Computation of the configuration degree of freedom of a spatial parallel mechanism by using reciprocal screw theory

In this paper, we propose a programmable algorithm to investigate the configuration degree of freedom (CDOF) of a spatial parallel mechanism in one Cartesian coordinate system with reciprocal screw theory. According to the physical meaning of reciprocal screws, we first obtain the terminal constraints of every kinematic chain which connects the end-effector with the fixed base, and then gain the free motion(s) of the end-effector and its degree of freedom (DOF). Through analyzing the controllability of the end-effector, we investigate the instantaneous screw expressions for the free motions of the end-effector of a spatial parallel mechanism and the CDOF of the mechanism. The whole mathematical analysis process can be directly embedded in a kind of CAD software, in which the imperfect Kutzbach Grübler formulas or its amendments are mostly utilized to analyze the DOF.