Computationally Efficient Kinematics for Manipulators with Spherical Wrists Based on the Homogeneous Transformation Representation

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Abstract
Most manipulators in use today are kinematically simple, and closed-form symbolic equations are the most efficient means of expressing their kinematics. The analysis presented in this paper is based on the use of homogeneous transforma tions to describe position and orientation. Using these methods, kinematic equations are obtained directly in a form suitable for computer implementation. The equations are numerically stable and are obtained almost automatically. The resulting equations involve the minimum number of mathematical operations.

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