Abstract. The aim of our investigation is to understand the mechanisms which control the movement of the human arm. The arm is here considered as a redundant system: the shoulder, elbow and wrist joints, which provide three degrees of freedom, combine to move the hand in a horizontal plane, i.e. a two dimensional space. Thus the system has one extra degree of freedom. Earlier investigations of the static situation led to the hypothesis that independent cost functions were attached to each of the three joints and that the configuration chosen for a given target position is that which provides the minimum total cost (Cruse 1986). The aim of the current investigation was to look for measurable values corresponding to the hypothetical cost functions. Experiments using pointers of different lengths attached to the hand showed that the strategy in choosing the joint angles are independent of the limb length. The muscle force necessary to reach a given angle is increased by a spring mounted across a joint. In this situation the angles of the loaded joint are changed for a given target point to give way to the force effect. This leads to the conclusion that the hypothetical cost functions are not independent of the physiological costs necessary to hold the joint at a given angle. The cost functions seem to depend on joint angle and on the force which is necessary to hold the joint in a given position. Cost functions are measured by psychophysical methods. The results show U-shaped curves which can be approximated by parabolas. The position of minimum cost (maximum comfort) for one joint showed no or weak dependency on the angles of the other joints. For each subject these "psychophysical" cost functions are compared with the hypothetical cost functions. The comparison showed reasonable agreement. This supports the assumption that the psychophysically measured "comfort functions" provide a measure for the hypothetical cost functions postulated to explain the targeting movements. Targeting experiments using a four joint arm which has two extra degrees of freedom showed a much larger scatter compared to the three joint arm. Nevertheless, the results still conform to the hypothesis that also in this case the minimum cost principle is applied to solve the redundancy problem. As the cost function for the whole arm shows a large minimum valley, quite a large range of arm positions is possible of about equal total costs. The scatter does not result from pure randomness but seems to be mainly produced by the fact that the angles at the end of the movement depend on the value of the joint angles at the beginning of the movement.

In order to examine path planning and the control of redundant degrees of freedom in the human arm, the movements of the shoulder, elbow and wrist were recorded as subjects moved a pointer to a target and avoided a simple obstacle. With respect to joint control, the results show that the extra degree of freedom provided by the wrist is incorporated into target movements in a systematic manner for both large and small obstacles; it is not used only when there is no geometrical alternative. For the wrist, two strategies are apparent, depending upon the length of the obstacle. Wrist extension predominates for shorter obstacles, while flexion or extension and flexion predominate for longer obstacles. These wrist movements shorten the effective length of the distal segments (lower arm plus hand and pointer) and thus reduce the excursion required at the proximal joints. In part, they correspond to assuming the most comfortable arm configuration at each point in the new path necessitated by the obstacle and can be described by static cost functions. However, wrist extension is also used to move the hand and pointer away from the obstacle as shoulder and elbow movements carry the wrist itself towards the obstacle. Wrist flexion is also used to move the pointer tip rapidly past the obstacle. These components, which cannot be explained by static cost functions alone, confirm for the human arm the hypothesized use of redundant degrees of freedom in obstacle avoidance. With respect to path planning, the results show that the minimum distance between pointer and obstacle remains fairly constant over a large range of obstacle lengths; this relative invariance is interpreted to support the hypothesis that workspace coordinates are important for movement planning. However, minimum distance and several other path parameters do depend significantly on the orientation and location of the movement in the workspace. This inhomogeneity implies that movement planning does not occur exclusively in workspace coordinates; it suggests an influence of joint space criteria. In frontal movements, for example, the systematic decline in the minimum distance with increasing obstacle length is interpreted as a compromise reducing the amount of extra joint movement and the discomfort of arm configurations.

Abstract. The movements studied involved moving the tip of a pointer attached to the hand from a given starting point to a given end point in a horizontal plane. Three joints -the shoulder, elbow and wristwere free to move. Thus the system represented a redundant manipulator. The coordination of the movements of the three joints was recorded and analyzed. The study concerned how the joints are controlled during a movement. The results are used to evaluate several current hypotheses for motor control.

Control of arm movements when the number of joints exceeds the degrees of freedom necessary for the task requires a strategy for selecting specific arm configurations out of an infinite number of possibilities. This report reviews strategies used by human subjects to control the shoulder, elbow, and wrist (three degrees of freedom) while moving a pointer to positions in a horizontal plane (two degrees of freedom). Analysis of final arm configurations assumed when the pointer was at the target showed the following: (a) Final arm configurations were virtually independent of the configuration at the start of the pointing movement, (b) subjects avoided configurations subjectively felt to be uncomfortable (e.g., those with extreme flexion or extension of the wrist), and (c) the results could be simulated by assigning hypothetical cost functions to each joint and selecting the arm configuration that minimized the sum of the costs. The fitted cost functions qualitatively agreed with psychophysically determined comfort; they appeared to depend on joint angle and on muscular effort. Simple neural networks can learn implicit representations of these cost functions and use them to specify final arm configurations. The minimum cost principle can be extended to movements that use the fingers as a fourth movable segment. For this condition, however, experiments showed that final configurations of the arm depended upon initial configurations. Analysis of movement trajectories for arms with three degrees of freedom led to a control model in which the minimum cost principle is augmented by a mechanism that distributes required joint movements economically among the three joints and a mechanism that implements a degree of mass-spring control.

Hill and Kroemer (1986) and Kroemer and Hill (1986) found that the preferred vertical direction of gaze is lower with a nearer binocular stimulus than with a more distant one. A model is proposed that relates this phenomenon to characteristics of the resting state of the oculomotor system. Three predictions of the model were tested, based on measurements of the preferred vertical gaze direction and dark vergence in the same subject sample. On average the effect of observation distance on the preferred vertical gaze direction served to reduce the discrepancy between the resting state of vergence, operationally defined as dark vergence, and actual convergence during inspection of the binocular stimulus. Second, dark vergence data from individual subjects could be successfully used to predict whether they raised or lowered their eyes on inspection of a binocular stimulus as compared with the preferred vertical gaze direction while viewing a monocular stimulus. Finally, predictions of the size of the change of the preferred vertical gaze direction on introduction of a binocular stimulus produced only small and non-significant correlations.