Arm position constraints during pointing and reaching in 3-D space.

Arm movements in 3-D space were studied to investigate the reduction in the number of rotational degrees of freedom in the shoulder and elbow during pointing movements with the fully extended arm and during pointing movements to targets in various directions and at various distances relative to the shoulder, requiring flexion/extension in the elbow. The postures of both the upper arm and forearm can be described by rotation vectors, which represent these postures as a rotation from a reference position to the current position. The rotation vectors describing the posture of the upper arm and forearm were found to lie in a 2-D (curved) surface both for pointing with the fully extended arm and for pointing with elbow flexion. This result generalizes on previous results on the reduction of the number of degrees of freedom from three to two in the shoulder for the fully extended arm to a similar reduction in the number of degrees of freedom for the upper arm and forearm for normal arm movements involving also elbow flexion and extension. The orientation of the 2-D surface fitted to the rotation vectors describing the position of the upper arm and forearm was the same for pointing with the extended arm and for movements with flexion/extension of the elbow. The scatter in torsion of the rotation vectors describing the position of the upper arm and forearm relative to the 2-D surface was typically 3-4 degrees, which is small considering the range of approximately 180 and 360 degrees for torsional rotations of the upper arm and the forearm, respectively. Donders' law states that arm posture for pointing to a target does not depend on previous positions of the arm. The results of our experiments demonstrate that the upper arm violates Donders' law. However, the variations in torsion of the upper arm are small, typically a few degrees. These deviations from Donders' law have been overlooked in previous studies, presumably because the variations are relatively small. These variations may explain the larger scatter of the rotation vectors for arm movements (3-4 degrees) than reported for the eye (1 degree). Unlike for saccadic eye movements, joint rotations in the shoulder during aiming movements were not all single-axis rotations. On the contrary, the direction of the angular velocity vector varied during the movement in a consistent and reproducible way, depending on amplitude, direction, and starting position of the movement. These results reveal several differences between arm movements during pointing and saccadic eye movements. The implications for our understanding of the coordination of eye and arm movements and for the planning of 3-D arm movements are discussed.