Conceptual Framework for Tolerances in Computer Aided Design

本研究的目的是开发一种概念性的 公差问题自动化解决的基础 计算机辅助设计 研究将在 三个主题：（1）为这项工作提供基础， 将开发数学表示法， 表示为模型的赋范向量空间上的约束 变分（M空间）。 (2)为了证明它的效用， 表明M空间表示建立了一个基础， 用于制定公差的数学模型 分析和公差综合问题。 它将会显示 最一般的三维问题可以在 无论是最坏情况还是统计基础， 可以使用尺寸和几何公差。 (3)到 证明存在一个有效的计算框架 对于这些数学模型的自动化解决方案， 建模技术将得到扩展，以提供有效的方法 用于建模零件和组件语义。

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.