Constraints on arm position when pointing in three dimensions: Donders' law and the Fick gimbal strategy

1. While making saccades between targets with the head stationary, eye positions are constrained to two of the possible three degrees of freedom. Classically this constraint has been described by Donders' and Listing's laws. The objective was to determine whether these laws also apply for the straight arm when pointing between different targets. Thus we determined whether the arm adopts only one angular position for every pointing direction (Donders' law) and whether these positions can be described by rotations from a reference position about axes that lie in a plane (Listing's law). 2. The angular positions (orientations) of the arm in three-dimensional space were studied as subjects pointed with a straight arm at different targets. Arm position was measured with the search coil technique by means of coils attached to the back of the hand. Pointing was studied over a range of +/- 45 degrees in all directions from a central target located 45 degrees to the right of the straight-ahead position. 3. The positions of the arm in space were described by quaternion vectors, i.e., a particular position was described in terms of the axis and amplitude of a rotation from a reference position to that position. Using this description, it was found that the straight arm adopted a similar orientation (standard deviations ranged from 2.8 to 4.8 degrees) when pointing at a particular target irrespective of which target from which it had moved. 4. The angular position vectors for arm positions associated with relatively small movements (e.g., less than +/- 30 degrees) lay in a flat surface with minimal torsion. At first sight, this surface appeared to be similar to Listing's plane of the eye. However, for positions associated with larger movements (e.g., +/- 45 degrees) it became apparent that, unlike the eye, the surface deviated from one obeying Listing's law, i.e., it was twisted and showed torsion like that produced by rotations around the horizontal and vertical axes of a Fick gimbal. (The characteristic of a Fick gimbal is that the vertical axis is fixed, whereas the horizontal axis moves with the gimbal.) 5. Although there were differences between subjects, all showed a twisted position vector surface. The twist was always in the same direction, and it was always less than that of a Fick gimbal. 6. This position vector surface had a similar shape whether the arm was stationary or was moving between targets, whether subjects pointed with or without vision, and whether the pointing arm had moved between targets or from a bent-elbow position on the lap.(ABSTRACT TRUNCATED AT 400 WORDS)