How do Motor Systems Deal with the Problems of Controlling Three-Dimensional Rotations?

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Abstract
Rotations are fundamental to motor control, not only for orienting to stimuli but also in the joint articulations that underlie translational movements. Studying three-dimensional (3-D) rotations of the simplest joint system, the eye, has provided general insights into the neural control of movement. First, in selecting one 3-D eye orientation for each two-dimensional (2-D) gaze direction, the oculomotor system generates a behavior called Listing's law that constrains eye position to a 2-D plane, Listing's plane. This selection is made internally by an inverse kinematic transformation called the Listing's law operator. Second, the oculomotor system incorporates the inherent multiplicative relationship between rotational velocity and position to generate the 3-D movement and position commands required by Listing's law. Finally, the coordinate systems for these commands appear to align with Listing's plane rather than with anatomic structures. Recent investigations have revealed similar behavioral constraints in the orientations of the head and arm, suggesting that the neural mechanisms for Listing's law may have analogues in many motor systems.