Application of topological graphs to analyze and synthesize planetary gear trains is an effective approach in searching for innovative planetary gear trains.Topological graphs of basic structure and fundamental units of PGTs are discussed as the basis of topological theory.According to the further research of the law of PGTs diversification and inversion

the basic and method of PGTs graph library establishment is obtained.Thus graph library based on variation law is presented as a simple and practical way to create a great number of new PGTs.