The structure of positional tolerance evaluation: I constructive geometric approach Original Research Article

A general geometric framework is developed to quantify the structure of positional tolerance evaluation. The data graph, overlay graph, and configuration framework of a feature set is defined and used in the evaluation of positional tolerance. Two functionals based on the configuration framework are introduced and lead to the development of optimal matings. The configuration functional quantifies the amount of “turning” the framework will allow while satisfying the mating condition, while the mating functional is used to assess optimal mating conditions. A constructive geometric procedure is used to develop the configuration and mating functionals for a given feature vector and tolerance specifications. Numerical examples are used to illustrate the form of the functionals and the procedures involved in the analysis.