This paper introduces a measure of the orientation capability of manipulator wrists, and a means of representing orientation capability. Wrists with the various combinations of roll, pitch and yaw joints, with one, two or three joints are studied. It is shown that for all non-degenerate orthogonal three joint wrists, the image space representing the orientation capability is doubly-covered, and the possibilities for restricting joint angles to make it singly-covered are given. Degenerate postures for each configuration are also given, and singularity-free wrists with three joints are discussed.

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