Similarity recognition and isomorphism identification of planar kinematic chains. (March 2020)

• Record Type: Journal Article
• Authors: Sun, Liang; Cui, Rongjiang; Ye, Zhizheng; Zhou, Yuzhu; Xu, Yadan; Wu, Chuanyu
• Is Part Of: Mechanism and machine theory. Volume 145(2020)
• Publication Date: 2020-03
• Subjects: Kinematic chain -- Similarity recognition -- Isomorphism identification -- Multibar single-hinged kinematic chain; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2019.103678
• Languages: English
• ISSNs: 0094-114X

Abstract

Highlights: Method for the similarity recognition and isomorphism identification is proposed. It effectively detects planar single and multiple joints KCs, etc. Remarkable efficiency advantages in identifying isomorphism of multibar single-hinged KC. Isomorphism identification method conforms to the definition of isomorphism in graph theory. Abstract: 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 one-degree-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.