Generalized Mobility and Decoupling Conditions of Closed-Loop Mechanism

This paper purposes a new kinematic analysis approach of closed-loop mechanisms based on the linear dependence of twists. First, the generalized velocity equation of closed-loop mechanisms is established by means of the exponential product form of rigid body motion. Second, the condition of the decoupling of closed-loop mechanism is obtained. Third, a simple analysis approach for decoupling analysis of the mechanism is proposed. Next, the approach is proven by the analysis of the decoupling mechanism and partial decoupling mechanisms and the synthesis of a decoupling spherical mechanism. The examples indicate that the actuation wrench is related with the linear dependence of the kinematic joints of the close-loop mechanism. This broadens the traditional knowledge about the actuation wrenches based on the reciprocal screw theory.