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

Abstract

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)

Kinematic Rules for Upper and Lower Arm Contributions to Grasp Orientation

“…The large torsional shifts that occurred with the change in target orientation from horizontal to vertical suggests that taskspecific violations of Donders' Law occur when grasp formation is essential for the successful completion of a movement. However, Donders' Law of the upper arm appears to hold for similar grasp orientations across grasping space, at least as well as it does for pointing movements in human subjects (Gielen et al 1997;Hore et al 1992;Medendorp et al 2000;Miller et al 1992;Straumann et al 1991). Moreover, the shape of the Donders' surfaces did not change significantly for different grasp orientations.…”

“…The 3-D patterns of upper and lower arm orientations at the end of the reaching and grasping movement (when arm transport velocity fell below 5 cm/s) were computed for each subject. This was done by fitting a second-order surface to the rotation vector data (Hore et al 1992;Medendorp et al 2000;Miller et al 1992;Straumann et al 1991;Theeuwen et al 1993) as follows…”

“…One of the ways that one postural configuration may be chosen over another is Donders' Law, which, when applied to the arm, suggests that the amount of torsion is a unique function of arm position relative to the body (Crawford and Vilis 1995;Hore et al 1992;Miller et al 1992). In most studies of Donders' Law of the arm, torsion is defined as rotation about a body fixed axis that would align with the arm while it points straight ahead.…”

“…This has led some to suggest that the arm-control system might possess a Donders' operator that takes in desired pointing direction and outputs a command for desired threedimensional (3-D) arm orientation (Crawford and Vilis 1995). In contrast to the observations suggesting a consistent and reproducible reduction of the number of degrees of freedom (Crawford and Vilis 1995;Hore et al 1992;Miller et al 1992), other authors have reported violations of Donders' Law for the arm (Gielen et al 1997;Soechting et al 1995), particularly when the forearm is allowed to move (Medendorp et al 2000).…”

“…Once recruited, does it follow some graded linear or nonlinear rule of upper arm/lower arm (forearm) coordination? Finally, it is not known how such rules would interact with the other aspects of Donders' Law, like the position-dependencies in arm torsion that are thought to optimize various aspects of limb control and task demands (Hore et al 1992;Medendorp et al 2000;Straumann et al 1991).…”