A prototype of feature-based design for assembly

A rigorous mathematical theory of tolerances is an important step toward the automated solution of tolerancing problems. This paper develops a mathematical theory of tolerances in which tolerance specifications are interpreted as constraints on a normed vector space of model variations (M-space). This M-space provides concise representations for both dimensional and geometric tolerances, without deviating from the established tolerancing standards. This paper extends the authors’ previous work to include examples of geometric orientation and form tolerances. We show that the M-space theory supports the development of effective algorithms for the solution of tolerancing problems. Through the use of solid modeling technology, it is possible to automate the solution of such problems.