Simultaneous Coordination of Two Rigid Body Motions Through Infinitesimally Separated Positions

A generalized mathematical approach is developed to guide two rigid bodies for simultaneous coordination of their infinitesimally separated positions. Mathematical relationships are developed to incorporate up to fourth-order derivatives while specifying infintesimally separated positions. The approach is demonstrated by considering an eight-link mechanism. It is shown that for a maximum of five precision positions of the two rigid bodies, a maximum of 1024 design solutions are possible.