Abstract: In order to obtain all kinds of kinematic chains that both with R and P joints in the structural synthesis of planar mechanisms, a new structural synthesis method of planar mechanisms is developed by integrating Assur groups as elements in the modified adjacency matrix. A modified group-based adjacency matrix is hence proposed based on the previous study. All assembly forms of Assur groups in the modified group-based adjacency matrix can be determined. The connection forms of all R joints of the Assur groups in the assembly forms are permutated step by step following the proposed connection constrains and isomorphism is detected in the process. Structural forms with R and P joints are hence obtained using permutation of all types of Assur groups in the connection forms, and the inverse problems are revealed in the synthesis. This generates a total of 364 kinds of structural forms of 6-bar linkages with R and P joints which are determined for the first time using the proposed method and demonstrates the efficiency and practicality of the proposed method.

Key words: Group-based adjacent matrix, Isomorphism detecting in the stages, Structural synthesis, Synthesis by stage