearly balanced each other out. The mean absolute deviation was 2.53" (standard deviation = 1.29"), showing that both clockwise and counterclockwise deviations were small. The mean absolute deviations for the four axes-namely , horizontal, top-right/ bottom-left, vertical, and top-leftlbottom-right-were 2.67,2.31,2.19,and 2.96", respectively (standard deviations = 1.26", 1.48", 0.97", and 1.28", respectively). Passage Through the Centre of the Circle, To determine whether subjects passed through the centre of the circle, we isolated the x and y coordinates of the middle sample of each movement. Next, we determined for each movement the accuracy with which the centre was passed (in cm) by calculating the distance between the middle of the movement and the centre. Finally, we averaged these distances across the movements performed within a trial.

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The analysis showed that subjects moved through the centre. The mean deviation from the centre was 0.23 cm (standard deviation = 0.13 cm). For the horizontal, top-righthottom-left, vertical, and top-lefthottomright axes, the mean deviations from the centre were 0.24,0.22,0.26, and 0.22 cm, respectively (standard deviations = 0.14,0.13,0.13,and 0.11 cm, respectively). These deviations can be considered very small relative to the movement amplitudes that subjects produced. Produced Amplitudes. To check whether subjects produced the appropriate amplitudes and realized the amplitude changes gradually, we conducted a linear-regression analysis on the sequences of the realized pen-tip displacements. For each trial, we determined the size of the strokes between the smallest and largest strokes of the sequence and analysed the relation between stroke number and stroke size. In the incremental condition, stroke size increased from 0.3, 0.5, and 0.7 cm, to 4.9, 9.4, and 18.1 cm, in the 5-, lo-, and 20-cm Largest-Amplitude conditions, respectively. As indicated by the correspondence between the final stroke sizes (4.9, 9.4, and 18.1 cm) and the corresponding target values (5, 10, and 20 cm), subjects did reasonably well at approximating the target amplitudes. The mean slopes in these conditions were 0.23,0.56, and 1.20, respectively; the corresponding 1.2 values were 0.98,0.97, and 0.97. These results indicate that amplitudes increased gradually, as demanded by the task. In the decremental condition, stroke sizes decreased from 4.7, 9.0, and 17.2 cm, to 0.3, 0.6, and 1.1 cm in the 5-, lo-, and 20-cm LargestAmplitude conditions, respectively. The mean slope values in these conditions were -0.27, -0.57, and -1.21, respectively; the corresponding 8 values were 0.95, 0.96, and 0.96. These results indicate that subjects produced smooth and accurate amplitude decreases in the decremental condition, just as they produced smooth and accurate amplitude increases in the incremental condition. Timing. Because subjects were supposed to change the amplitudes of their drawing movements continuously throughout each trial, it was important to check that the time when they began changing amplitudes occurred early in the trials and the time when they stopped changing amplitudes occurred late in the trials. Fortunately, we had estimates of these two events-namely, tl and t2, respectively. The mean tl values in the 4-, 7-, and 10-sec trials were 1.16, 1.91, and 2.52 sec, respectively, F(2, 12) = 180.20, p < 0.01. Thus, mean tl occurred early in the trials, although it occurred later in the trial the longer the trial duration. The corresponding t2 values were 2.91, 4.98, and 7.42 sec, respectively, F(2, 12) = 316.90, p < 0.01. The t2 results imply that subjects complied


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with the instruction to take more time realizing the required amplitude changes in longer trials. Taking t2 - t l as the period during which amplitudes continued to change, the continuous-change period was 1.75 sec, 3.07 sec, and 4.90 sec in the short, medium, and long trials, respectively. These values indicate that subjects did not perfectly match the continuous-change period with the trial duration. Nevertheless, they adjusted the continuous-change period according to the overall length of the trial, as required. Movement Frequencies. A further way to check on the continuity of subjects’ performance is to evaluate the movement frequencies that subjects produced. The 4-, 7-, and 10-sec Trial-Duration conditions demanded high, medium, and low movement frequencies, respectively. Trial Duration had a main effect on movement frequency, F(2, 12) = 4.81, p < 0.05. Mean movement frequency decreased from 3.88 to 3.22 to 3.08 strokes per second in the 4-, 7-, and 10-sec Trial Durations, respectively. Thus, although the observed frequency variations were small, Trial Duration influenced the production rate in the manner we expected.

Optional Frequency Effects

Having reviewed those aspects of performance that were required, we now turn to those aspects of performance that were up t o the subjects. We begin with those aspects of movement frequency that were not required, but which subjects varied nonetheless. Figure 5 shows mean movement frequency as a function of Trial Duration; the effects of Largest Amplitude and Direction of Amplitude Change are also shown. Largest Amplitude had a main effect on movement frequency, F(2, 12) = 18.06, p < 0.01. Movement frequency decreased from 3.69 to 3.45 to 3.03 strokes per second in the 5-, lo-, and 20-cm LargestAmplitude conditions, respectively. The latter relation between movement amplitude and movement frequency replicates the findings of Rosenbaum et al. (1991), who also found that smaller amplitudes elicited higher frequencies, and that larger amplitudes elicited lower frequencies. The main effect of Direction of Amplitude Change was not significant [F(l, 6) = 0.831. Mean movement frequencies in the incremental and decremental trials were 3.51 and 3.29 strokes per second, respectively. However, the Direction of Amplitude Change x Trial Duration interaction was significant, F(2, 12) = 7.97, p < 0.01. In the 4-sec trials, mean movement frequency was lower in the incremental condition than in the decremental condition; in the 7-sec trials, mean movement frequency was also lower in the incremental condition than in the decremental condition (but

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only in the 20-cm Largest-Amplitude condition); in the 10-sec trials, mean movement frequency was higher in the incremental condition than in the decremental condition. Relative Contributions of Limb Segments

Effects of Largest Amplitude and Trial Duration. Figure 6 shows the relative contribution of the limb segments as a function of Largest Amplitude and Trial Duration. The results are averaged across Movement Axes and Directions of Amplitude Change. The contribution of the fingers and the contribution of the hand decreased as Largest Amplitude increased, F(2, 12) = 17.04, p < 0.01, and F(2, 12) = 38.36, p < 0.01, respectively. By contrast, the contribution of the forearm and the contribution of the upper arm increased as Largest Amplitude increased, F(2, 12) = 25.84, p < 0.01 and F(2, 12) = 54.21, p < 0.01, respectively. These results confirm our predictions regarding hypothesized optimal amplitudes of limb-segment motions: larger effectors contributed more to larger amplitudes, and smaller effectors contributed more to smaller amplitudes. These results are analogous to those obtained by Rosenbaum et al. (1991). The main effect of Trial Duration on Gmb-segment selection was not significant, probably because Trial Duration’gave rise to small variations in movement frequency. Nonetheless, Trial Duration had discernible effects on the selection of limb segments. As seen in Figure 6, the contribution of the fingers was largest in the 4-sec Trial Duration condition

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(highest movement frequency), the contribution of the hand was largest in the 7-sec Trial Duration condition (medium movement frequency), and the contribution of the forearm and upper arm contributions was largest in the 10-sec Trial Duration condition (low movement frequency), although this was true only in the 20-cm Largest-Amplitude conditions and to a marginal degree in the 10-cm Largest Amplitude conditions. All of these results, though marginal in extent, follow the predicted trends. The only result that does not was that when the Largest Amplitude was 5 cm, the contributions of the forearm and upper arm were larger in the 4-sec Trial Duration condition (high frequency) than in the 7-sec (medium frequency) or 10-sec (low frequency) Trial Duration conditions. The reasons for the latter outcome are unclear.

Effects of Movement Axis and Direction of Amplitude Change. Whereas the results just discussed were averaged over Movement Axis and Direction of Amplitude Change, the results to be discussed next include those factors. Figure 7 presents an overview of the effects of Movement Axis and Direction of Amplitude Change on the relative contribution of the fingers (top-left graph), hand (top-right graph), forearm (bottom-left graph), and upper arm (bottom-right graph) to the average displacement of the end effector. The results are presented in the form of polar plots averaged across Largest Amplitudes and Trial Durations (the two factors reviewed in the last section). Movement Axis did not have a significant main effect on mean endeffector displacement [ F ( 3 , 18) = 2.36, p > 0.101. On average, subjects

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MEULENBROEK ET AL.


Fingers

Forearm

Hand

Upper arm

FIG. 7. Relative limb-segment contribution (top left: fingers; top right: hand; bottom left: forearm; bottom right: upper arm) as a function of Movement Axis (indicated by straight radial lines emanating from the centre of each circle) and Direction of Amplitude Change (solid lines: incremental condition; dotted lines: decremental condition), The centre of each circle represents a limb-segment contribution of O%, and the circumference of each circle represents a contribution of 75% to end-effector displacement. The solid lines and dotted lines between the straight radial line segments simply connect the observed-value points on the radial lines. The areas within the solid- and dotted-line polygons show the limb segment’s “functional work space”, The polygons are symmetric about the centre of each circle because the two radial lines extending in opposite directions from the centre of each circle represent the same data values.

produced equally large back-and-forth movements along the four axes. However, Movement Axis affected the contribution of the individual effectors. The contribution of the fingers, which in general was small (less than lo%), was not influenced by Movement Axis [ F ( 3 , 18) = 1.73, p > 0.101. However, the contribution of the hand varied significantly as a function of Movement Axis, F(3, 18) = 6.34, p < 0.01. The hand contributed more to vertical movements and to top-rightlbottom-left movements than to horizontal movements or top-left/bottom-right movements, as predicted. The contributions of the forearm and upper arm also varied significantly as a function of Movement Axis, F(3, 18) = 51.14, p < 0.01, and F(3, 18) = 42.62, p < 0.01, respectively. The forearm contributed more to horizontal movements and to top-right/bottom-left movements



291

than to vertical movements or to top-lefthottom-right movements, again as predicted (at least as concerns the relative absence of forearm contributions in the top-leftbottom-right direction). The reverse was true for the upper arm: the upper arm contributed more to vertical movements and to top-leftfbottom-right movements than to horizontal movements or to top-right/bottom-left movements, as predicted. Direction of Amplitude Change did not affect the contribution of the fingers [F(1,6) = 1.78, p > 0.101. However, hand contribution was significantly larger when subjects started with small amplitudes (26.4%) than when they started with large amplitudes (19.9%), F(1, 6) = 6.57, p < 0.01.Forearm contribution did not vary as a function of Direction of Amplitude Change [F(l,6) = 0.70, p > 0.251. However, upper-arm contribution was significantly smaller when subjects started with small amplitudes (31.7%) than when they started with large amplitudes (38.3%), F(1, 6) = 8.02,p < 0.01.Given that end-effector displacement did not vary as a function of Direction of Amplitude Change [F(1, 6) = 2.70, p > 0.101,these results confirm our predictions concerning the effects of hysteresis on limb-segment selection insofar as the hand and upper arm are concerned: the contribution of the more distal limb segments (i.e. the fingers and hand) was larger when subjects started with small amplitudes than when they started with large amplitudes, but the contribution of the more proximal limb segments (i.e. the forearm and upper arm) was larger when subjects started with large amplitudes than when they started with small amplitudes. These asymmetries can be ascribed to a preference for maintaining use of the starting limb-segment for as long as possible. Timing of Limb-Segment Involvement

A more detailed picture of hysteresis can be obtained by analysing the timing of limb-segment involvement. Figure 8 presents the mean values of ATfh and ATha as a function of Trial Duration (top panel), Largest Amplitude (middle panel), and Movement Axis (bottom panel), both for the incremental (white bars) and decremental (dark bars) conditions. Trial Duration had a significant main effect on ATfh, F(2, 12) = 6.21, p < 0.05.Mean ATfh values were 216, 272, and 509 msec in the 4-,7-, and 10-sec Trial-Duration conditions, respectively. Trial Duration had only a marginally significant main effect on ATha, F(2, 12) = 3.40,p < 0.07. Mean ATha values were 76, 196, and 333 msec in the 4, 7-, and 10-sec Trial-Duration conditions, respectively. These results show that time delays of limb-segment involvement were larger when subjects moved at a slow pace than when they moved at a fast pace. Largest Amplitude affected ATfh, F(2, 12) = 14.86,p < 0.01.The mean values of ATfh were 550,328,and 120 msec in the 5-, lo-,and 20-cm Largest-Amplitude conditions, respectively. ATha, however, was not


292

MEULENBROEK ET AL.

FIG. 8. Duration of time delays in lirnb-segment involvement (ATfhand ATha) as a function of Trial Duration (top panel), Largest Amplitude (middle panel), and Movement Axis (lower panel) for the incremental (white bars) and decremental (dark bars) conditions.

affected by Largest Amplitude [F(2, 12) = 1.93, p > 0.101. The mean values of ATha were 249, 230, and 127 msec in the 5 , lo-, and 20-cm Largest-Amplitude conditions, respectively. These results only partially support our predictions. As we predicted, the delay between finger and hand involvement decreased as Largest Amplitude increased. However, the delay between hand and arm involvement, although it was in the predicted direction, did not depend significantly on Largest Amplitude. Movement Axis had a significant effect on AT@, F(3, 18) = 6.65, p < 0.01, but did not have a significant effect on ATha. As seen in Figure 8, AT@ was largest for movements along the vertical axis, second largest for movements along the top-left/bottom-right axis, and smallest for movements along the horizontal and top-righdbottom-left axes. The effects of Movement Axis on ATha, by contrast, were quite variable and inconsistent. The effect of Direction of Amplitude Change on ATfh confirmed our expectations. The mean value of AT@ was 543 msec in the incremental condition and 123 msec in the decremental condition, F(1, 6) = 35.40,



293

p < 0.01. Given the definitions of ATfi in the incremental and decremental conditions, these results imply that when strokes became progressively larger, the hand became involved later than did the fingers, but when strokes became gradually smaller, the hand stopped earlier than the fingers. More importantly, the fact that the magnitude of ATfh was larger in the incremental than in the decremental condition confirms the predicted hysteresis effect. The effect of Direction of Amplitude Change on ATha was not significant [F(l,6) = 1.39, p > 0.251. The mean value of ATha was 234 msec in the incremental condition and 169 msec in the decremental condition. This outcome implies that in the incremental condition the arm started moving 234 msec later than the hand, but in the decremental condition the arm stopped moving 169 msec before the hand. This difference was not statistically reliable, however. Nonetheless, the finding that the mean values of ATha were positive, as were the mean values of ATfh, confirms our expectation that there would be successive finger, hand, and arm involvement in incremental conditions, as well as successive arm, hand, and finger involvement in decremental conditions. Finally, the effect of Direction of Amplitude Change on ATfh interacted with the effects of Trial Duration, F(2, 12) = 6.13,p < 0.05,and Largest Amplitude, F(2, 12) = 14.18, p = 0.01,but not with Movement Axis (p > 0.85). The effects of Trial Duration and Largest Amplitude on ATP were more pronounced in the incremental condition than in the decremental condition. No such interactions were found with respect to ATha.

CONCLUSIONS The present study has shown that the selection of limb-segment patterns during drawing depends on the optimal amplitudes and frequencies of motion of the effectors that can contribute to achievement of the task, the suitability of the effectors for movement along the required drawing axes, and hysteresis. We consider each of these factors as well as the broader implications of our findings. First, with regard to optimal amplitudes and frequencies of motion, we found that in the 5-cm Largest-Amplitude condition the fingers contributed most, but in the 10-cm and 20-cm Largest-Amplitude conditions the forearm and the upper arm contributed most. Furthermore, we found that subjects adopted a high, medium, and low movement frequency in these conditions. In general, the results almost fully agree with the findings of Rosenbaum et al. (1991),who showed that for the finger a high frequency and small amplitude is optimal, for the hand a medium frequency and medium amplitude is optimal, and for the arm a low frequency and large amplitude is optimal.


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The second factor that affected limb-segment selection was Movement Axis. Movements between the top left and bottom right heavily involved the fingers and the upper arm, movements between the top right and bottom left heavily involved the hand and forearm, and movements in the vertical and horizontal directions involved combinations of fingers, hand, and arm. These results agree with our expectations and confirm and extend earlier findings concerning the involvement of the fingers and hand in small-amplitude drawing movements (Meulenbroek & Thomassen, 1991). The third factor that affected limb-segment selection was the tendency to maintain already-selected limb-segment patterns. This tendency, which gave rise to hysteresis effects, was mainly observed in conditions where subjects performed at a relatively slow pace. Hysteresis took the form of delayed additions of limb segments to already-performing limb segments in incremental or decremental conditions. The demonstration of hysteresis in this context is the first we know of for limb-segment selection, although hysteresis has previously been demonstrated in studies of hand-orientation choices for manipulation tasks (Rosenbaum & Jorgensen, 1992) and in studies of bimanual finger oscillation (Haken et al., 1985). The hysteresis results, like the other results obtained here, suggest that the selection of limb segments for drawing behaviour is based on considerations of efficiency. The anatomical configurations that are selected are optimally suited to the task to be performed and, once selected (either before movement initiation or during movement execution if conditions prompt selection of new configurations), continue to be used for as long as reasonable. Continuing with an already selected configuration for as long as possible may be viewed as a way of reducing the computational burden on the selection mechanism. Conceivably, performance continues until feedback indicates that the ongoing method is no longer efficient. At that point, feedback triggers a decision for a new Iimb-segment pattern. We have no direct evidence for such reliance on feedback. However, we consider it an appealing strategy from a computational perspective, because it obviates the need for anticipation of the ease or difficulty of ongoing, but continually changing, movements. Further research is, of course, needed to evaluate the feedback hypothesis in greater detail and to distinguish it from a feedforward account of hysteresis. The latter issue aside, the clear implication of the data we have collected is that efficiency considerations are vital to a complete understanding of movement selection. This perspective is gaining strength in other domains of motor control, notably in studies of the kinematics of single points viewed as representing the motion of the entire arm (e.g. Flash & Hogan, 1985). Given that efficiency criteria appear to characterize the motions of end-effectors, it is perhaps not surprising that they enter as well into the selection of entire limb segment patterns. The details of the computations


295

still need to be worked out, however. The approach taken here illustrates how progress toward this difficult aim may be achieved. That efficiency influences recruitment of limb segments for a highly practised task such as drawing suggests that planning with respect to efficiency becomes an integral part of the skills we learn.


REFERENCES Bernstein, N. (1967). The coordination and regulation of movement. London: Pergamon. Flash, T., & Hogan, N. (1985). The coordination of arm movements: An experimentally confirmed mathematical model. The Journal of Neuroscience, 5 , 1688-1703. French, A.P. (1971). Vibrations and waves. New York: W.W. Norton & Co. Haken, H., Kelso, J.A.S., & Bunz, H. (1985). A theoretical model of phase transitions in human hand movements. Biological Cybernetics, 51, 347-356. Meulenbroek, R.G.J., & Thomassen, A.J.W.M. (1991). Stroke-direction preferences in drawing and handwriting. Human Movement Science, 10, 247-270. Rabiner, L.R., & Gold, B. (1975). Theory and application of digitalsignalprocessing. Englewood Cliffs, NJ: Prentice-Hall. Raibert, M.H. (1977). Moror control and learning by the state-space model. Technical Report AI-TR-439, Artificial Intelligence Laboratory, MIT. Rosenbaum. D.A., & Jorgensen, M.J. (1992). Planning macroscopic aspects of manual control. Human Movement Science, 11, 61-69. Rosenbaum, D.A., Marchak, F., Barnes, H.J., Vaughan, J., Slotta, J., & Jorgenson, M.J. (1990). Constraints on action selection: Overhand versus underhand grips. In M. Jeannerod (Ed.), Attention and performance XI11 (pp. 321-342). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc. Rosenbaum, D.A., Slotta, J.D., Vaughan, J., & Plamondon, R. (1991). Optimal movement selection. Psychological Science, 2, 86-91. Rosenbaum, D.A., Vaughan, J., Jorgensen, M.J., Barnes, H.J., & Stewart, E. (1992). Plans for object manipulation. In D.E. Meyer & S. Kornblum (Eds.), Attention andperformance XIV-A silver jubilee: Synergies in experimental psychology, artificial intelligence and cognitive neuroscience (pp. 803-820). Cambridge: MIT Press, Bradford Books. Soechting, J.F., & Lacquaniti, F. (1981). Invariant characteristics of a pointing movement in man. The Journal of Neuroscience, I , 710-720. Soechting, J.F., Lacquaniti, F., & Terzuolo, C.A. (1986). Coordination of arm movements in three-dimensional space. Sensorimotor mapping during drawing movement. Neuroscience, 17, 295-31 1. Teulings, H.L., & Maarse, F.J. (1984). Digital recording and processing of handwriting movements. Human Movement Science, 3 , 193-219. Thelen, E., Kelso, J.A.S., & Fogel, A. (1987). Self-organizing systems and infant motor development. Developmental Review, 7, 39-65. Turvey, M.T. (1990). Coordination. American Psychologist, 45(8), 938-953. Van Emmerik, R.E.A., & Newell, K.M. (1990). The influence of task and organismic constraints on intralimb and pen-point kinematics in a drawing task. Acts Psychologica, 73, 171-190. Winer, B.J. (1962). Staristical principles in experimental design. New York: McGraw-Hill. Woltring, H.J. (1975). Calibration and measurement in 3-dimensional monitoring of human motion by optoelectronic means. Biorelemetry, 2, 169-196. Revised manuscript received 5 October 1992

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APPENDIX A


Estimation of Movement Functions from the Selspot Data The end-effector displacement function was derived from the xy data of LED 1 (closest to the pen tip). These data were normalized for movement axis. Thus, in the horizontal and diagonal conditions, the xy data of LED 1 were rotated so that the movements of the end-effector along the instructed movement axis coincided with the y-coordinate, and the movements of the end effector perpendicular to the instructed movement axis coincided with the x-coordinate. Consequently, x displacement could be regarded as noise and was discarded from the analysis, but y displacement could be regarded as the end-effector displacement function. The finger-amplitude function reflects activity of the finger-thumb system as revealed by the distance between LED 1 and LED 2, as these LEDs were situated on the most distal joint of the index finger and the first metacarpophalangeal joint, respectively. Smaller distances between LED 1 and LED 2 were assumed to reflect finger flexion, whereas larger distances between LED 1 and LED 2 were assumed to reflect finger extension. The wrist-angle function was defined by the angle between LEDs 2, 3, and 4, reflecting rotations of the hand about the wrist joint. The arm-rotation function was defined by the angle between LEDs 3 and 4 (both situated on the forearm) and the front table edge. To determine this angle, we created for each Selspot sample a virtual fifth LED corresponding to the front edge of the table. The x and y values of LED 5 were identical to the x and y values of LED 4, but a constant value was added to the x values of LED 5 to create a horizontal distance between LEDs 4 and 5. The angle between LEDs 3, 4,and 5 was then considered to reflect rotations of the forearm in the horizontal plane. Movements of the forearm perpendicular to the drawing surface were considered to be negligible given the constraints imposed by the drawing task and the instructions. Finally, the arm-translation function was derived by determining the displacement along the instructed movement axis of an artificially created virtual sixth LED on the forearm. The position of LED 6 was estimated for each Selspot sample separately and was defined as a point in space situated 18 cm away from LED 3 on a straight line running through LEDs 3 and 4,3 cm past LED 4;18 cm was the estimated average distance between the wrist and the point on the forearm around which forearm rotations were assumed to occur. The xy data of LED 6 were rotated in the same way as the xy data of LED 1. After rotation, the y component of the displacement of LED 6 was considered to reflect that component of the translation of the arm which contributed to the displacement of the end effector along the instructed movement axis. Arm translation was considered to reflect activity of the upper arm. Note that the above five functions reflected variations of the position of the limb segment around its mean position within a trial, just as the end-effector displacement function reflected the variation of the position of LED 1 around its



297

mean position within a trial. It should also be noted that, although we applied a post hoc correction of the LED displacement data for parallax effects, finger-thumb activity may have been slightly underestimated as a result of the top-view recording. A second caveat concerns the fact that only when the displacement of an individual LED (real or virtual) was used to determine one of the five functions mentioned in the previous paragraph were its xy data normalized for axis (for the reasons mentioned earlier). When the displacement data of more than one LED were used for this purpose, normalization for axis was not considered relevant and was therefore not applied. Finally, note that the wrist-angle function and the arm-rotation function were the only two functions representing angles. The end-effector displacement, the finger-amplitude, and the arm-translation functions represents amplitudes. In order to determine the relative contribution of the limb segments to displacements of the end effector, we converted the wrist-angle function and the arm-rotation function to a hand-amplitude function and a forearm-amplitude function,

APPENDIX B Stroke Identification from the Selspot Data A time index was derived to identify onsets and offsets of strokes. The time index was estimated by means of quadratic interpolation through the sample nearest the extremum and its two neighbouring samples (Teulings & Maarse, 1984). Two consecutive time indices were considered to represent the start and end of a stroke. For each stroke, the net displacement of the end effector and the net amplitudes of the fingers, hand, forearm, and upper arm were calculated. Strokes whose end-effector displacements were less than 0.2 cm were discarded. The series of end-effector displacements derived from the Selspot recordings according to the above procedure were compared to the series of pen-tip displace-

'The wrist-angle function and arm-rotation function (expressed in degrees) were converted to a hand-displacement function and a forearm displacement function (expressed in cm), as follows. We assumed that the length of the (fingerless) hand was 8 cm. The distance between the wrist and the point on the forearm around which forearm rotations were assumed to occur was assumed to be 18 cm. We also assumed that rotations of the hand around the wrist and rotations of the forearm around the elbow were circular movements. Consequently, the hand-displacement function (in cm) could be considered equal to the wrist-angle function (in degrees) divided by 360 (degrees) after multiplying these fractions by 50.28 (i.e. 2 7 ~. 8.0 cm). Likewise, the forearm displacement function (in cm) could be considered equal to the forearm rotation function (in degrees) divided by 360 (degrees) after multiplying these fractions by 113.14 (i.e. 2.rr . 18.0 cm). The analyses revealed that the assumed radii of the hand and forearm rotation (8 and 18 cm) resulted in realistic amplitude ranges (in cm) of the wrist angle and forearm angle (see Results section).


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ments derived from the Calcomp recordings t o check for a c ~ u r a c y In . ~ addition, we determined the degree t o which the end-effector displacement was equal t o the sum of the limb-segment amplitudes.' To analyse the relationship between endeffector displacements and limb-segment amplitudes, we determined for each trial one limb-segment pattern. First, we calculated the mean limb-segment amplitudes across the strokes of a trial. Then, we converted these mean limb-segment amplitudes t o percentages of the average of the sum of the limb-segment amplitudes across the strokes of a trial. This resulted in a limb-segment pattern consisting of four percentages (of which the total was lOO%), reflecting the relative contribution of the limb segments t o the average displacement of the end effector. T h e relative contributions of the fingers, hand, forearm, and upper arm were analysed by means of separate ANOVAs according t o a 2 Directions of Amplitude Change X 3 Largest Amplitudes X 3 Trial Durations x 4 Movement Axes factorial design. To ensure normal distributions, proportions were converted t o fractions and transformed by means of a trigonometric function (Winer, 1962). The adjusted fractions were the cell entries of the ANOVAs. T h e fifth A N O V A o n the unadjusted mean displacements of the end effector was also conducted according t o the same factorial design. 4The correspondence between displacement of the pen tip (recorded by means of the digitizer), and displacement of the end-effector (i.e. LED 1 , recorded by means of the Selspot system) was restricted to a comparison of the largest pen-tip displacement and the largest end-effector displacement. The mean size of the largest pen-tip displacementswas 10.55 cm, which is 1.12 cm (i.e. 9.5%) less than the mean largest (instructed) amplitude (11.67 cm, the average of 5, 10, and 20 cm). The mean size of the largest end-effector displacements was 10.22 cm, which was 0.33 cm less than the mean largest pen-tip displacements. This small difference of only 3% can be attributed to the neglect of the curvilinear form of end-effector displacementsin the Selspot analysis. These results show that there was a high correspondence between the largest pen-tip and largest end-effector displacements. 5For each stroke, we established the degree to which the sum of the limb-segment amplitudes equalled the end-effector displacement. If subjects did not move the trunk during the production of a stroke, the sum of the limb-segment amplitudes should be roughly equal to the displacement of the end-effector. If this condition is met, the limb-segment patterns can be expressed as percentages of end-effector displacement, thus reflecting the relative involvement of the limb segments. The check consisted of calculating, for each stroke, the sum of the limb-segment amplitudes, and expressing this sum as a percentage of the endeffector displacement of the stroke. Then these percentages were averaged across the strokes of a trial. The means of these average percentages were 90.4, 87.7, and 90.7% in the 5-, lo-, and 20-cm largest-amplitude conditions, respectively. Subsequently, an SPSSX multipleregression analysis was conducted using a model in which the end-effector displacement was regarded as a linear combination of the individual limb-segment amplitudes. The slope values for the fingers, hand, forearm, and upper arm were 0.04, 0.14, 0.53, and 0.49, respectively. Each limb segment contributed significantly0, < 0.01) to the end-effector displacement. The multiple correlation was 0.96. These results indicate that there was a reliable correspondence (90%) between the sum of the limb-segment amplitudes and the end-effector displacements. The undershoot is presumably related to an underestimation of finger-thumb activity (see Method section) and to an underestimation of the size of the hand (only 8 cm), an underestimation of the distance between the wrist and the centre of rotation of the forearm, and, finally, the imperfect phase relationships between the limb-segment activity functions (see Figure 3).


299

APPENDIX C


Estimation of t7 and t2 from the Selspot Data The first step in the analysis was to introduce a rotation of the xy data (middle part of Figure 4) so the y displacement could be considered to represent LED movements along the instructed movement axis and the x displacement could be considered to represent LED movements perpendicular to the instructed movement axis. Thus, the x displacement could be considered as discardable noise. Note that the LED position of interest (on the y axis) oscillates about its mean position, and the amplitude of the oscillation gradually increases. The next step was to take the absolute value of each sample of the displacement function (lower part of Figure 4). Then two points (tl and t2) were fitted to the function, so three straight-line segments, two with zero slope and one with non-zero slope, were fitted to the data to minimize the sum of squared deviations of the points from the lines. The two fitted points, corresponding to the inflection points of the three-line series, represent t l and t2-the times of initiation and termination of the amplitude change in LED displacement. With this procedure, the t l and t2 values of all four LEDs were determined. A possible objection to the analyses of tl and t2 is the neglect of the phase relationship of LED movements. Although the axes of the movements of LED 1 can be considered to correspond closely to the axes of the movements of the pen tip, this is probably less true for the movements of LEDs 2, 3, and 4. To examine whether LEDs were moving in or out of phase at the times of initiation and termination, we conducted a control analysis directed at 2-sec time intervals of the y displacement functions of the LED movements (see the middle graph of Figure 4). We determined the correlation of 2 sec of the y-displacement function of LED 1 surrounding t l with the same time interval within the y-displacement function of LED 2. A positive correlation implied that the two LEDs were moving in phase, and a negative correlation implied that they were moving out of phase, i.e. in opposite directions. According to this procedure we analysed the phase relationship between LED 1 and 2, LED 1 and 3, and LED 1 and 4 at the times of initiation (in the incremental condition) and at the times of termination (in the decremental condition) of all the LEDs. Negative correlations were observed in only 4% of the trials, equally distributed across experimental conditions. The mean of the correlations between LED 1 and 2 amounted to 0.96. Between LEDs 1 and 3 and LEDs 1 and 4, the mean correlations were 0.92 and 0.90, respectively. These high correlations show that LEDs almost never moved out of phase. The present results therefore relate to the relative involvement of the limb segments to the displacement of the end effector along required movement axes.

Limb-segment Selection in Drawing Behaviour

Limb-segment Selection in Drawing Behaviour

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