Mobility analysis of parallel mechanisms based on screw theory and mechanism topology

A practical method for mobility analysis of mechanisms is presented in this article, which is based on the screw theory and the topology structure of mechanisms. The proposed method can be summarized as one core principle and two key techniques. The core principle is that the series connection of kinematic pairs is equivalent to the superposition of corresponding degrees of freedom, and the parallel connection of kinematic pairs is equivalent to the superposition of corresponding constraints. The first key technique for analyzing the mobility of mechanisms is to correctly identify the series and parallel connection relationship between all kinematic pairs, that is, the mechanism topology structure. Another key technique is transforming the screws and reciprocal screws from local coordinate systems to the global coordinate system. First, the above-mentioned method is presented in theory. Then, several examples are analyzed using it, which validate its effectiveness and universality.