Screw Theory and Singularity Analysis of Parallel Robots

It is well known that the singularity analysis of a parallel manipulator is often very complicate. In fact, it exists multi-criterions to determine the singular behaviour of a parallel manipulator, for example: rank condition criterion of screw set X of the parallel mechanism, second order criterion of screw set X, transverse criterion etc. The aim of this paper is to explain a general method to analyze the relationship between the different criterions of singular configurations with the help of screw theory. We find that the second order criterion is the most important one to determine whether the singular configuration is bifurcated through a large amount of parallel manipulator analysis