A comprehensive graph theory representation for computer aided design of complex planar mechanisms

The primary objectives of this research include establishing a systematic procedure for type synthesis of mechanisms, and outlining specific graph-theory-based algorithms which could be used to implement the steps of the procedure on a digital computer. The contributions are intended to fill gaps in existing knowledge, and to provide a coherent theoretical basis on which to implement the approach.; The process of mechanism design is broken down into a manageable sequence of well-defined steps. At different stages in the mechanism design process, the requirements of the mechanism representation vary. The role that graph theory has played within the continuum of pictorial and symbolic representations is revealed by describing the myriad of different representations, and pointing out their limitations for any particular aspect of mechanism design. Graph theory is shown to be extremely useful as a symbolic representation throughout the conceptual phase of mechanism design (type synthesis).; Among the major contributions of this work is the utilization of an alternative graph representation (called the line graph) for automatically generating a computer graphics display of a mechanism represented by its graph. The method includes an efficient algorithm for transforming the graph into its associated line graph.; A new "family" of graph-theory-based algorithms is introduced in which the adjacency matrix and its powers is the primary data structure. Several detailed examples from the area of the topological analysis of mechanisms are used to illustrate the general technique. One of the examples introduces a new criteria for determining the optimum choice of output link for a given mechanism topology and dimensional synthesis task. Another example is an algorithm for automatically formulating dimensional synthesis procedures, which can be used as the basis of a "front end" for an existing computer-aided dimensional synthesis program.; Finally, a new and comprehensive graph theory representation for the topological analysis of planetary gear trains is introduced. In this representation, the geometric axis of all concentric gears is explicitly represented, thereby eliminating the ambiguity associated with the conventional graph representation. Using this representation, some surprising results are obtained concerning the usefulness of certain planetary gear trains.