Exp Brain Res (2002) 142:365–373 DOI 10.1007/s00221-001-0925-4

R E S E A R C H A RT I C L E

David A. Rosenbaum · Robert W. Gregory

Development of a method for measuring movement-related effort Biomechanical considerations and implications for Fitts’ law

Received: 16 May 2001 / Accepted: 17 September 2001 / Published online: 13 December 2001 © Springer-Verlag 2001

Abstract An emerging view in motor control research is that voluntary movements typically require little effort. Nonetheless, there is no agreed-upon method for measuring movement-related effort. To pursue such a method, we conducted two experiments. In the first, participants oscillated the forearm about the elbow in the horizontal plane at different frequencies. After performing each task, they gave an effort rating. The forearm movements caused a cursor to move back and forth between two targets on a computer screen, and we changed the gain of the system, requiring different angular displacements to produce the same cursor displacement, thus keeping the visual demands the same while varying the motor demands. Surprisingly, the ratings increased as the amplitudes of forearm rotation decreased, and the performance scores that participants received were also worse the smaller the amplitudes of forearm rotation. The latter result suggests that participants simply rated as effortful those movements for which knowledge of results indicated poor performance. To seek a more direct link between motor activity and rated effort, in the second experiment we asked participants to oscillate the forearm about the elbow in the horizontal plane at different metronome-specified frequencies, but we allowed participants to generate whatever angular displacements they wished to incur different levels of prescribed effort. With this procedure, we found that angular velocity was proportional to prescribed effort. The simplicity of this outcome suggests that the method used in the second experiment can be used in the future as a means of evaluating biomechanically related effort. The surprising finding of the first experiment suggests that Fitts’ Law depends both on perception and on motor control. D.A. Rosenbaum (✉) · R.W. Gregory 642 Moore Building, Department of Psychology, Pennsylvania State University, University Park, PA 16802, USA e-mail: [email protected] Present address: R.W. Gregory, Center for Human Motor Research, University of Michigan, 401 Washtenaw Avenue, Ann Arbor, MI 48109, USA

Keywords Aiming · Effort · Fitts’ Law · Movement · Human

Introduction Because most physical tasks can be achieved in different ways, a core question in motor control research is how movements that are performed differ from movements that could be performed but are not. An emerging view is that movement choices are not dictated entirely by physical constraints nor by interactions among limb segments. Instead, a factor distinguishing movements that are performed from those that are not is that the level of effort involved in performed movements is lower. Given the growing belief in the importance of effort in motor control, it is crucial to have a definition of effort and, in turn, a way of measuring it. To our knowledge, although a number of investigators have asked participants to report the effort they experience while performing different, complex tasks (for reviews, see Borg 1982, 1990; and Russell 1997), there has been very little research in which effort ratings have been used to investigate the microstructure of motor control. One exception is a study by Burgess et al. (1995) in which participants gave effort ratings for isometrically generated torques. Burgess et al. found that ratings of effort were positively related to generated torques. To our knowledge, effort ratings have not been obtained for isotonic movements that are carefully graded with respect to one or more kinematic or kinetic variables. Given the focus of modern motor control research on the microstructure of movement control, we thought it was important to develop a method for relating judgments of effort to kinematic or kinetic variables of isotonic movements. The aim of the present study was to develop such a method.

Experiment 1 We focused on a very simple task: oscillation of the forearm about the elbow joint in the horizontal plane. Our

366 Fig. 1 Schematic drawing of the experimental setup used in experiment 1

idea was that, by sorting out methodological issues that arise in this simple situation, we could establish effective procedures for more complex, multijoint tasks. We asked participants to perform different combinations of angular displacement and frequency, where for each combination participants gave an effort rating. We expected effort ratings to increase with greater angular displacements and to increase at a higher rate the shorter the time in which the same angular displacements could be made (i.e., the higher the angular velocity). Method Ten right-handed subjects (five women and five men; age 24.5±3.0 years, height 1.73±0.10 m, mass 69.4±17.9 kg) participated. Their task was to move a line up and down on a computer monitor between two target zones (Fig. 1). The movements were paced with a metronome and the position of the line depended on the angle of the elbow. In different conditions, the range of motion (ROM) through which the elbow moved was varied, as was the movement frequency. To avoid confounding the visual and motor demands of the task, we set up the experiment such that the visual targets and the line that moved up and down were the same in all conditions. Each subject was asked to move his/her forearm through five different ROMs (10°, 30°, 50°, 70°, and 90°) at five different frequencies (0.33 Hz, 0.50 Hz, 0.67 Hz, 0.83 Hz, and 1.0 Hz) for 20 cycles. After completing a trial, the subject was asked to give a rating of perceived effort (RPE) on a scale of 1–5, where 1 meant least effort and 5 meant most effort. There were 25 conditions (5 ROMs × 5 frequencies), which were presented to subjects in random order. All subjects performed two trials in each ROM × frequency condition in two separate rounds. The first trial for a given condition in each round was for practice; no RPE was requested after this trial. The second trial served as the experimental trial, at the end of which an RPE was obtained. The reason for obtaining an RPE only after the second trial was to allow the rating to reflect the difficulty of moving within a given condition irrespective of the condition tested before. After the first and second trials, a score was calculated on a scale of 0–100 to reflect the spatial and temporal accuracy of the participants’ movements. This score was conveyed to the participant to encourage accurate performance. After all 25 conditions were tested in two consecutive trials per condition, the entire protocol was repeated. The second round was included to enable participants to calibrate their RPEs based on exposure to the full range of conditions. Participants sat at a table with the chest pressed against the table’s edge. The upper arm rested on the table with the elbow at or

near the middle of its ROM and with the shoulder joint flexed 90°. The participant flexed and extended the forearm with respect to the stationary upper arm. A goniometer (Biometrics, UK) was attached to the elbow to measure the angular displacement of the forearm. The signal from the goniometer controlled a cursor on a computer monitor which allowed the participant to view the angular displacement of the forearm. The participant was asked to move the cursor between two seen target zones such that motions of the forearm in the 10°, 30°, 50°, 70°, and 90° ROM conditions all required motions of ±50% of the required ROM centered about the midpoint of the elbow joint’s ROM. Thus, the elbow had to move ±5° in the 10° ROM condition, ±15° in the 30° ROM condition, and so on. Each target had a width corresponding to 20% of the ROM for that particular condition. Participants viewed the same display in all conditions, ensuring that visual properties of the display were not responsible for condition differences. The gain of the output from the goniometer was adjusted so different angular displacements of the elbow joint caused equivalent displacements of the cursor depending on the required ROM. The data acquisition and display program used Labview software (National Instruments, Austin, Tex., USA). A metronome signaled the required frequencies of cursor movement between the target zones. The metronome was set to beep twice during each movement cycle and subjects were instructed to reverse the direction of the forearm movement with each metronome beat. Upon completion of each trial and after giving an RPE after completing the second trial in each condition, the subject was shown a score that equaled a spatial accuracy value plus a temporal accuracy value. The spatial accuracy value was obtained by calculating a normalized spatial error for each flexion/extension movement as the participant attempted to hit the target line with the cursor. The normalized spatial error equaled the rectified spatial error (the absolute number of degrees by which the subject missed the target) divided by the specified ROM for a particular trial. The values for the normalized spatial error lay between 0 and 1. To have a best spatial score of 50 and a worst spatial score of 0, the normalized spatial scores for the 40 movements (20 each of flexion and extension) were summed, then multiplied by 1.25, and then subtracted from 50. The temporal accuracy value was obtained by calculating a normalized temporal error for each flexion/extension movement as the subject attempted to hit the target line with the cursor at the frequency specified by the metronome. The normalized temporal error equaled the rectified temporal error (the absolute number of milliseconds by which the subject was above or below the specified period) divided by the number of milliseconds required to complete the movement as determined by the specified frequency. The values for the normalized temporal error lay between 0 and 1. To have a best temporal score of 50 and a worst temporal score of 0, the displayed score was determined by taking the normalized temporal value for the 40 movements (20 each of flexion and extension), summing these normalized temporal values, multiplying the sum by 1.25, and then subtracting this number from 50. The spatial and temporal accuracy scores were then combined to provide an overall accuracy score on a scale from 0 to 100.

Results The data were analyzed in three stages. First, we evaluated the quality of performance, then we evaluated the effort ratings, and finally we evaluated the relation between quality of performance and rated effort. Each of these analyses is discussed in turn here. Quality of performance To check that subjects performed the tasks as required and that differences in performance quality across condi-

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Fig. 2 Performance scores as a function of frequency and range of motion in experiment 1. Estimate of ±1 SE

tions were negligible, we evaluated the feedback scores that subjects received (see Fig. 2). These scores were subjected to an analysis of variance (ANOVA) that evaluated the effects of Frequency (0.33 Hz, 0.50 Hz, 0.67 Hz, 0.83 Hz, and 1.00 Hz) × ROM (10°, 30°, 50°, 70°, 90°) × Subjects (1–10). The ANOVA yielded a highly significant interaction between frequency and ROM, F4, 36=3.65, P<0.001. As shown in Fig. 2, mean scores decreased as frequency increased and as ROM decreased. Moreover, the effect of frequency grew and became more consistent as the ROM decreased. Effort ratings The mean effort ratings (see Fig. 3) were subjected to an ANOVA that was used to assess the effects of Frequency (0.33 Hz, 0.50 Hz, 0.67 Hz, 0.83 Hz, and 1.00 Hz) × ROM (10°, 30°, 50°, 70°, 90°) × Subjects (1–10). The interaction between Frequency and ROM did not approach statistical significance (F16, 14=0.53, P>0.90). However, the main effect of Frequency was highly significant (F4, 36=7.00, P<0.001). Effort ratings increased as required frequency increased. A test of increasing linear trend for rated effort as a function of required frequency was highly significant (F1, 9=8.69, P<0.02). Pairwise difference tests (Newman-Keuls, alpha=0.05) showed that the 1.0-Hz condition differed significantly from each of the other conditions except for the 0.83-Hz condition and that none of the other frequency conditions differed significantly from each other. In the same analysis, the main effect of ROM was highly significant (F4, 36=6.59, P<0.001). As shown in Fig. 3, mean effort ratings decreased as ROM increased. A test of decreasing linear trend for rated effort as a function of ROM was highly significant (F1, 9=6.40, P<0.04). Pairwise difference tests (Newman-Keuls, alpha=0.05) showed that the 10° ROM condition differed from all the others, but that none of the other ranges differed significantly from one another.

Fig. 3 Ratings of perceived effort as a function of frequency and range of motion in experiment 1. Estimate of ±1 SE

Relation between performance quality and effort ratings If rated effort increased as quality of performance decreased, one would expect a negative correlation between scores and effort. To test this prediction, we computed the within-subject correlation between RPEs and Scores. The mean of the individual subject correlations was r=–0.52. A one-tailed t-test designed to evaluate the hypothesis that the correlations were significantly less than zero yielded a statistically significant outcome (t(9)=–4.80, P<0.001). Thus, RPEs increased as quality of performance decreased. Those conditions that were hard were perceived as effortful, and those conditions that were easy were perceived as less effortful. Discussion The results of the first experiment were surprising. Contrary to our expectations, RPEs decreased rather than increased with movement amplitude. We wondered whether this result may have reflected some other aspect of performance unrelated to biomechanics. The most obvious candidate was that participants’ effort ratings reflected their a posteriori judgments about the effectiveness of satisfying the spatial and temporal demands of the rhythmic aiming task. Consistent with this hypothesis, RPEs and performance scores were negatively correlated. Another possible explanation of the results of experiment 1 is that RPEs reflected aspects of force control. This model, which is developed in the Appendix, turns out to have academic interest only, for, as the second experiment shows, the results of experiment 1 were indeed due to retrospective judgments of aiming accuracy, not to force control.

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Apart from the issue of how effort ratings were determined in experiment 1, participants’ performance scores were significant for what they reveal about the speed and accuracy of aiming. The best-known principle concerning aiming speed and accuracy is Fitts’ Law (Fitts 1954), which states that the time needed to move to a spatial target increases as the distance to the center of the target increases and as the width of the target decreases. Importantly, there is no term in Fitts’ Law for the constraints associated with the effector(s) used for the aiming. Nonetheless, the rate at which movement time increases with target distance and target width depends on the effector used. The rate of increase is lower for the finger than for the wrist, which in turn is lower than the forearm (Langolf et al. 1976). Furthermore, as seen in the present experiment, the effective ROM of the effector used for aiming has a marked influence on movement time. Even when the visually specified amplitude and tolerance are fixed, the smaller the effective ROM of the effector used for aiming, the more time is needed for each increment in the ratio of target distance to target radius.

Experiment 2 The second experiment was designed to test the hypothesis that the effort ratings in experiment 1 reflected participants’ responses to the feedback they received about their aiming accuracy. Recall that we were led to believe that participants’ effort ratings reflected knowledge of results. This was because there was a significant negative correlation between feedback scores and effort ratings in experiment 1. To test the hypothesis that effort ratings were modulated by knowledge of results, we devised an alternative method for evaluating perceived effort. Whereas in experiment 1 we had participants move at different prescribed frequencies over different prescribed amplitudes and then asked for their effort ratings, we had participants in experiment 2 move at different prescribed frequencies and allowed them to cover different amplitudes to generate different levels of prescribed effort. The main dependent measure in the second experiment was the distance covered at each movement frequency for each prescribed level of effort. We expected this new method to have two advantages over the one used in experiment 1. First, it enabled us to use higher rates of movement than was possible in the first experiment where there was a need to make corrective movements. Second, the protocol was simpler and could be implemented more quickly and easily than was the case in experiment 1. We felt this was important, because a primary motivation of this project was to develop a method that could be used quickly and easily in clinical settings. Method Each of three frequencies was specified with a metronome, and each frequency was tested at three prescribed effort levels. For

each of the 3×3=9 combinations of specified effort and frequency, the participant was allowed to cover whatever amplitude he or she wanted with the forearm, alternately flexing and extending the elbow joint while leaving the upper arm immobile and keeping the entire arm resting on the table at chest height. Ten right-handed participants (five women and five men, age 24.6 ±4.9 years, height 1.70 ±0.10 m, mass 65.6 ±13.5 kg) participated. None had taken part in experiment 1. Each participant was asked to produce elbow/flexion extension movements in the horizontal plane for 20 s. The request to the participant was to produce movements that engendered levels of effort corresponding to ratings of 1, 2, or 3, where 1 meant very little effort, 2 meant medium effort, and 3 meant a lot of effort. Each effort level was supposed to be produced at each of three frequencies (1.5 Hz, 2.5 Hz, or 3.5 Hz). The nine resulting conditions (three effort ratings × three frequencies) were tested in random order. All participants performed one trial of each condition in two rounds. The first round was for practice and was designed to allow participants to experience the full range of efforts and frequencies. The second round was for data collection. Participants sat at a table with the chest pressed against the front edge and the upper arm resting on the table in a position that resulted in approximately 90° of shoulder joint flexion. Before the beginning of each trial, the forearm was brought to rest approximately midway between the extremes of the elbow joint’s flexion/extension ROM. A goniometer was attached to the elbow joint to measure the angular displacement of the forearm as the participant flexed and extended the forearm with respect to the stationary upper arm. A computer-generated metronome was used to signal the required movement frequencies. The metronome was set to beep twice during each movement cycle (i.e., at each movement reversal). Thus, the metronome beat at frequencies of 3.0 Hz, 5.0 Hz, and 7.0 Hz for the 1.5-Hz, 2.5-Hz, and 3.5-Hz movement frequencies, respectively. Once the participant indicated that he or she was ready, the experimenter read the RPE required for that particular condition, waited for the subject to say it back, and then initiated the data acquisition program and metronome signal with a single buttonpress. The participant was free to listen to the metronome for as long as necessary to “get the feel” of the currently required movement frequency. Then he or she initiated the movement whenever they desired. Once movement began, data were recorded for 20 s. Participants were instructed to begin their movements in either the flexion or extension direction as they saw fit. They were instructed to oscillate the forearm in time with the metronome, reversing movement direction with each beep and moving the forearm through any desired ROM as long as the movement corresponded to the RPE assigned for that trial and followed the timing pattern established by the metronome. The data acquisition program used Labview software. The middle portion of the 20-s data collection period was selected for data analysis to avoid start-up and ending effects. The first and last positive-going angular accelerations of the forearm in the data analysis period, which began approximately 5 s after the start of the trial and ended approximately 5 s before the end of the trial, defined the beginning and end of the observed movement period, respectively. Positive-going zero-crossings during the observed period were used to define the beginnings of the intermediate movement cycles. The variables calculated for each movement cycle were cycle time, cycle displacement, and flexion and extension peak angular acceleration. These variables were used to calculate mean values for all cycles in each trial. The data analysis was performed using MATLAB software (Mathworks, Natick, Mass., USA).

Results We analyzed the data in two stages: First we evaluated the quality of performance in terms of temporal accuracy; then we evaluated the relationship between movement kinematics and effort ratings.

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Temporal accuracy To check that subjects performed the tasks as required and that movement timing did not change as effort levels varied for any required movement frequency, we evaluated temporal accuracy. The estimated cycle times were subjected to an ANOVA that let us evaluate the effects of Effort (1, 2, and 3) and Frequency (1.5 Hz, 2.5 Hz, and 3.5 Hz). There was no significant effect of Effort (F2, 81=0.03, P>0.96). However, as expected, given the experimental design and our informal observation that subjects complied with the instructions, there was a significant effect of Frequency (F2, 81=2729.14, P<0.0001). Pairwise difference tests (Newman-Keuls, alpha=0.05) showed that each of the frequency conditions differed significantly from one another. The interaction between Effort and Frequency was not significant (F4, 81=0.46, P>0.76). As a whole, the results concerning temporal accuracy indicated that participants performed the conditions as required and that timing was not altered by prescribed effort.

Fig. 4 Relationship between angular displacement and prescribed effort for the three movement frequencies in experiment 2. Error bars represent ±1 SE for each mean

Kinematics Mean angular displacements per movement cycle (see Fig. 4) were subjected to an ANOVA to assess the effects of Frequency (1.5, 2.5, and 3.5 Hz) and Effort (1, 2, and 3). The interaction between Frequency and Effort did not approach statistical significance (F4, 81=1.25, P>0.29). However, the main effect of Frequency was highly significant (F2, 81=11.79, P<0.0001). Angular displacement decreased as required frequency increased. Pairwise difference tests (Newman-Keuls, alpha=0.05) showed that the mean angular displacement of each of the frequency conditions differed significantly from each of the others. The main effect of Effort was also highly significant (F2, 81=23.78, P<0.0001). Mean angular displacement increased as required effort increased. Pairwise difference tests (Newman-Keuls, alpha=0.05) showed that all the effort conditions differed significantly from one other. To estimate the relative magnitudes of the torques in the different experimental conditions, we calculated mean peak flexion acceleration and mean peak extension acceleration, taking the means within participants over movement cycles. Note that flexion acceleration and extension acceleration were both angular accelerations. The means (see Fig. 5) were subjected to an ANOVA to assess the effects of Frequency and Effort. The interaction between these factors did not reach statistical significance for peak flexion acceleration (F4, 81=0.43, P>0.78), or for peak extension acceleration (F4, 81=0.86, P>0.49). However, the main effect of Frequency was highly significant both for peak flexion acceleration (F2, 81=9.86, P<0.0001) and for peak extension acceleration (F2, 81=10.64, P<0.0001). Both peaks increased as required frequency increased. Pairwise difference tests (Newman-Keuls, alpha=0.05) showed that peak flexion acceleration and peak extension acceleration differed significantly between the 1.5-Hz and 2.5-Hz conditions

Fig. 5 Peak angular accelerations (degrees per second squared) for extension (values above zero) and flexion (values below zero) for prescribed effort levels of 1 (circles), 2 (squares), and 3 (triangles) at each of the three prescribed frequencies. Error bars represent ±1 SE for each mean. The points are shifted slightly to the left for effort level 1 and slightly to the right for effort level 3 to reveal terminations of all error bars. Data from experiment 2

and between the 1.5-Hz and 3.5-Hz conditions. The main effect of Effort was also highly significant for peak flexion acceleration (F2, 81=17.79, P<0.000001), and for peak extension acceleration (F2, 81=23.03, P<0.0001). Peak flexion acceleration and peak extension acceleration both increased (both had higher absolute values) as required effort increased. Discussion The main result of experiment 2 was that angular displacement increased with prescribed effort and decreased

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with prescribed frequency (Fig. 4). Because peak flexion and peak extension angular acceleration increased (had higher absolute values) both as effort increased and as frequency decreased, it is likely that overall net muscular and inertial forces acting on the subject’s forearm contributed to a greater sense of effort. This idea is considered further in the General discussion section.

General discussion The concept of effort as it relates to motor behavior is not clearly defined. It is reasonable to hypothesize that effort is directly proportional to physical quantities involved in movement production, but what those physical quantities are remains to be established. Researchers have proposed that movements are chosen to minimize such physical quantities as mean squared jerk (Flash and Hogan 1985), mean torque change (Uno et al. 1989), and peak work (Soechting et al. 1995). These variables and others have been proposed either for optimization or “satisficing” (see Rosenbaum et al. 2001) in motor control; the term “satisficing” refers to the idea of being anywhere below some threshold value. In principle, one could use effort ratings to choose among these hypothesized quantities, where the stronger the positive correlation between the quantity and the effort ratings it yields, the greater could be one’s confidence that effort depends on that quantity. To pursue this approach, one needs a method of obtaining effort ratings. As mentioned earlier, few investigators have collected effort ratings in tasks using finely graded movements to explore detailed features of motor control (Burgess et al. 1995). We sought such a method here. In the first experiment we asked participants to move a cursor between two seen targets in time with a metronome. The gain of the system relating elbow angular displacement to the linear displacement of the cursor was varied and participants reported the effort they experienced after seeing how well they did. This experiment yielded two surprising results. The first was that, when the gain was high (small elbow angular displacements yielded large cursor linear displacements), aiming performance was poor, but, when the gain was low (small elbow angular displacements yielded small cursor linear displacements), aiming performance was better. The second surprising result was that rated effort increased as angular displacements decreased. With respect to the first of these outcomes, the finding that small angular displacements were harder to control than were large angular displacements is surprising in view of the widely held belief that movement variability increases with increases in movement velocity (amplitude divided by time; see Meyer et al. 1990). Our results involving gain changes suggest that this relation may be due both to visual perception and to motor control. If the growth of movement variability with movement amplitude were due only to how well people can

visually estimate distances and target widths, then when visual perception is held constant, as was the case in experiment 1, one would expect movement accuracy to remain the same. This prediction was disconfirmed in the first experiment, showing that visual perception alone cannot be the sole source of Fitts’ Law. On the other hand, because performance was worse when participants had to cover small angular amplitudes than when they had to cover large angular amplitudes, one can conclude that there was a motoric contribution to movement accuracy, which, surprisingly, was opposite to the one posited in the classic assumption of increasing variability with increasing velocity (Meyer et al. 1990). Why movement accuracy was lower for large gain than for small gain is unclear. One possibility is that large-amplitude displacements allow for more muscle control strategies than do small-amplitude displacements. In any case, the findings just reviewed suggest that muscle control plays a small role in Fitts’ Law and actually counteracts the normal relation between amplitude and variability. The results of experiment 1 suggest that vision plays an extremely strong role that counteracts and masks the motorically based tendency for accuracy to deteriorate as limbmovement amplitudes get smaller. The second surprising finding of experiment 1 was that rated effort increased as angular displacements decreased. As noted earlier, this unexpected outcome appeared to be due to participants assigning effort ratings which reflected dissatisfaction with performance feedback. In effect, participants may have reasoned, “If my score was very poor, this must have been a task that takes a lot of effort.” Reflecting on the latter outcome, we sought to establish a more direct relation between effort ratings and biomechanical activity, so in the second experiment we reversed the functional role of effort ratings and angular displacements. Whereas in experiment 1 we prescribed angular displacements and let effort ratings vary, in experiment 2 we let angular displacements vary and prescribed effort ratings; frequency was prescribed in both experiments. In experiment 2 we found that participants covered greater angular displacements as instructed effort increased and that angular displacements increased as frequency decreased (see Fig. 4). A straightforward biomechanical hypothesis can account for this result, namely, that effort was directly related to angular velocity. Support for this hypothesis is seen in Fig. 6, which shows the same data as in Fig. 4 but plotted in a different way. Here we divide mean angular displacement by movement period and plot the resulting ratio, mean angular velocity, as a function of prescribed effort. The quality of the linear relation between angular velocity and effort is reasonably good. Over 95% of the variance is accounted for with the linear fit (P<0.001), and the zero intercept of the best-fitting straight line is close to zero, which is the value expected for an angular velocity associated with no effort at all. The quality of the obtained linear fit supports the hypothesis that angular velocity and effort were directly related.

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Fig. 7 Schematic diagram of the two-link chain used to simulate arm movements observed in experiment 1 Fig. 6 Relationship between mean angular velocity and prescribed effort for the three movement frequencies of experiment 2

Because angular velocity is a kinematic variable, one wonders whether the relation between angular velocity and effort can be ascribed to kinetic factors. We think it can be, because higher angular velocities are associated with higher net muscle and inertial forces. Consistent with this interpretation, we found in experiment 2 that peak flexion accelerations and peak extension accelerations increased with angular velocity. Given that angular acceleration and torque are linked, as is well known from Newtonian mechanics (also see Brown and Cooke 1984), it is likely that overall net muscle and inertial forces acting on the typical participant’s forearm contributed to participants’ RPEs. The increased muscular forces associated with larger torques in this context may also be interpreted within the framework of the typical triphasic pattern of agonist-antagonist-agonist muscle activity seen in a broad range of movements with varying speed and amplitude (Brown and Cooke 1981; Hallett and Marsden 1979; Karst and Hasan 1987). In single-joint movements, the initial agonist burst produces the muscle force necessary to overcome limb inertia and initiate movement. This force must increase with increasing movement velocity due to the increase in momentum. In addition, increased antagonist activity as well as the second burst of agonist activity also increases to produce larger decelerative forces required when movement speed increases (Cooke and Brown 1990). Taking these factors into account, it is reasonable to suppose that the RPEs in experiment 2 were related to the muscular forces that participants generated. According to this line of reasoning, muscle force and sense of effort are indeed related. Having reached this conclusion on the basis of the method used in experiment 2, it seems reasonable to recommend that method for future research. The technique can be used with different limb segments or combinations of limb segments, for movements with different

orientations and loads, and with normal and clinical populations. Regarding clinical populations, by relying on velocity-effort graphs like the one in Fig. 6, it should be possible to ascertain how well patients respond to treatments by referring to the slope of the function relating velocity to effort. As a patient’s ability to move a limb segment becomes easier, the slope of his or her effort-velocity curve should get steeper. Having a numerical quantity to refer to (the slope of the function relating velocity to effort) could be a boon to both clinical and basic research. Acknowledgements This work was supported by NSF grant SBR-9308671, an NIMH Research Scientist Development Award, a Pennsylvania State University Liberal Arts grant, and an intramural grant from the Moss Rehabilitation Research Institute, MossRehab Hospital, Philadelphia, Pa. We thank an anonymous reviewer for very helpful feedback on an earlier version of this article.

Appendix This appendix presents a force-control model for the results of experiment 1. Consider the muscle groups responsible for flexing and extending the elbow joint. Suppose, as shown in Fig. 7, that these muscle groups act on a chain of two rigid links corresponding to the upper arm (link 1) and forearm/hand (link 2). The lengths and masses of the segments can be chosen to model the inertial parameters of a human arm. Using standard anthropometric data (Winter 1990) for a person 185.4 cm tall with a mass of 72.7 kg (physical dimensions of a typical male subject in this study), the segment lengths and masses are 30.0 cm and 2.0 kg, respectively, for link 1, and 37.8 cm and 1.6 kg, respectively, for link 2. The center of mass (CM) of link 2, which consists of the hand and forearm, can be shown to be located 25.8 cm from the proximal end of the segment. A hinge joint simulating the elbow joint connects the two links. The use of a hinge joint constrains the system to 1 degree of freedom

372 Fig. 8a, b Theoretical values of force as a function of time when absolute values of extensor baseline force and flexor baseline force were either low (a) or high (b). The sum of forces is the same in the two panels. By hypothesis, the left panel corresponds to a large range of motion, whereas the right panel corresponds to a small range of motion

whose dimension of motion can be restricted to the horizontal plane. The two muscle groups can be assumed to act on link 2, thereby changing the position of link 2 relative to link 1. For simplicity, the two muscle groups can be considered to exert their forces perpendicularly at all times with respect to link 2 at that segment’s CM location. It is assumed that link 1 remains stationary at all times. With the physical characteristics described above, one can generate movements of link 2 corresponding to the combinations of ROM and frequency in the present experiment (see Fig. 8). To model the behavior, force production by the extensor and flexor muscle groups can be simulated with sine waves (one for each muscle group) as a function of time, t: (1) (2) where f denotes frequency, Amplitude is more than 0, ExtensorBaselineForce is more than zero, and FlexorBaselineForce less than zero. Note that the two muscles are assumed to generate forces in phase, so the implicit term for phase is zero. The forces of the two muscles can be summed at each moment in time to yield a sinusoidal time-varying total force: (3) Equation 1, Eq. 2, and Eq. 3 can be used to simulate movements of different frequency and range of motion by varying f and amplitude, respectively. Stiffness can be varied by changing the baseline force terms, which may be achieved physiologically by changing the level of muscle cocontraction. The goal of the simulation is to generate realistic movements whose accompanying stiffness properties predict effort ratings, assuming that perceived effort is directly related to the sum of the two muscles’s rectified forces over 20 motion cycles. To achieve the simulation, we required the net force acting on link 2 at the beginning of each trial be 0 N and

Fig. 9 Theoretically derived values of summed rectified force as a function of frequency and range of motion

that link 2 was in a flexed position with respect to link 1 such that it could subsequently cover the required ROM and be extended or flexed for equal amounts of time in each movement cycle. The forces generated by the extensor and flexor muscle groups were constrained to be equal and opposite at the beginning of each trial. The movement of link 2 was initiated by an increase in the force of the extensor muscle and a decrease in the absolute force of the flexor muscle, resulting in a net force acting on the link to produce a clockwise movement of link 2 about the hinge joint connecting links 1 and 2 (i.e., extension of link 2 with respect to link 1). Based on the sinusoidal increases and decreases in the forces of the extensor and flexor muscle groups, link 2 could be moved sinusoidally (Fig. 8). To fit the model, the absolute values of the baseline forces were calculated as follows: (4) (5) Exponentiation of f and ROM allowed either of these raised terms to equal zero. Equation 4 and Eq. 5 imply

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References

Fig. 10 Relationship between theoretically determined values of summed rectified force and observed ratings of perceived effort

that absolute baseline force increases with f and decreases with ROM. Inherent in the claim that the absolute baseline force increases with f is the well-known positive relation between spring stiffness and resonant frequency (French 1971). Amplitude was allowed to vary as a function of ROM as follows: (6) The five constants in Eq. 4 and Eq. 6 were chosen to produce forces that were physically realistic (including the constraint that Extensor force was never negative and that Flexor force was never positive) and to yield a high correlation between RPE and summed rectified force over time. The summed rectified forces for the five frequency and five ROM conditions are shown in Fig. 9. The relation between observed RPE and theoretical summed rectified force over time, or Impulse, is shown in Fig. 10. The correlation between Impulse and experimentally observed RPE was r=0.86 (r2=0.75) for these five parameters. The corresponding regression equation was: (7) These results indicate that it is possible to relate perceived effort to physically realistic muscle force patterns.

Borg GAV (1982) Psychophysical bases of perceived exertion. Med Sci Sports Exerc 14:377–381 Borg G (1990) Psychophysical scaling with applications in physical work and the perception of exertion. Scand J Work Environ Health [Suppl 1] 16:55–58 Brown SH, Cooke JD (1981) Amplitude- and instruction-dependent modulation of movement-related electromyogram activity in humans. J Physiol (Lond) 316:97–107 Brown SH, Cooke JD (1984) Initial agonist burst duration depends on movement amplitude. Exp Brain Res 55:523–527 Burgess PR, Cooper TA, Gottlieb GL, Latash ML (1995) The sense of effort and two models of single-joint motor control. Somatosens Mot Res 12:343–358 Cooke JD, Brown SH (1990) Movement-related phasic muscle activation. II. Generation and functional role of the triphasic pattern. J Neurophysiol 63:465–472 Fitts PM (1954) The information capacity of the human motor system in controlling the amplitude of movement. J Exp Psychol 47:381–391 Flash T, Hogan N (1985) The coordination of arm movements: an experimentally confirmed mathematical model. J Neurosci 5:1688–1703 French AP (1971) Vibration and waves. Norton, New York Hallet M, Marsden CD (1979) Ballistic flexion movements of the human thumb. J Physiol (Lond) 294:33–50 Karst GM, Hasan Z (1987) Antagonist muscle activity during human forearm movements under varying kinematic and loading conditions. Exp Brain Res 67:391–401 Langolf GD, Chaffin DB, Foulke JA (1976) An investigation of Fitts’ Law using a wide range of movement amplitudes. J Mot Behav 8:113–128 Meyer DE, Smith JEK, Kornblum S, Abrams RA, Wright CE (1990) Speed-accuracy tradeoffs in aimed movements: toward a theory of rapid voluntary action. In: Jeannerod M (ed) Motor representation and control (Attention and performance XIII) Erlbaum, Hillsdale, NJ, pp 173–226 Rosenbaum DA, Meulenbroek RG, Vaughan J, Jansen C (2001) Posture-based motion planning: applications to grasping. Psychol Rev 108:709–734 Russell WD (1997) On the current status of rated perceived exertion. Percept Mot Skills 84:799–808 Soechting JF, Buneo CA, Herrmann U, Flanders M (1995) Moving effortlessly in three dimensions: Does Donders’s Law apply to arm movement? J Neurosci 15:6271–6280 Uno Y, Kawato M, Suzuki R (1989) Formation and control of optimal trajectory in human multijoint arm movement: minimum torque-change model. Biol Cybern 61:89–101 Winter DA (1990) Biomechanics and motor control of human movement (2nd edn) Wiley, New York

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