A Mathematical Model for Geometric Tolerances

This paper presents a mathematical model for specifying geometric tolerances. This model along with a syntax of tolerance specification will be referred to as the Tolerance Specification Language (TSL). TSL can be used to interpret ANSI Y14.5 geometric tolerancing specifications. The formalization of TSL is based on a set theoretic approach, especially on the concept of offset solids. In this model there is no classification of tolerance types, and there are no restrictions on the use of feature types. Instead, TSL allows the designer to control a feature from expanding, shrinking, or deforming beyond a specified tolerance value. All the tolerancing assertions in TSL apply to surface features and generate uniform tolerance zones. Using two and one dimensional tolerance specification facilities, TSL can approximate ANSI statements that apply to derived features, or generate non-uniform tolerance zones. The appendix of this paper discusses many examples from ANSI and their equivalent TSL form.