The singularity study of spatial hybrid mechanisms based on screw theory

Abstract

In this paper, a novel methodology based on screw theory to study the singularity of spatial hybrid mechanisms is presented. According to the physical meaning of inverse screws, we introduce the equivalent kinematic screws to replace the function of those of the parallel limbs, and therefore the hybrid branch can be transformed into a pure series kinematic chain which can facilitate the whole analytical process of the singularity of complex spatial hybrid mechanisms. In fact, this methodology can be widely used to solve the singularity problems of spatial hybrid mechanisms based on the analysis of their kinematic characters.

The kinematics and statics of manipulators

“…First, one can discuss the motion of the end-effectors of parallel manipulators. Since kinematic screw systems of a hybrid kinematic chain can be equivalently substituted by kinematic screw systems of a series kinematic chain according to the reciprocal screw theory [32], one may just discuss the situation that the kinematic chains each connected with the endeffector are all serial. Assume that the number of driving inputs of the mechanism is n and the number of kinematic chains connected with the end-effector is p. According to equation (2), for the kth (k = 1, 2, .…”