Are the Orientations of the Head and Arm Related during Pointing Movements?

Abstract

The head, eye, and shoulder are each free to rotate around three mutually 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 dimensions, three-dimensional (3-D) rotations are noncommutative. Therefore, the orientation of a rigid body following sequential rotations about two different axes depends on the order of the rotations.

In this article, we demonstrate that only two degrees of freedom are used during orienting movements of the head and pointing movements of the arm. This provides a unique orientation of head and arm for each gaze or pointing direction despite the noncommutativity of three-dimensional rotations. This observation is in itself not new. We found, however, that (a) the two-dimensional “rotation surface,” which describes the orientation of the head for all gaze directions, is curved, unlike the analogous flat plane for the eye. (b) The rotation surface for the head is curved 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 space during gaze shifts of the eye and head is not uniquely determined for a given direction of gaze. This finding argues against a perceptual basis for the reduction of rotational degrees of freedom.

Key Words:

• Listing's law
• reduction of degrees of freedom
• rotation vectors
• torsion