Computer-aided structure decomposition theory of kinematic chains and its applications

Rigid sub-chain detection and isomorphism identification are two of the most difficult problems in the computer-aided structure synthesis of kinematic chains. This paper aims to find an efficient solution which can be fulfilled within the computer itself to the problem of rigid sub-chain detection of planar kinematic chains, especially for complex planar mechanisms. Based on the array representation of the loops of kinematic chains, this paper first introduces two operations of loops, the “Θ” and “⊕” operations. Then a new theory of structure decomposition of kinematic chains is proposed on the basis of the concept of the independent loop set. After that a new method grounded on the theory is proposed for rigid sub-chain detection. Finally, the optimized algorithm for structure decomposition is presented and the corresponding program for rigid sub-chain detection is developed as well.