Geometric tolerancing: II. Conditional tolerances

In a companion paper, we examined the representation of geometric tolerances in solid models from the perspective of certain functional requirements. We showed that assembly and material bulk requirements can be specified as virtual boundary requirements (VBRs). Here, we study the related issue of deriving equivalent alternative specifications. Specifically, we first explore the reasons for converting VBRs to another form of tolerances designated as conditional tolerances (CTs). We then develop a theoretical basis for converting VBRs to CTs and derive CTs for some common and practical VBRs. We thereby demonstrate the difficulties in finding a general-purpose algorithm for such conversions and also show that some of the CT formulas used in current practice are incorrect.