Tolerance Maps for Line Profiles Formed by Intersecting Kinematically Transformed Primitive Tolerance Map Elements

Abstract

For the purposes of automating the assignment of tolerances during design, a math model, called the ToleranceMap (TMap), has been produced for most of the tolerance classes that are used by designers. Each TMap is a hypothetical pointspace that represents the geometric variations of a feature in its tolerancezone. Of the six tolerance classes defined in the ASME/ANSI/ISO Standards, profile tolerances have received the least attention for representation in computer models. The objective of this paper is to provide a comprehensive treatment of TMap construction for any lineprofile by using primitive TMap elements and their Boolean intersection. The method requires (a) decomposing a profile into segments, each of constant curvature; (b) creating a solidmodel TMap primitive for each in a common global reference frame; and (c) combining these by Boolean intersection to generate the TMap for a complete lineprofile of any shape. Freeform portions of a profile are modeled as a series of closely spaced points and subsequent formation of short circular arcsegments, each formed from the circle that osculates to three adjacent points.