On the Kinematics of the UPS Wrist for Real Time Control

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Abstract
A parallel structure is used in the design of the UPS wrist to allow for a large payload, high speed, high repeatability, and a large workspace. Because of the inherent design and machining difficulties involved with spherical mechanisms, a spatial mechanism has been adopted. In creating such a 3-DOF spatial mechanism, many practical design problems are unavoidable, and direct analysis of the mechanism becomes extremely difficult. In this paper, we discuss the concept of using an equivalent mechanism to simplify the kinematic analysis. By using this method, we have derived a closed-form solution for the inverse kinematics, as well as a formulation for the forward kinematics. We have also developed a numerical algorithm for the forward kinematics, and a methodology for implementing the results of the analysis. The results of this study have enabled real time control and force control to become feasible for the UPS wrist.

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