Systematic Methodologies for the Automatic Enumeration of the Topological Structures of Mechanisms
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This thesis proposes new algorithms for the enumeration of the topological structure of mechanisms. The definitions of dual graph and dual of a contracted graph are modified to provide a one-to-one correspondence between graphs. In this study, three efficient algorithms have been developed for automatic enumeration and structural representation of graphs.
The first method enumerates conventional graphs by deriving the vertex-to- vertex incident matrix directly. The second method derives conventional graphs from contracted graph families by the arrangement of binary chains. The row vector formed by listing of binary vertex chains is used instead of the vertex-to-vertex incident matrix. The third method uses the edge-to-vertex incident matrix as the expression of graphs instead of the vertex-to-vertex incident matrix. The dual of a conventional graph is derived from the dual of a contracted graph by the arrangement of parallel edges. A conventional graph is formed from the dual graph by the following definition of a dual graph.
Two tables of conventional graphs with seven and eight vertices, and with up to eleven edges have been developed. We believe that the results of these conventional graphs are new. Mechanisms of higher pair joints with six loops and seven or eight links can now be synthesized from these tables.