Instantaneous Kinematics of Three-Parameter Motions Available to Purchase

In this paper we study the instantaneous kinematics of a three-link open-chain system. We derive concise closed-form expressions to determine the angular velocity, the pitch, and the instantaneous screw axis that describe the three-parameter motion of the terminal link of the three-link chain relative to the fixed base. Using two joint angular velocity ratios as variable parameters we interpret the double-infinity of solutions as a family of cylindroids. For illustrative purposes, we present an analysis of the arm subassembly of two well-known robot manipulators.