Conceptual Design of Dual Cam Mechanisms Using Graph Theory

This paper presents the theory of graphs and how they can be applied to the conceptual design of dual-cam mechanisms. The graph theory was used to validate the results of previous authors (Hain and Pryor). Several applications of dual cam mechanisms are reviewed. Algorithms using a process of bit mapping were used to developed all possible non-isomorphic graphs for various classes of mechanisms. A classification method was developed using common occurring substructures found in the graphs. This classification scheme was used for conversion of graphs into schematics. Once the results of Hain were verified, the investigation turned to mechanisms with two cams. The generated schematics represent the basic configurations for all the non-isomorphic mechanisms studied. The graph theory was able to generate seven colored graphs for five-bar, 1 D.O.F. mechanisms with one cam. For six-bar, 1 D.O.F. dual cam mechanisms, over 110 colored graphs were generated. Finally, 12 colored graphs were generated for five-bar, 2 D.O.F. dual cam mechanisms. Two designs of mechanisms using dual cams were examined. The graphs of the mechanisms were checked against the tables of graphs developed during this investigation. The method presented in this paper has shown to be both exhaustive and complete. The graphs developed are non-isomorphic (unique). The method is not limited to single degree of freedom mechanisms nor is it limited to the number of desired links. This was a problem encountered in previous investigations. The application of graph theory to the generation of mechanisms did not exhibit these limitations.