This paper details an accessible geometric derivation of the forward and inverse kinematics of a parallel robotic linkage known as the Canfield joint, which can be used for pointing applications. The original purpose of the Canfield joint was to serve as a human wrist replacement, and it can be utilized for other purposes such as the precision pointing and tracking of antennas, telescopes, and thrusters. We build upon previous analyses, and generalize 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 assumptions necessary to analyze this type of parallel robotic linkage. Specific guidance is included for engineering use cases.

翻译：本文详细介绍了可获取的被称为Canfield联合体的平行机器人连接的前向和反动动脉学的可获取的几何推算,该连接体可用于指点应用。Canfield联合体的最初目的是作为人体手腕的替换,可用于天线、望远镜和推进器的精确指针和跟踪等其他目的。我们以先前的分析为基础,将其归纳为包括三条腿中一条腿被冻结的情况;动脉学也大大普及,超越了故障模式,详情在其中。这项工作的核心是说明和澄清分析这种平行机器人连接体所需的假设。工程使用案例包括了具体指导。