Adding Sub-chain Method for Structural Synthesis of Planar Closed Kinematic Chains

For at least the past five decades, structural synthesis has been used as a main means of finding better mechanisms with some predefined function. In structural synthesis, isomorphism identification is still a problem unsolved well, and to solve this problem is very significant to the design of new mechanisms. According to the given degree of freedom (DOE) and link connection property of planar closed chain mechanisms, vertex assortment is obtained. For solving the isomorphism problem, a method of the adding sub-chains is proposed with the detailed steps and algorithms in the synthesizing process. Employing this method, the identification code and formation code of every topological structure are achieved, therefore many isomorphic structures could be eliminated in time during structural synthesis by comparing those codes among different topological graphs, resulting in the improvement of synthesizing efficiency and accuracy, and the approach for eliminating rigid sub-chains in and after the synthesizing process is also presented. Some examples are given, including how to add sub-chains, how to detect simple rigid sub-chains and how to obtain identification codes and formulation codes et al. Using the adding sub-chain method, the relative information of some common topological graphs is given in the form of table. The comparison result is coincident with many literatures, so the correctness of the adding sub-chain method is convinced. This method will greatly improve the synthesizing efficiency and accuracy, and has a good potential for application.