Similarity recognition and isomorphism identification of planar kinematic chains

摘要

Similarity recognition and isomorphism identification (SRII) of kinematic chains (KCs) are key problems facing their innovative regenerative design and configuration synthesis. Although various detection methods have been proposed, most of them are based on topological characteristics or some codings, which are only suitable for single type KC and error identification is generated in some cases. In this study, a set of SRII methods is proposed based on the graph theory definition of similarity and isomorphism. These are appropriate for planar single and multiple joints KCs, planetary gear trains (PGTs), contracted graphs, and multicolor graphs. The computational complexity and effectiveness of the algorithm are assessed on 10-bar, 15-bar, 21-bar, 28-bar, and 42-bar single-joint KCs, 4-bar tricolor topological graphs, and 8-bar contracted graphs. All the results are in agreement with those in the cited literature, and the advantage in isomorphism identification efficiency of the multibar single-hinged KC is evident. Finally, SRII are performed for all 8-bar onedegree-of-freedom (1-DOF) and 9-bar 2-DOF planar single-hinged KCs, all 8-bar 1-DOF KCs with two multiple joints, and all 6-bar 1-DOF rotation graphs through identification program, with the aim to provide a reference for the application of the algorithm. (C) 2019 Elsevier Ltd. All rights reserved.