A Computational Synthesis Approach of Mechanical Conceptual Design Based on Graph Theory and Polynomial Operation

The design synthesis is the key issue in the mechanical conceptual design to generate the design candidates that meet the design requirements. This paper devotes to propose a novel and computable synthesis approach of mechanisms based on graph theory and polynomial operation. The graph framework of the synthesis approach is built firstly, and it involves: (1) the kinematic function units extracted from mechanisms; (2) the kinematic link graph that transforms the synthesis problem from mechanical domain into graph domain; (3) two graph representations, i.e., walk representation and path representation, of design candidates; (4) a weighted matrix theorem that transforms the synthesis process into polynomial operation. Then, the formulas and algorithm to the polynomial operation are presented. Based on them, the computational flowchart to the synthesis approach is summarized. A design example is used to validate and illustrate the synthesis approach in detail. The proposed synthesis approach is not only supportive to enumerate the design candidates to the conceptual design of a mechanical system exhaustively and automatically, but also helpful to make that enumeration process computable.