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This paper details an accessible geometric derivation of the forward andinverse kinematics of a parallel robotic linkage known as the Canfield joint,which can be used for pointing applications. The original purpose of theCanfield joint was to serve as a human wrist replacement, and it can beutilized for other purposes such as the precision pointing and tracking ofantennas, telescopes, and thrusters. We build upon previous analyses, andgeneralize them to include the situation where one of the three legs freezes;the kinematics are also substantially generalized beyond failure modes,detailed within. The core of this work states and clarifies the assumptionsnecessary to analyze this type of parallel robotic linkage. Specific guidanceis included for engineering use cases.

A Geometric Approach to the Kinematics of the Canfield Joint