This paper illustrates a new application of planar curvature theory to the geometric problem of trajectory generation by a two-link manipulator. The theory yields the instantaneous speed ratio, and the rate of change of the speed ratio, which correspond to the geometry of a desired point trajectory. Separate from the purely geometric speed ratio problem (i.e., the coordination problem) is the time based problem of controlling the joint rates in order to move with the specified path variables. Introduction A rigid body, constrained to move in a plane with N independent degrees of freedom, where 1 < N < 3, is known as a planar TV-parameter motion, denoted by M N . This paper discusses the arm-subassembly of a planar manipulator, whose terminal link is a planar M 2 motion. The purpose is to illustrate a new application of classical curvature theory to the problem of trajectory generation by a multi-degree-of-freedom rigid body system, in this case a planar robot manipulator. Previously, curvature theory has been applied to the dimensional synthesis of planar mechanisms. The new application of the theory illustrated here is a problem of motion synthesis by industrial manipulators
