Derivation of valid contracted graphs from simpler contracted graphs for type synthesis of closed mechanisms

Contracted graph (CG) is a basic and effective tool for deriving topology graphs which are widely used for type synthesis of closed mechanisms. This paper focuses on the derivation of valid CGs from simpler CGs by adding edge and the identification of their isomorphism. First, the concepts of CGs are explained, and the numbers of vertices and edges in CGs are determined. Second, many different CGs are constructed from associated linkages. Based on the numbers of different edges, many CGs corresponding to the same associated linkage are grouped and the isomorphic/invalid CGs are identified and deleted. Third, many complex valid CGs are derived from simpler valid CGs or virtual CGs by adding edge. Finally, two application examples of the CGs are illustrated for type synthesis of closed mechanisms.

► Explain the concepts of contracted graphs CG and determine the numbers of vertices and edges.
► Make rules and construct contracted graphs from associated linkages AL by rules.
► Group contracted graphs corresponding to the same AL and identify the isomorphic/invalid CGs.
► Derive many complex valid CGs from simpler valid CGs or virtual CGs by adding edge.
► Construct three closed mechanisms using valid contracted graphs.