A Recursive Decomposition Algorithm for 3D Assembly Geometric Constraint System with Closed-loops

Numerical methods are always employed to solve 3D assembly geometric constraint system with closed-loops which can not be decomposed by the existing decomposition methods, but their inherent inefficiency and instability can not be overcome.In this paper, with the analysis of the structural constraint of serial kinematic chain and the topological structure of geometric constraint closed-loop graph, a recursive decomposition algorithm for 3D geometric constraint system with closed loops is proposed.The basic idea of the proposed algorithm is to introduce the equivalent geometric constraint combination to substitute the structural constraint of serial kinematic chain, and separate the geometric constraint subsystems which can be solved independently from the geometric constraint system with closed-loops.The proposed method can decompose most 3D geometric constraint closed loop systems which are always solved by numerical method into a series of geometric constraint subsystems between two rigid bodies which can be solved by analytical or reasoning method, so that the computational efficiency and stability can be improved dramatically.Finally, a typical example has been given to validate the correctness and effectiveness of the proposed method.