For the purposes of automating the assignment of tolerances during design, a math model, called the Tolerance-Map (T-Map), has been produced for most of the tolerance classes that are used by designers. Each T-Map is a hypothetical point-space that represents the geometric variations of a feature in its tolerance-zone. 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 T-Map construction for any line-profile by using primitive T-Map elements and their Boolean intersection. The method requires (a) decomposing a profile into segments, each of constant curvature; (b) creating a solid-model T-Map primitive for each in a common global reference frame; and (c) combining these by Boolean intersection to generate the T-Map for a complete line-profile of any shape. Freeform portions of a profile are modeled as a series of closely spaced points and subsequent formation of short circular arc-segments, each formed from the circle that osculates to three adjacent points.
Tolerance-Maps for Line-Profiles Formed by Intersecting Kinematically Transformed Primitive Tolerance-Map Elements
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received June 18, 2015; final manuscript received March 23, 2016; published online April 29, 2016. Assoc. Editor: Vijay Srinivasan.
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He, Y., Davidson, J. K., Kalish, N. J., and Shah, J. J. (April 29, 2016). "Tolerance-Maps for Line-Profiles Formed by Intersecting Kinematically Transformed Primitive Tolerance-Map Elements." ASME. J. Comput. Inf. Sci. Eng. June 2016; 16(2): 021005. https://doi.org/10.1115/1.4033236
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