Perceptual distortion contributes to the curvature of human reaching movements

Unconstrained point-to-point human arm movements are generally gently curved, a fact which has been used to assess the validity of models of trajectory formation. In this study we examined the relationship between curvature perception and movement curvature for planar sagittal and transverse arm movements. We found a significant correlation (P<0.0001, n=16) between the curvature perceived as straight and the curvature of actual arm movements. We suggest that subjects try to make straight-line movements, but that actual movements are curved because visual perceptual distortion makes the movements appear to be straighter than they really are. We conclude that perceptual distortion of curvature contributes to the curvature seen in human point-to-point arm movements and that this must be taken into account in the assessment of models of trajectory formation.     

Endpoints of arm movements to visual targets

Reaching out for objects with an unseen arm involves using both visual and kinesthetic information. Neither visual nor kinesthetic information is perfect. Each is subject to both constant and variable errors. To evaluate how such errors influence performance in natural goal-directed movements, we asked subjects to align a real 5-cm cube, which they held in their hand but could not see, with a three-dimensional visual simulation of such a cube. The simulated cube was presented at one of four target locations at the corners of an imaginary tetraeder. Subjects made successive, self-paced movements between these target locations. They could not see anything except the simulated cube throughout the experiment. Initial analysis of the spatial dispersion of movement endpoints demonstrated that the major source of errors under these conditions was visual. Further analysis of the relationship between variability of the starting positions and endpoints showed that the errors were primarily in judging the endpoint, rather than the direction or amplitude of the required movement vector. The findings support endpoint control of human goal-directed movements.     

Coordinated responses following mechanical perturbation of the arm during prehension

We have investigated how the control of hand transport and of hand aperture are coordinated in prehensile movements by delivering mechanical perturbations to the hand transport component and looking for coordinated adjustments in hand aperture. An electric actuator attached to the subject's right arm randomly pulled the subject backwards, away from the target, or pushed them towards it, during a quarter of the experimental trials. A compensatory adjustment of hand aperture followed the immediate, mechanical effects of the perturbation of hand transport. The adjustment appeared to return the subject towards a stereotyped spatial relation between hand aperture and hand transport. These spatial patterns suggest how the two components may be coordinated during prehension. A simple model of this coordination, based on coupled position feedback systems, is presented.     

Origins and violations of the 2/3 power law in rhythmic three-dimensional arm movements

The 2/3 power law, the nonlinear relationship between tangential velocity and radius of curvature of the end-effector trajectory, is thought to be a fundamental constraint of the central nervous system in the formation of rhythmic endpoint trajectories. However, studies on the 2/3 power law have been confined largely to planar drawing patterns of relatively small size. With the hypothesis that this strategy overlooks nonlinear effects that are constitutive in movement generation, the present experiments tested the validity of the power law in elliptical patterns that were not confined to a planar surface and which were performed by the unconstrained 7-degrees of freedom (DOF) arm, with significant variations in pattern size and workspace orientation. Data were recorded from five human subjects where the seven joint angles and the endpoint trajectories were analyzed. Additionally, an anthropomorphic 7-DOF robot arm served as a "control subject" whose endpoint trajectories were generated on the basis of the human joint angle data, modeled as simple harmonic oscillations. Analyses of the endpoint trajectories demonstrate that the power law is systematically violated with increasing pattern size, in both exponent and the goodness of fit. The origins of these violations can be explained analytically based on smooth, rhythmic trajectory formation and the kinematic structure of the human arm. We conclude that, in unconstrained rhythmic movements, the power law seems to be a by-product of a movement system that favors smooth trajectories, and that it is unlikely to serve as a primary movement-generating principle. Our data rather suggest that subjects employed smooth oscillatory pattern generators in joint space to realize the required movement patterns.     

Adaptation of arm trajectory during continuous drawing movements in different dynamic environments

Human subjects can readily adapt their movement trajectories to different dynamic or visuomotor environments. The focus of the current study was to determine whether subjects could simultaneously adapt to multiple dynamic environments. Subjects (n=5) drew ellipses continuously for 70 s using a torquable manipulandum under six distinct dynamic conditions, representing the combination of load type (spring, viscous, and inertia) and load direction (assisting and opposing). Each subject performed two control, ten load, and five washout trials. A significant effect of force condition on the trajectory of the movement was found in 26 of 30 cases (6 conditions × 5 subjects); the magnitude of the distortion differed across the conditions. The extent of adaptation also differed across the loads. Opposing inertia and viscosity led to fast adaptation. However, assisting inertia and viscosity were associated with relatively slow adaptation. The results of adaptation to the stiffness conditions were not consistent. Following sudden removal of the load we saw an additional disturbance of the trajectory (after-effect), which was often the mirror image of the original distortion. The shape and size of the after-effect were different across load conditions. These results show that human subjects can adapt to a variety of different dynamic transformations and that the time-course of adaptation is dependent on both the state space and the direction of the load. Electronic Publication     

Deficits in the coordination of multijoint arm movements in patients with hemiparesis: evidence for disturbed control of limb dynamics

This study provides a detailed analysis of disturbances in the kinematics and dynamics of the acceleration phase of multijoint arm movements in six patients with chronic hemiparesis. Movements of the dominant and nondominant limbs were also examined in three control subjects. Subjects performed rapid movements from a central starting point to 16 targets located equidistantly around the circumference of a circle. Support of the upper limb was provided by an air-bearing apparatus, which allowed very low friction movements in the horizontal plane. We found that patients retained the capacity to modulate, in response to target direction, the initial direction of movements performed with the paretic limb. However, in comparison to the nonparetic limb or control subjects, movements of the paretic limb were misdirected systematically. An inverse dynamics analysis revealed an abnormal spatial tuning of the muscle torque at the elbow used to initiate movements of the paretic limb. Based on electromyographic recordings, similar spatial abnormalities were also apparent in the initial activations of elbow muscles. We argue that these spatial abnormalities result from a systematic disturbance in the control signal to limb muscles that cannot be attributed to previously identified mechanisms such as weakness, spasticity mediated restraint, or stereotypic muscle activation patterns (muscle synergies). Instead, our analysis of movement dynamics and simulation studies demonstrate that the spatial abnormalities are consistent with an impaired feedforward control of the passive interaction torques which arise during multijoint movements. This impaired control is hypothesized to reflect a degradation of the internal representation of limb dynamics that occurs either as a primary consequence of brain injury or secondary to disuse.     

Slowing of human arm movements during weightlessness: the role of vision

The human motor system responds to weightlessness by the slowing of movement. It has been suggested that deficits in visuo-motor co-ordination cause this effect. We studied the mechanisms of the slowing of movement in three long-term missions to the Russian space station Mir. In particular, the role of vision in the control of movement in microgravity has been studied in these experiments on seven cosmonauts, pre-, in-, and post-flight. The cosmonauts made arm movements to visual targets under the following conditions of visual control: no visual control, interrupted visual control, and undisturbed visual control. The results showed that the slowing of movement during weightlessness was manifested by decreases of peak velocity and peak acceleration, was not associated with a prolongation of the movement phase of deceleration, and was not affected by manipulation of the conditions of visual control. The slowing of movement tended to subside after the months of the flight and completely disappeared within days after the landing. Accuracy of the movements strictly depended on the constraints imposed on the vision and remained unaffected in-flight. The data presented demonstrate that the slowing of movement in microgravity is not directly related to deficits in sensori-motor co-ordination and is not associated with a reduction of the accuracy of movement. The strategy for motor control in microgravity seems to be directed towards the generation of smooth movements and the maintenance of their accuracy. Electronic Publication     

Goal-directed arm movements in absence of visual guidance: evidence for amplitude rather than position control

Summary 1. The control of pointing arm movements in the absence of visual guidance was investigated in unpracticed human subjects. The right arm grasped a lever which restricted the movement of the right index fingertip to a horizontal arc, centered between the axes of eye rotation. A horizontal panel directly above the arm prevented visual feedback of the movement. Visual stimuli were presented in discrete positions just above panel and fingertip. A flag provided visual feedback on fingertip position before each pointing movement (Exp. A and B), or before a movement sequence (Exp. C). 2. When subjects pointed from straight ahead to eccentric stimulus positions (Exp. A), systematic and variable pointing errors were observed; both kinds of errors increased with stimulus eccentricity. When subjects pointed from 30 deg left to stimuli located further right (Exp. B), errors increased with stimulus position to the right. Taken together, these findings suggest that pointing accuracy depends not primarily on stimulus position, but rather on required movement amplitude. 3. When subjects performed sequences of unidirectional movements (Exp. C), systematic and variable errors increased within the sequence. A quantitative analysis revealed that this increase can be best described as an accumulation of successive pointing errors. 4. We conclude that both findings, error increase with amplitude, and accumulation of successive errors, when considered together strongly support the hypothesis that amplitude, rather than final position, is the controlled variable of the investigated movements.     

Modulation of cutaneous reflexes in arm muscles during walking: further evidence of similar control mechanisms for rhythmic human arm and leg movements

Stimulation of cutaneous nerves innervating the hand evokes prominent reflexes in many arm muscles during arm cycling. We hypothesized that the mechanisms controlling reflex modulation during the rhythmic arm swing of walking would be similar to that documented during arm cycling. Thus, we expected cutaneous reflexes to be modulated by position in the walking cycle (phase dependence) and be different when walking compared to contraction while standing (task dependence). Subjects performed static postures similar to those occurring during walking and also walked on a treadmill while the superficial radial nerve was electrically stimulated pseudorandomly throughout the step cycle. EMG was recorded bilaterally from upper limb muscles and kinematic recordings were obtained from the elbow and shoulder joints. Step cycle information was obtained from force-sensing insoles. Analysis was conducted after averaging contingent upon the occurrence of stimulation in the step cycle. Phase-dependent modulation of cutaneous reflexes at early (~50–80 ms) and middle (~80–120 ms) latencies was observed. Coordinated bilateral reflexes were seen in posterior deltoid and triceps brachii muscles. Task dependency was seen in that reflex amplitude was only correlated with background EMG during static contraction (75% of comparisons for both early and middle latency reflexes). During walking, no significant relationship between reflex amplitude and background EMG level was found. The results show that cutaneous reflex modulation during rhythmic upper limb movement is similar to that seen during arm cycling and to that observed in leg muscles during locomotion. These results add to the evidence that, during cyclical movements of the arms and legs, similar neural mechanisms observed only during movement (e.g. central pattern generators) control reflex output. Electronic Publication     

Directional specificity of postural muscles in feed-forward postural reactions during fast voluntary arm movements

Healthy subjects performed bilateral fast shoulder movements in different directions while standing on a force platform. Anticipatory postural adjustments were seen as changes in the electrical activity of postural muscles as well as displacements of the center of pressure and center of gravity. Postural muscle pairs of agonist-antagonist commonly demonstrated triphasic patterns starting prior to the first electromyographic (EMG) burst in the prime-mover muscle. Proximal postural muscles demonstrated the largest anticipatory increase in the background activity during movements in one of the two opposite directions (forward or backwards). These changes progressively decreased when movements deviated from the preferred direction and frequently disappeared during movements in the opposite direction. The patterns in distal muscles varied across subjects and could demonstrate larger anticipatory changes during movements forward and backwards as compared to movements in intermediate directions. Bilateral addition of inertial loads to the wrists did not change the general anticipatory patterns, while making some of their features more pronounced. Anticipatory postural adjustments were followed by later changes in the activity of postural muscles, also reflected in the mechanical variables. Changes in leg joint angles revealed a hip-ankle strategy during shoulder flexions and an ankle strategy during shoulder extensions. The study demonstrates different behaviors of proximal and distal muscles during anticipatory postural adjustments in preparation for fast arm movements. We suggest that the proximal muscles produce a general pattern of postural adjustments, while distal muscles take care of fine adjustments that are more likely to vary across subjects.     

On the role of static and dynamic visual afferent information in goal-directed aiming movements

Movement planning has been shown to be optimized when the participant is permitted to see his or her hand resting on the starting base prior to movement initiation. However, this proposition is opposed by contradictory results. In the present study, we wanted to determine whether these conflicting results were caused by procedural differences. The results showed that seeing one's hand on the starting base did not result in more accurate aiming movement than when this information was not available. However, lower aiming errors were found when one was asked to foveate the starting base and then the target prior to movement initiation, but only when no dynamic visual information was available during movement. When an aiming movement was performed while one's hand was visible in visual periphery, foveating the starting base or not prior to movement initiation did not modify aiming accuracy. These results suggest that gazing at the starting base and then at the target provides an eye-based representation of the movement to be performed that can be used by the CNS to plan a manual aiming movement. Information for better planning of the direction – but not the extent – dimension of an upcoming movement can also be derived from dynamic visual information available in peripheral vision. Electronic Publication     

Systematic errors of planar arm movements provide evidence for space categorization effects and interaction of multiple frames of reference

Healthy humans performed arm movements in a horizontal plane, from an initial position toward remembered targets, while the movement and the targets were projected on a vertical computer monitor. We analyzed the mean error of movement endpoints and we observed two distinct systematic error patterns. The first pattern resulted in the clustering of movement endpoints toward the diagonals of the four quadrants of an imaginary circular area encompassing all target locations (oblique effect). The second pattern resulted in a tendency of movement endpoints to be closer to the body or equivalently lower than the actual target positions on the computer monitor (y-effect). Both these patterns of systematic error increased in magnitude when a time delay was imposed between target presentation and initiation of movement. In addition, the presence of a stable visual cue in the vicinity of some targets imposed a novel pattern of systematic errors, including minimal errors near the cue and a tendency for other movement endpoints within the cue quadrant to err away from the cue location. A pattern of systematic errors similar to the oblique effect has already been reported in the literature and is attributed to the subject's conceptual categorization of space. Given the properties of the errors in the present work, we discuss the possibility that such conceptual effects could be reflected in a broad variety of visuomotor tasks. Our results also provide insight into the problem of reference frames used in the execution of these aiming movements. Thus, the oblique effect could reflect a hand-centered reference frame while the y-effect could reflect a body or eye-centered reference frame. The presence of the stable visual cue may impose an additional cue-centered (allocentric) reference frame. Electronic Publication     

Velocity curves of human arm and speech movements

Summary The velocity curves of human arm and speech movements were examined as a function of amplitude and rate in both continuous and discrete movement tasks. Evidence for invariance under scalar transformation was assessed and a quantitative measure of the form of the curve was used to provide information on the implicit cost function in the production of voluntary movement. Arm, tongue and jaw movements were studied separately. The velocity curves of tongue and jaw movement were found to differ in form as a function of movement duration but were similar for movements of different amplitude. In contrast, the velocity curves for elbow movements were similar in form over differences in both amplitude and duration. Thus, the curves of arm movement, but not those of tongue or jaw movement, were geometrically equivalent in form. Measurements of the ratio of maximum to average velocity in arm movement were compared with the theoretical values calculated for a number of criterion functions. For continuous movements, the data corresponded best to values computed for the minimum energy criterion; for discrete movement, values were in the range of those predicted for the minimum jerk and best stiffness criteria. The source of a rate dependent asymmetry in the form of the velocity curve of speech movements was assessed in a control study in which subjects produced simple raising and lowering movements of the jaw without talking. The velocity curves of the non-speech control gesture were similar in form to those of jaw movement in speech. These data, in combination with similar findings for human jaw movement in mastication, suggest that the asymmetry is not a direct consequence of the requirements of the task. The biomechanics and neural control of the orofacial system may be possible sources of this effect.     

Are arm trajectories planned in kinematic or dynamic coordinates? An adaptation study

There are several invariant features of pointto-point human arm movements: trajectories tend to be straight, smooth, and have bell-shaped velocity profiles. One approach to accounting for these data is via optimization theory; a movement is specified implicitly as the optimum of a cost function, e.g., integrated jerk or torque change. Optimization models of trajectory planning, as well as models not phrased in the optimization framework, generally fall into two main groups-those specified in kinematic coordinates and those specified in dynamic coordinates. To distinguish between these two possibilities we have studied the effects of artificial visual feedback on planar two-joint arm movements. During self-paced point-to-point arm movements the visual feedback of hand position was altered so as to increase the perceived curvature of the movement. The perturbation was zero at both ends of the movement and reached a maximum at the midpoint of the movement. Cost functions specified by hand coordinate kinematics predict adaptation to increased curvature so as to reduce the visual curvature, while dynamically specified cost functions predict no adaptation in the underlying trajectory planner, provided the final goal of the movement can still be achieved. We also studied the effects of reducing the perceived curvature in transverse movements, which are normally slightly curved. Adaptation should be seen in this condition only if the desired trajectory is both specified in kinematic coordinates and actually curved. Increasing the perceived curvature of normally straight sagittal movements led to significant (P<0.001) corrective adaptation in the curvature of the actual hand movement; the hand movement became curved, thereby reducing the visually perceived curvature. Increasing the curvature of the normally curved transverse movements produced a significant (P<0.01) corrective adaptation; the hand movement became straighter, thereby again reducing the visually perceived curvature. When the curvature of naturally curved transverse movements was reduced, there was no significant adaptation (P>0.05). The results of the curvature-increasing study suggest that trajectories are planned in visually based kinematic coordinates. The results of the curvature-reducing study suggest that the desired trajectory is straight in visual space. These results are incompatible with purely dynamicbased models such as the minimum torque change model. We suggest that spatial perception-as mediated by vision-plays a fundamental role in trajectory planning.     

The horizontal curvature of point-to-point movements does not depend on simply the planning space

Point-to-point movements constrained to the horizontal plane are generally straight, although they exhibit slight deviations from straightness. Unconstrained horizontal movements (i.e., movements where the hand is lifted) are more curved in their projection onto the horizontal plane than constrained movements. It has been argued that this difference in horizontal curvature is due to differences in the space in which the movements were planned (joint space versus work space, respectively). The current study challenged this explanation. We found that horizontal curvature of constrained movements increased when moving over a round surface compared to moving over a flat surface and when friction was low compared to when friction was high. Because all these movements were constrained movements this suggests that the earlier reported differences in horizontal curvature between constrained and unconstrained movements may not originate from a difference in the movements’ planning space. The discussion addresses how factors related to planning and factors related to biomechanics may contribute to the magnitude of horizontal curvature in unconstrained and constrained movements.     

Motor strategies involved in the performance of sequential movements

Summary The present study analyses the strategies adopted by normal subjects when they are asked to make two separate movements as rapidly as possible one after the other. Five subjects performed the following sequential movements in their own time. 1) Squeeze an isometric force transducer between fingers and thumb to a force of 30 N and then flex the elbow of the same arm through 15°. 2) Squeeze the transducer with one hand and then flex the elbow of the other arm. 3) Perform an isotonic opposition of finger and thumb and then flex the elbow of the same arm. 4) First flex the elbow through 15, 30 or 45° and then squeeze the transducer. 5) Flex and then extend the elbow as rapidly as possible. In tasks 1–4 there was no correlation between the times taken to complete the two separate components of the sequence. Because of this we suggest that the two movements remained under the control of two separate motor programmes. In contrast, in task 5, the times taken for the two components were correlated and hence we suggest that in this case a single programme was used to perform the sequence. In tasks 1–3, in which the mean duration of the first movement was some 135–162 ms, there was a mean pause of about 85 ms before the start of the second movement. Subjects tended to chose a minimum inter-onset latency between the start of the first and the start of the second movement of a sequence of some 230 ms. The reason for this appeared to be that if subjects were encouraged to decrease their interonset latencies to less than 200 ms, the speed of the second movement decreased sharply. However, if the duration of the first movement was prolonged as in task 4, the second movement could be delayed, although there now was little or no pause between the two movements. We conclude that when a single motor programme is run, it is followed by a relative refractory period. If a second programme is run within this period, it cannot be executed without loss of speed. Switching from one motor programme to another is achieved with an optimal minimum delay of 200 ms. Sequential movements which are controlled by a single programme do not share this limitation.     

Reaching movements in children: accuracy and reaction time development

The present study was undertaken to follow the development of the capability to produce adult-like fast and precise movements reaching visual targets, during childhood. A two-dimensional reaching task was used. We focussed on pre-planning capabilities, by instructing subjects to produce movements as fast as possible, preventing corrections after initiation of movement. The capability of information processing and accurate motor response production were assessed by measuring reaction time (RT, the time elapsed between target presentation and movement onset), movement time (MT, the time elapsed between movement onset and movement end) and precision of response (correlation of response extent and direction with target distance and direction). One child (male) was tested repeatedly since age 6 until age 9. At age 7, RTs decreased. At age 8, accuracy increased, after a temporary decrease at 7. Both accuracy and RT eventually reached the adult level. MTs were similar to the adult ones right from the beginning and they never changed significantly. The results were confirmed in four groups of five children each, aged 6, 7, 8 and 9, respectively. A control group of five adults was also tested. It is concluded that, between age 6 and 9, children become capable of quickly processing visual target information and producing accurate fast and uncorrected reaching trajectories based upon proprioceptive information only, like those typical of adults, by shortening RTs and improving precision, while maintaining adult-like MTs throughout. The capability of quickly reacting to a target acting as a `Go’ signal (measured by RT) and that of information processing to program an accurate motor trajectory (measured by the precision achieved) appear not to be developmentally linked, the former improving earlier, the latter later.     

Misdirections in slow goal-directed arm movements and pointer-setting tasks

Summary Information about the direction of the virtual line between two positions in space (directional information) is used in many decision-making and motor tasks. We investigated how accurately directional information is processed by the brain. Subjects performed two types of task. In both tasks they sat at a table. In the first task they had to move their hand slowly and accurately from an initial position 40 cm in front of them to visually presented targets at a distance of 30 cm from the initial position (movement task). We analysed the initial movement direction. In the second task subjects had to position pointers in the direction of the targets as accurately as they could (perceptive task). We found that in the movement task the subjects started the movements to most targets in a direction that deviated consistently from the direction of the straight line between initial position and target position. The maximum deviation ranged from 5–10° for the various subjects. The mean standard deviation was 4°. In the perceptive task the subjects positioned the pointer in similarly deviating directions. Furthermore, we found that the maximum deviation in the pointer direction depended on the length of the pointer: the smaller the pointer, the larger the consistent deviations in the pointer direction. The shortest pointer showed deviations comparable to the deviations found in the movement task. These findings suggest that the deviations in the two tasks stem from the same source.     

Torques generated at the human elbow joint in response to constant position errors imposed during voluntary movements

The stiffness of the human elbow joint was investigated during targeted, 1.0-rad voluntary flexion movements at speeds ranging from slow (1.5 rad/s) to very fast (6.0 rad/s). A torque motor produced controlled step position errors in the execution of the movements. The steps began at the onset of movement, rose to an amplitude of 0.15 rad in 100 ms, and had a duration equal to movement duration. The net joint torque (muscle torque) resisting the step perturbation was computed from the applied torque, the joint acceleration, and the limb inertia. Subjects resisted the imposed step changes with approximately step changes in the net muscle torque. The mean resistance torque divided by the step amplitude was computed and is referred to as the stiffness. The stiffness increased with the voluntary movement speed, over the range of speeds (1.5–6 rad/s). The stiffness increased linearly with the magnitude of the net muscle torque on the unperturbed trials (referred to as background torque). The stiffness changed by only 20% when the step amplitude ranged from 0.05 to 0.15 rad. The mechanical resonant frequency (f _r), estimated from the average stiffness estimates, ranged from 0.8 to 3.0 Hz. The resonant frequency approximately equaled the principal frequency component of the movement f _m. On average: f _r = 0.96 f _m+0.46. During the fixed, 100-ms rise time of the step, the resistance was not linearly related to the background torque. At slower speeds the resistance was relatively greater during this rise time. However, when the imposed step perturbation was modified so that its rise time occurred in a time proportional to the movement duration (rather than in the fixed, 100-ms, time), the muscle torque resisting the motor during this rise time was proportional to the background torque. When these modified step responses were plotted on a time scale normalized to the movement duration, they all had approximately the same shape. Apparently the muscle viscosity scaled with the stiffness so as to maintain the constant response shape (constant damping ratio). The observed tuning of the mechanical properties to the movement speed is suggested to be important in the robust generation of smooth stereotyped voluntary movements.     

Asymmetric velocity and acceleration profiles of human arm movements

Summary Displacement, velocity, acceleration and jerk (change of acceleration with time) were analyzed for arm flexion movement over a wide range of movement amplitudes and speeds. Relative time to peak velocity or relative duration of acceleration, k, was approximately 0.5 for the movements with intermediate speed (about 0.5 s in movement time), i.e., symmetric velocity and acceleration profiles. For the slow and ballistic movements, k shifted towards values below and above 0.5, respectively creating asymmetric profiles. Consistent k-dependence of movement time, peak velocity, maximum acceleration and maximum deceleration were observed. Jerk cost, the square of the magnitude of jerk integrated over the entire movement, was calculated for each movement. A dynamic optimization technique to minimize jerk cost under the constraint on jerk input was applied to interpret the results, assuming that a major goal of skilled movements was to produce optimally smooth movements. The constrained minimum-jerk model explained speed dependent asymmetry of the velocity and acceleration profiles. Jerk cost consumed by the movements with intermediate speed approximately satisfied minimum-cost criterion predicted by the model but was higher than the criterion for slow and ballistic movements. The results suggested that optimality criteria other than jerk cost also should be considered to predict movement profiles over the entire range of speeds.