Unified Theory of Topological and Geometric Problems in Mechanical Design and Manufacturing

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This grant will provide support for developing theoretical foundations for describing and solving gometric and topological problems in mechanical product design and manufacture. A theory will be developed to encompass a taxonomy and morphology of generic classes of geometric and topological problems, their characterization, and their respective solvability conditions. The theory will provide an understanding of the scope and limitations of generic solution techniques. The unified characterization will contain representation of topological and geometric entities at multiple abstraction levels, a standard set of topological and geometric relations, and a minimum set of generic design tasks or issues. High level problem definitions will be encoded in the form of generic geometry exemplars that will contain not only geometry templates, but also mechanisms to specify the design task or goal. Methods for mapping high level problems to low level standard geometric tasks will also be investigated. If successful, this research will lead to a uniform treatment of geometric problems in diverse areas and will enhance integration between different parts of the product design process. In the long run, the results of this project have the potential to extend the scope of CAD/CAM in automating design and manufacturing tasks both upstream (preliminary design) and downstream (manufacturing planning). This research will also benefit the development of standards for exchange of parametric geometry data between different computer aided design systems used throughout the product development process, thus reducing development cost and the time to market.