Decision tree and lie algebra method in the singularity analysis of parallel manipulators

The singularity analysis of a parallel manipulator is often very complicated. There exist multi-criterions to determine the singular behavior of a parallel manipulator, for example: rank condition criterion of a screw set chi of the parallel mechanism, second order criterion of screw set chi, transverse criterion etc. This paper aims to explain a general method to analyze the relationship between the different criterions of singular configurations with the help of the decision tree method for the first time. 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.