ARE THE ORIENTATIONS OF THE HEAD AND ARM RELATED DURING POINTING MOVEMENTS

The head, eye, and shoulder are each free to rotate around three mutua lly orthogonal axes. These three degrees of freedom allow a given gaze or pointing direction of the eye, head, or arm to be obtained in many different possible orientations. Unlike translations in three dimensi ons, three-dimensional (3-D) rotations are noncommutative. Therefore, the orientation of a rigid body following sequential rotations about t wo different axes depends on the order of the rotations. In this artic le, we demonstrate that only two degrees of freedom are used during or ienting movements of the head and pointing movements of the arm. This provides a unique orientation of head and arm for each gaze or pointin g direction despite the noncommutativity of three-dimensional rotation s. This observation is in itself not new. We found, however, that (a) the two-dimensional ''rotation surface,'' which describes the orientat ion of the head for all gaze directions, is curved, unlike the analogo us flat plane for the eye. (b) The rotation surface for the head is cu rved differently than that for the arm. This result argues against the hypothesis that the orientations of head and arm are directly coupled during pointing. It also implies that the orientation of the eye in s pace during gaze shifts of the eye and head is not uniquely determined for a given direction of gaze. This finding argues against a perceptu al basis for the reduction of rotational degrees of freedom.