Kinematics and kinetics of multijoint reaching in nonhuman primates

The present study identifies the mechanics of planar reaching movements performed by monkeys (Macaca mulatta) wearing a robotic exoskeleton. This device maintained the limb in the horizontal plane such that hand motion was generated only by flexor and extensor motions at the shoulder and elbow. The study describes the kinematic and kinetic features of the shoulder, elbow, and hand during reaching movements from a central target to peripheral targets located on the circumference of a circle: the center-out task. While subjects made reaching movements with relatively straight smooth hand paths and little variation in peak hand velocity, there were large variations in joint motion, torque, and power for movements in different spatial directions. Unlike single-joint movements, joint kinematics and kinetics were not tightly coupled for these multijoint movements. For most movements, power generation was predominantly generated at only one of the two joints. The present analysis illustrates the complexities inherent in multijoint movements and forms the basis for understanding strategies used by the motor system to control reaching movements and for interpreting the response of neurons in different brain regions during this task.     

Kinetic and kinematic adaptation to anisotropic load

Different investigators have proposed that multi-joint arm movements are planned with respect to either the path of the hand or the forces and torques acting about the moving joints. In this experiment, we examined the kinematic and kinetic response of the motor system when a load was applied to the forearm, which reduced the natural anisotropy of the arm. We asked two questions: (1) when the movement path changes upon the introduction of the novel load, do muscle torques at the shoulder and elbow remain the same as they were before the load was applied? and (2) when the path is restored partially as the novel load is learned, do changes in muscle torque occur preferentially at one or the other joint? Participants performed rapid arm movements to a target with and without the novel load attached to their arm. Changes in hand path and muscle torque profiles were examined immediately after the application of the load and again following 30 practice trials. The introduction of the load increased the curvature of hand paths for each participant and resulted in changes in the magnitude and time course of muscle torque at both joints, although to a greater extent at the shoulder. After practice with the load, hand paths and elbow muscle torques resembled those produced with no load. Muscle torques produced at the shoulder, however, did not return to pre-load patterns. These observations provide support for the idea that movements are initiated by planned muscle torques and that as the movement proceeds muscle torques are regulated in order to produce hand paths that conform approximately to a kinematic plan.     

Coordination of multi-joint arm movements in cerebellar ataxia: Analysis of hand and angular kinematics

Kinematic abnormalities of fast multijoint movements in cerebellar ataxia include abnormally increased curvature of hand trajectories and an increased hand path and are thought to originate from an impairment in generating appropriate levels of muscle torques to support normal coordination between shoulder and elbow joints. Such a mechanism predicts that kinematic abnormalities are pronounced when fast movements are performed and large muscular torques are required. Experimental evidence that systematically explores the effects of increasing movement velocities on movement kinematics in cerebellar multijoint movements is limited and to some extent contradictory. We, therefore, investigated angular and hand kinematics of natural multijoint pointing movements in patients with cerebellar degenerative disorders and healthy controls. Subjects performed self-paced vertical pointing movements with their right arms at three different target velocities. Limb movements were recorded in three-dimensional space using a two-camera infrared tracking system. Differences between patients and healthy subjects were most prominent when the subjects performed fast movements. Peak hand acceleration and deceleration were similar to normals during slow and moderate velocity movements but were smaller for fast movements. While altering movement velocities had little or no effect on the length of the hand path and angular motion of elbow and shoulder joints in normal subjects, the patients exhibited overshooting motions (hypermetria) of the hand and at both joints as movement velocity increased. Hypermetria at one joint always accompanied hypermetria at the neighboring joint. Peak elbow angular deceleration was markedly delayed in patients compared with normals. Other temporal movement variables such as the relative timing of shoulder and elbow joint motion onsets were normal in patients. Kinematic abnormalities of multijoint arm movements in cerebellar ataxia include hypermetria at both the elbow and the shoulder joint and, as a consequence, irregular and enlarged paths of the hand, and they are marked with fast but not with slow movements. Our findings suggest that kinematic movement abnormalities that characterize cerebellar limb ataxia are related to an impairment in scaling movement variables such as joint acceleration and deceleration normally with movement speed. Most likely, increased hand paths and decomposition of movement during slow movements, as described earlier, result from compensatory mechanisms the patients may employ if maximum movement accuracy is required.     

Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model.

Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model. A number of invariant features of multijoint planar reaching movements have been observed in measured hand trajectories. These features include roughly straight hand paths and bell-shaped speed profiles where the trajectory curvatures between transverse and radial movements have been found to be different. For quantitative and statistical investigations, we obtained a large amount of trajectory data within a wide range of the workspace in the horizontal and sagittal planes (400 trajectories for each subject). A pair of movements within the horizontal and sagittal planes was set to be equivalent in the elbow and shoulder flexion/extension. The trajectory curvatures of the corresponding pair in these planes were almost the same. Moreover, these curvatures can be accurately reproduced with a linear regression from the summation of rotations in the elbow and shoulder joints. This means that trajectory curvatures systematically depend on the movement location and direction represented in the intrinsic body coordinates. We then examined the following four candidates as planning spaces and the four corresponding computational models for trajectory planning. The candidates were as follows: the minimum hand jerk model in an extrinsic-kinematic space, the minimum angle jerk model in an intrinsic-kinematic space, the minimum torque change model in an intrinsic-dynamic-mechanical space, and the minimum commanded torque change model in an intrinsic-dynamic-neural space. The minimum commanded torque change model, which is proposed here as a computable version of the minimum motor command change model, reproduced actual trajectories best for curvature, position, velocity, acceleration, and torque. The model's prediction that the longer the duration of the movement the larger the trajectory curvature was also confirmed. Movements passing through via-points in the horizontal plane were also measured, and they converged to those predicted by the minimum commanded torque change model with training. Our results indicated that the brain may plan, and learn to plan, the optimal trajectory in the intrinsic coordinates considering arm and muscle dynamics and using representations for motor commands controlling muscle tensions.     

The effect of movement direction on joint torque covariation

It has been proposed that unconstrained upper limb movements are coordinated via a kinetic constraint that produces dynamic muscle torques at each moving joint that are a linear function of a single torque command. This constraint has been termed linear synergy (Gottlieb et al. J Neurophysiol 75:1760–1764, 1996). The current study tested two hypotheses: (1) that the extent of covariation between dynamic muscle torques at the shoulder and elbow varied with the direction of movement and (2) that the extent to which muscle torques deviated from linear synergy would be reproduced by a simulation of pointing movements in which the path of the hand was constrained to be straight. Dynamic muscle torques were calculated from sagittal plane pointing movements performed by 12 participants to targets in eight different directions. The results of principal component analyses performed on the muscle torque data demonstrated direction-dependent variation in the extent to which dynamic muscle torques covaried at the shoulder and elbow. Linear synergy was deviated from substantially in movement directions for which the magnitude of muscle torque was low at one joint. A simulation of movements with straight hand paths was able to accurately estimate the amount of covariation between muscle torques at the two joints in many directions. These results support the idea that a kinematic constraint is imposed by the central nervous system during unconstrained pointing movements. Linear synergy may also be applied as a coordinating constraint in circumstances where its application allows the path of the moving endpoint to remain close to a straight line.     

Differences in control of limb dynamics during dominant and nondominant arm reaching

This study compares the coordination patterns employed for the left and right arms during rapid targeted reaching movements. Six right-handed subjects reached to each of three targets, designed to elicit progressively greater amplitude interaction torques at the elbow joint. All targets required the same elbow excursion (20 degrees ), but different shoulder excursions (5, 10, and 15 degrees, respectively). Movements were restricted to the shoulder and elbow and supported on a horizontal plane by a frictionless air-jet system. Subjects received visual feedback only of the final hand position with respect to the start and target locations. For motivation, points were awarded based on final position accuracy for movements completed within an interval of 400-600 ms. For all subjects, the right and left hands showed a similar time course of improvement in final position accuracy over repeated trials. After task adaptation, final position accuracy was similar for both hands; however, the hand trajectories and joint coordination patterns during the movements were systematically different. Right hand paths showed medial to lateral curvatures that were consistent in magnitude for all target directions, whereas the left hand paths had lateral to medial curvatures that increased in magnitude across the three target directions. Inverse dynamic analysis revealed substantial differences in the coordination of muscle and intersegmental torques for the left and right arms. Although left elbow muscle torque contributed largely to elbow acceleration, right arm coordination was characterized by a proximal control strategy, in which movement of both joints was primarily driven by the effects of shoulder muscles. In addition, right hand path direction changes were independent of elbow interaction torque impulse, indicating skillful coordination of muscle actions with intersegmental dynamics. In contrast, left hand path direction changes varied directly with elbow interaction torque impulse. These findings strongly suggest that distinct neural control mechanisms are employed for dominant and non dominant arm movements. However, whether interlimb differences in neural strategies are a consequence of asymmetric use of the two arms, or vice versa, is not yet understood. The implications for neural organization of voluntary movement control are discussed.     

Commonalities and differences in control of various drawing movements

Characteristics of control at the shoulder and elbow during nine types of drawing movements were studied in the present work. The task was to repetitively track a template, depicted on a horizontal table, with the index finger at a cyclic frequency of 1.5 Hz. The templates were a circle, four ovals and four lines of different orientations. The wrist was immobilized and the movement consisted of rotations at the shoulder and elbow joints. The studied movements varied in a wide range with respect to the amplitude of elbow and shoulder movements and relative phase between them. Kinetic analysis included analysis of torque signs, impulses, and timing. It demonstrated that the role of muscle torque in movement production was different at the two joints. During eight out of the nine movement types, the muscle torque at the shoulder accelerated and decelerated this joint and almost completely coped with the influence of the interactive torque arising from elbow motion. Conversely, interactive torque generated by shoulder motion played a dominant role in elbow acceleration and deceleration, whereas muscle torque at the elbow adjusted passive elbow movement to the various template shapes. EMG data were in agreement with the conclusions made from the kinetic analysis. Collectively, these data support the hypothesis that the two joints have different functions in movement production. The shoulder creates a foundation for motion of the entire arm through the interactive torque, and the elbow serves as a fine-tuner of the end-point movement. Control of the shoulder was similar across the eight movement types and the differences in the end-point path were provided by variations in elbow control. The two joints exchanged roles during one movement type, namely, drawing the line tilted right. During this movement, the elbow musculature generated motion at this joint and the shoulder musculature counteracted mechanical influence of this motion on the shoulder position. The findings suggest that during drawing movements, the control strategy exploits intersegmental dynamics of the shoulder-elbow mechanical linkage.     

Intrinsic joint kinematic planning. II: Hand-path predictions based on a Listing’s plane constraint

This study was aimed at examining the assumption that three-dimensional (3D) hand movements follow specific paths that are dictated by the operation of a Listing’s law constraint at the intrinsic joint level of the arm. A kinematic model was used to simulate hand paths during 3D point-to-point movements. The model was based on the assumption that the shoulder obeys a 2D Listing’s constraint and that rotations are about fixed single-axes. The elbow rotations were assumed to relate linearly to those of the shoulder. Both joints were assumed to rotate without reversals, and to start and end rotating simultaneously with zero initial and final velocities. Model predictions were compared to experimental observations made on four right-handed individuals that moved toward virtual objects in “extended arm”, “radial”, and “frontal plane” movement types. The results showed that the model was partially successful in accounting for the observed behavior. Best hand-path predictions were obtained for extended arm movements followed by radial ones. Frontal plane movements resulted in the largest discrepancies between the predicted and the observed paths. During such movements, the upper arm rotation vectors did not obey Listing’s law and this may explain the observed discrepancies. For other movement types, small deviations from the predicted paths were observed which could be explained by the fact that single-axis rotations were not followed even though the rotation vectors remained within Listing’s plane. Dynamic factors associated with movement execution, which were not taken into account in our purely kinematic approach, could also explain some of these small discrepancies. In conclusion, a kinematic model based on Listing’s law can describe an intrinsic joint strategy for the control of arm orientation during pointing and reaching movements, but only in conditions in which the movements closely obey the Listing’s plane assumption.     

Expertise-dependent modulation of muscular and non-muscular torques in multi-joint arm movements during piano keystroke

The problem of skill-level-dependent modulation in the joint dynamics of multi-joint arm movements is addressed in this study using piano keystroke performed by expert and novice piano players. Using the measured kinematic and key-force data, the time varying net, gravitational, motion-dependent interaction (INT), key-reaction (REA), and muscular (MUS) torques at the shoulder, elbow, wrist, and metacarpophalangeal (MP) joints were computed using inverse dynamics techniques. INTs generated at the elbow and wrist joints, but not those at the MP joint, were greater for the experts as compared with the novices. REA at the MP joint, but not at the other joints, was less for the experts as compared with the novices. The MUSs at the MP, wrist, and elbow joints were smaller, and that at the shoulder joint was larger for the experts as compared with the novices. The experts also had a lesser inter-strike variability of key striking force and key descending velocity as compared with the novices. These findings indicated that the relationship among the INT, REA, and MUS occurring at the joints of the upper-extremity differed between the expert and novice piano players, suggesting that the organization of multi-joint arm movement is modulated by long-term motor training toward facilitating both physiological efficiency and movement accuracy.     

Modeling 3D object manipulation: synchronous single-axis joint rotations?

In the present paper we introduce a movement planning model that is capable of predicting object manipulation movements in three dimensions. A basic assumption of this model is that the joint kinematics of the movement are optimized, which implies that joint rotations are synchronous. Synchronous joint rotations can be considered as a simplifying strategy to control arm movements, thus controlling the timing of several segments as a whole rather than for each joint separately. We will discuss evidence for synchronous joint rotations in 2D and explain why 3D synchrony is much more complex to substantiate. Different joint-angle representations and measures of asynchrony yield conflicting results. After showing that our model predicts realistic hand paths for various movement directions (the center-out task), we focus on a task that involves re-orientation of a hand-held cylinder, thus especially zooming in on those degrees of freedom not taken into account in 2D models. The more the cylinder needs to be rotated, the more curved the hand path is. With respect to 3D synchrony, a representation of shoulder and elbow rotations as single-axis rotations comes closest to synchronous joint rotations, which suggests that the brain plans a movement in joint space as a single postural transition.     

Unconstrained three-dimensional reaching in Rhesus monkeys

To better understand normative behavior for quantitative evaluation of motor recovery after injury, we studied arm movements by non-injured Rhesus monkeys during a food-retrieval task. While seated, monkeys reached, grasped, and retrieved food items. We recorded three-dimensional kinematics and muscle activity, and used inverse dynamics to calculate joint moments due to gravity, segmental interactions, and to the muscles and tissues of the arm. Endpoint paths showed curvature in three dimensions, suggesting that maintaining straight paths was not an important constraint. Joint moments were dominated by gravity. Generalized muscle and interaction moments were less than half of the gravitational moments. The relationships between shoulder and elbow resultant moments were linear during both reach and retrieval. Although both reach and retrieval required elbow flexor moments, an elbow extensor (triceps brachii) was active during both phases. Antagonistic muscles of both the elbow and hand were co-activated during reach and retrieval. Joint behavior could be described by lumped-parameter models analogous to torsional springs at the joints. Minor alterations to joint quasi-stiffness properties, aided by interaction moments, result in reciprocal movements that evolve under the influence of gravity. The strategies identified in monkeys to reach, grasp, and retrieve items will allow the quantification of prehension during recovery after a spinal cord injury and the effectiveness of therapeutic interventions.     

Nonuniform distribution of reach-related and torque-related activity in upper arm muscles and neurons of primary motor cortex

The present study examined the activity of primate shoulder and elbow muscles using a novel reaching task. We enforced similar patterns of center-out movement while the animals countered viscous loads at their shoulder, elbow, both joints, or neither joint. Accordingly, we could examine reach-related activity during the unloaded condition and torque-related activity by comparing activity across load conditions. During unloaded reaching the upper arm muscles exhibited a bimodal distribution of preferred hand direction. Maximal reach-related activity occurred with hand movements mostly toward or away from the body. Arm muscles also exhibited a bimodal distribution of their preferred torque direction. Maximal torque-related activity typically occurred with shoulder-extension/elbow-flexion torque or shoulder-flexion/elbow-extension torque. Similar biases in reach-related and torque-related activity could be reproduced by optimizing a global measure of muscle activity. These biases were also observed in the neural activity of primary motor cortex (M1). The parallels between M1 and muscular activity demonstrate another link between motor cortical processing and the motor periphery and may reflect an optimization process performed by the sensorimotor system.     

General coordination of shoulder,elbow and wrist dynamics during multijoint arm movements

Studies of multijoint arm movements have demonstrated that the nervous system anticipates and plans for the mechanical effects that arise from motion of the linked limb segments. The general rules by which the nervous system selects appropriate muscle activities and torques to best deal with these intersegmental effects are largely unknown. In order to reveal possible rules, this study examined the relationship of muscle and interaction torques to joint acceleration at the shoulder, elbow and wrist during point-to-point arm movements to a range of targets in the horizontal plane. Results showed that, in general, dynamics differed between the joints. For most movements, shoulder muscle torque primarily determined net torque and joint acceleration, while interaction torque was minimal. In contrast, elbow and wrist net torque were determined by a combination of muscle and interaction torque that varied systematically with target direction and joint excursion. This "shoulder-centered pattern" occurred whether subjects reached targets using straight or curved finger paths. The prevalence of a shoulder-centered pattern extends findings from a range of arm movement studies including movement of healthy adults, neurological patients, and simulations with altered interaction effects. The shoulder-centered pattern occurred for most but not all movements. The majority of the remaining movements displayed an "elbow-centered pattern," in which muscle torque determined initial acceleration at the elbow and not at the shoulder. This occurred for movements when shoulder excursion was <50% of elbow excursion. Thus, both shoulder- and elbow-centered movements displayed a difference between joints but with reversed dynamics. Overall, these findings suggest that a difference in dynamics between joints is a general feature of horizontal plane arm movements, and this difference is most commonly reflected in a shoulder-centered pattern. This feature fits well with other general shoulder-elbow differences suggested in the literature on arm movements, namely that: (a) agonist muscle activity appears more closely related to certain joint kinematics at the shoulder than at the elbow, (b) adults with neurological damage display less disruption of shoulder motion than elbow motion, and (c) infants display adult-like motion first in the shoulder and last at the wrist.     

Disruptions in joint control during drawing arm movements in Parkinson’s disease

Impairments in control of multi-joint arm movements in Parkinsons Disease (PD) were investigated. The PD patients and age-matched elderly participants performed cyclical arm movements, tracking templates of a large circle and four differentially oriented ovals on a horizontal table. The wrist was immobilized and the movements were performed with shoulder and elbow rotations. The task was performed with and without vision at a cycling frequency of 1.5 Hz. Traces of the arm endpoint, joint-motion parameters represented by range of motion and relative phase, and joint-control characteristics represented by amplitude and timing of muscle torque were analyzed. The PD patients provided deformations of the template shapes that were not observed in movements of elderly controls. The deformations were consistent for each shape but differed across the shapes, making quantification of impairments in the endpoint movement difficult. In contrast, the characteristics of joint control and motion demonstrated systematic changes across all shapes in movements of PD patients, although some of these changes were observed only without vision. A specification of the PD influence was observed at the level of joint control and it was not distinguishable in joint and endpoint motion, because of the property of multi-joint movements during which control at each joint influences motion at the other joints. The results suggest that inability of PD patients to provide fine muscle torque regulation coordinated across the joints contributes to the altered endpoint trajectories during multi-joint movements. The study emphasizes the importance of the torque analysis when deficits in multi-joint movements are investigated, because specific impairments that can be detected in joint-control characteristics are difficult to trace in characteristics of joint and endpoint kinematics, because of interactions between joint motions.     

Selection of muscles for initiation of planar,three-joint arm movements with different final orientations of the hand

Muscle activities and joint rotations were examined at the shoulder, elbow, and wrist joints for pointing movements to targets in the horizontal plane. In such movements, multiple arm configurations are possible for a given target location. Thus, starting from the same initial configuration and for the same target location in space, the joint excursions could be varied. When no constraints were placed on the final orientation of the hand, the choice of muscles initially activated at the wrist joint was consistent with a function to resist inertial effects of proximal segment motion on the wrist joint. When subjects were asked to produce different final orientations of the hand for the same target location, the initial choice of muscles at the three joints was preserved in most trials, whether wrist flexion or extension was required to reach the final hand orientation. The relative onset times of muscle activity at the different joints were also not correlated with wrist excursion. This suggests a predetermined initial selection of muscles that is related to target location, not to joint angular excursion. The fact that the required final hand orientation was nevertheless achieved suggests that the planning of these pointing movements is not a unitary process, but is comprised of two components: a fixed initial muscle selection for a given target location in space, and a selection appropriate for the required joint excursions.     

The leading joint hypothesis for spatial reaching arm motions

The leading joint hypothesis (LJH), developed for planar arm reaching, proposes that the interaction torques experienced by the proximal joint are low compared to the corresponding muscle torques. The human central nervous system could potentially ignore these interaction torques at the proximal (leading) joint with little effect on the wrist trajectory, simplifying joint-level control. This paper investigates the extension of the LJH to spatial reaching. In spatial motion, a number of terms in the governing equation (Euler’s angular momentum balance) that vanish for planar movements are non-trivial, so their contributions to the joint torque must be classified as net, interaction or muscle torque. This paper applies definitions from the literature to these torque components to establish a general classification for all terms in Euler’s equation. This classification is equally applicable to planar and spatial motion. Additionally, a rationale for excluding gravity torques from the torque analysis is provided. Subjects performed point-to-point reaching movements between targets whose locations ensured that the wrist paths lay in various portions of the arm’s spatial workspace. Movement kinematics were recorded using electromagnetic sensors located on the subject’s arm segments and thorax. The arm was modeled as a three-link kinematic chain with idealized spherical and revolute joints at the shoulder and elbow. Joint torque components were computed using inverse dynamics. Most movements were ‘shoulder-led’ in that the interaction torque impulse was significantly lower than the muscle torque impulse for the shoulder, but not the elbow. For the few elbow-led movements, the interaction impulse at the elbow was low, while that at the shoulder was high, and these typically involved large elbow and small shoulder displacements. These results support the LJH and extend it to spatial reaching motion.     

Shoulder and elbow muscle activity in goal-directed arm movements

 This research examined the electromyographic (EMG) activity of shoulder and elbow muscles during reaching movements of the upper limb. Subjects performed goal-directed arm movements in the horizontal plane. Movements which varied in amplitude, speed, and direction were performed in different sections of the workspace. EMG activity was recorded from the pectoralis major, posterior deltoid, biceps brachii short head, brachioradialis, triceps brachii long head, and triceps brachii lateral head; motion recordings were obtained with an optoelectric system. The analysis focused on the magnitude and timing of opposing muscle groups at the shoulder and elbow joints. For hand movements within any given direction of the workspace direction, kinematic manipulations changed agonist and antagonist EMG magnitude and intermuscle timing in a manner consistent with previous single-joint findings. To produce reaching movements in different directions and areas of the workspace, shoulder and elbow agonist EMG magnitude increased for those hand motions which required higher angular velocities, while the timing between opposing muscle groups at each joint was invariant. Received: 11 January 1996 / Accepted: 24 February 1997     

Kinematics and control of frog hindlimb movements

1. The determinants of the motion path of the hindlimb were explored in both intact and spinal frogs. In the spinal preparations the kinematic properties of withdrawal and crossed-extension reflexes were studied. In the intact frog the kinematics of withdrawal and swimming movements were examined. Frog hindlimb paths were described in joint angle (intrinsic) coordinates rather than limb endpoint (extrinsic) coordinates. 2. To study withdrawal and crossed-extension reflexes, the initial angles at the hip, knee, and ankle were varied. Withdrawal and crossed extension were recorded in three dimension (3-D) with the use of an infra-red spatial imaging system. Swimming movements against currents of different speeds were obtained with high-speed film. 3. Three strategies were considered related to the form of the hypothesized equilibrium paths specified by the nervous system: all trajectories lie on a single line in angular coordinates; all trajectories are directed toward a common final position; and all trajectories have the same direction independent of initial joint configuration. 4. Joint space paths in withdrawal were found to be straight and parallel independent of the initial joint configuration. The hip and knee were found to start simultaneously and in 75% of the conditions tested to reach maximum velocity simultaneously. Hip-knee maximum velocity ratios were similar in magnitude over differences in initial joint angles. This is consistent with the observation of parallel paths and supports the view that the nervous system specifies a single direction for equilibrium trajectories. 5. Straight line paths with slopes similar to those observed in withdrawal in the spinal preparation were found in swimming movements in the intact frog. Straight line paths in joint space are consistent with the idea that swimming and withdrawal are organized and controlled in a joint-level coordinate system. The similarities observed between spinal and intact preparations suggest that a common set of constructive elements underlies these behaviors. 6. Path curvature was introduced when joint limits were approached toward the end of the movement. Depending on the initial joint angles, the joint movements ended at different times. When initial joint angles were unequal, joints moving from smaller initial angles reached their functional limits earlier and stopped first. 7. In withdrawal and crossed extension in the spinal frog, velocity profiles at a given joint were similar over the initial portion of the curve for movements of different amplitude. This is consistent with the idea that withdrawal and crossed-extension movements of different amplitude are produced by a constant rate of shift of the equilibrium position.     

The role of kinematic redundancy in adaptation of reaching

Although important differences exist between learning a new motor skill and adapting a well-learned skill to new environmental constraints, studies of force field adaptation have been used frequently in recent years to identify processes underlying learning. Most of these studies have been of reaching tasks that were each hand position was specified by a unique combination of joint angles. At the same time, evidence has been provided from a variety of tasks that the central nervous system takes advantage of the redundancy available to it when planning and executing functional movements. The current study attempted to determine whether a change in the use of joint motion redundancy is associated with the adaptation process. Both experimental and control subjects performed 160 trials of reaching in each of four adaptation phases, while holding the handle of a robot manipulandum. During the first and last adaptation phases, the robot motors were turned off. During phases 2 and 3 the motors produced a velocity-dependent force field to which experimental subjects had to adapt to regain relatively straight line hand movements during reaching to a target, while the motors remained off for the control group. The uncontrolled manifold (UCM) method was used to partition the variance of planar clavicle–scapular, shoulder, elbow and wrist joint movements into two orthogonal components, one (V _UCM) that reflected combinations of joint angles that were equivalent with respect to achieving the average hand path and another (V _ORT) that took the hand away from its average path. There was no change in either variance component for the control group performing 640 non-perturbed reaches across four ‘pseudo-adaptation’ phases. The experimental group showed adaptation to reaching in the force field that was accompanied initially by an increase in both components of variance, followed by a smaller decrease of V _UCM than V _ORT during 320 practice reaches in the force field. After initial re-adaptation to reaching to the null field, V _UCM was higher in experimental than in control subjects after performing a comparable number of reaches. V _UCM was also larger in the experimental group after re-adaptation when compared to the 160 null field reaching trials performed prior to initial force field introduction. The results suggest that the central nervous system makes use of kinematic redundancy, or flexibility of motor patterns, to adapt reaching performance to unusual force fields, a fact that has implications for the hypothesis that motor adaptation requires learning of formal models of limb and environmental dynamics.     

Superposition of independent units of coordination during pointing movements involving the trunk with and without visual feedback

Previous studies addressing the problem of the control of multiple degrees of freedom have examined the influence of trunk movement on pointing movements within the arm's reach. Such movements may be controlled by two functionally independent units of coordination (synergies): one involving only arm joints and producing the hand trajectory to the target (the transport synergy), and the other coordinating trunk and arm movements leaving the hand trajectory unchanged (the compensatory synergy). The question of whether or not this functional subdivision depends on visual feedback was addressed in the present study. We also tested whether or not the motor effects of different synergies are summated as independent components, a control strategy called "superposition." Finally, we investigated whether or not the relationship between different degrees of freedom within each synergy could be considered linear resulting in proportional changes in different joint angles. Seated subjects produced fast, uncorrected arm movements to an ipsi- or a contralateral target in the direction of +/-45 degrees to the sagittal midline of the trunk. Targets could be reached using the arm alone (control trials) or by combining the arm motion with a forward or backward trunk motion produced by hip flexion or extension (test trials), with and without visual feedback. The shape of the hand trajectory, its direction and tangential velocity, movement precision, joint angles and the sequence of the trunk and hand recruitment and de-recruitment were measured. In both visual conditions, the direction of the hand trajectory observed in control trials was generally preserved in test trials. In terms of sequencing, even in the absence of vision, the trunk movement was initiated before the onset of and outlasted the hand shift, indicating that the potential influence of the trunk on the hand movement was compensated by rotations in the elbow and shoulder joint. The analysis of other variables also implied that the effects of trunk recruitment on the hand trajectory were minor compared to those which could be observed if these effects were not compensated by appropriate changes in the arm joint angles. It was concluded that an arm-trunk compensatory synergy is present in pointing movements regardless of visual feedback. Principal component analysis showed that the relationship between elbow, shoulder and hip joint angles in individual arm and combined arm-trunk movements cannot be considered linear, implying that this relationship is adjusted according to the changing arm geometry. The changes in each arm joint angle (elbow, shoulder) elicited by a forward trunk bending in one block of trials were compared with those elicited by a backward bending in another block, whereas the hand moved to the same target in both blocks. These changes were opposite but of similar magnitude. As a result, for each moment of movement, the mean joint angle obtained by averaging across two directions of trunk motion was practically identical to that in control trials in which the trunk was motionless. It is concluded that the transport and arm-trunk compensatory synergies are combined as independent units, according to the principle of superposition. This principle may simplify the control of the coordination of a redundant number of degrees of freedom.