Conceptual Framework for Tolerances in Computer Aided Design

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The objective of this research is to develop a conceptual foundation for the automated solution of tolerancing problems in computer-aided design. The research will be organized under three topics: (1) To provide a basis for this work, a mathematical representation will be developed in which tolerances are expressed as constraints on a normed vector space of model variations (an M-space). (2) To prove its utility, it will be shown that the M-space representation establishes a foundation for the formulation of mathematical models for the tolerance analysis and tolerance synthesis problems. It will be shown that the most general three-dimensional problems can be solved on either a worst-case or statistical basis, and that both dimensional and geometric tolerances can be used. (3) To demonstrate the existence of an efficient computational framework for the automated solution of these mathematical models, solid modeling technology will be extended to provide effective methods for modeling part and assembly semantics.