A General Formula of Degree of Freedom for Parallel Mechanisms

Abstract

In this paper, a general formula of degree of freedom (DOF) for parallel mechanisms has been presented which could provide the full-cycle DOF. The key parameters in the formula can be determined via the position and orientation characteristic equations and their symbolic operations of serial and parallel mechanisms proposed by author and the symbolic operation is simple. It is totally different from the methods based on screw theory and based on displacement subgroup. The formula has been used for selection of driving pairs and determination of idle pairs. The formula may also be used for determining the DOF of other multi-loop mechanisms besides parallel mechanisms.