Series-Parallel Dualities in Actively Coordinated Mechanisms

Abstract

A deep symmetry between serial chain manipulators and fully parallel systems such as the Stewart platform is dem onstrated. This symmetry is shown to be a result of the well-known duality of motion screw axes and wrenches. The appearance of the inverse of the Jacobian matrix in force decomposition in the same role as the Jacobian in rate decomposition is also a consequence of this same duality and of the reciprocity relationship between the motion screw system and the wrench system of a kine matic joint. A geometric meaning of the columns of the Jacobian is demonstrated. A simple example of the appli cation of the ideas presented here to the understanding of the complex combinations of serial and parallel chains found in vehicle and multifingered hand problems is also presented.