Topological relation expression and verification of symmetrical parallel mechanism based on the evolution of chemical molecule

The research of parallel mechanism (PM) configuration involves many problems. From topology to configuration, dimensional constraint, etc., how to establish the relationship between topology and configuration with effective methods is a long-term challenge for the configuration design. In this paper, the chemical molecular spatial structure (CMSS) is linked with the configuration of symmetrical parallel mechanism (SPM). Starting from the methane molecule (CH4), a spatial structural topological relation is obtained. Based on graph theory and the spatial structural topological relation, a new expression method with topological graph and its kinematic pair adjacency matrix for spatial SPM is proposed. Then, the expression and analysis for the characteristics of spatial SPM are obtained. Finally, by taking the 3-RPS PM and the 3-RRC PM as examples, the effectiveness and corresponding consistency of the proposed expression method are successfully verified. The proposed new expression method paves the way for the subsequent digital and automated design and analysis of the SPM configuration.