Computer-aided analysis for topological structure of parallel mechanisms

The POC theory of topological structure design and analysis for PMs is established by Chinese scholars. The 12 topological characteristics proposed are innate topological invariants of the mechanism which reflect the essential features of structural theory, kinematics and dynamics. But the process of computation and analysis is complicated. In this paper, the principle, algorithm and implementation of computer-aided topological structure analysis of PMs are studied. Firstly, a symbolic description system for PMs is presented to describe the order of the kinematic joints and their orientation relations in a chain, and a kind of matrix expression is promoted to describe the POC set of chain. Then, according to the spatial dependence of the POC set element, the rules of union operation and intersection operation are developed, and the automatic calculation and analysis of POC set, the degree of freedom (DOF) are realized. Consequently, the optimal decomposition algorithm of PMs is studied based on the mechanism composition principle of the ordered single-open-chain (SOC) unit, and the coupling degree is obtained automatically. Finally, the automatic analysis software is developed by VC++, and a case study is presented for a 3T1R PM. The results show that the proposed union and intersection rules are effective and the method of structural decomposition is correct. The algorithm and software proposed are helpful to easily calculate and analysis the topological structure of PMs for more mechanism researchers and engineers.