An innovative graph-based approach for the topological structure of planetary gear mechanisms

Planetary gear mechanisms (PGMs) are commonly employed in mechanical applications. Graph theory is a useful tool for synthesizing PGM structures to develop new transmission systems. The synthesis of 1- and 2-degree-of-freedom (DOF) planetary gear trains received a lot of attention. Nevertheless, the synthesis results are inconsistent because previous graph representations were insufficient for the synthesis processes. This paper proposes a graph model that improves upon earlier models, introducing the concept of type-2 pseudo-isomorphic graphs. The vertex levels are used to construct PGM-spanning trees and define geared graphs. This approach avoids pseudo-isomorphic graphs and maintains a one-to-one correspondence between PGM elements and the graph. The 6-link 2-DOF PGM synthesis demonstrated the current graph representation, yielding 24 non-isomorphic mechanisms of 11 or more than previously reported. Possible explanations for the inconsistency of synthesis results with earlier studies are investigated, and the advantages of the modified graph over existing approaches are discussed in detail.