The geometric variations in a tolerance-zone can be modeled with hypothetical point-spaces called Tolerance-Maps (T-Maps) for purposes of automating the assignment of tolerances during design. The objective of this paper is to extend this model to represent tolerances on circular runout which limit geometric manufacturing variations to a specified tolerance-zone. Such a zone is an annular area at one transverse cross-section for spherical, conical, or cylindrical objects (features), but it is a short cylinder when the feature is a round or annular segment of a plane. Depending on the kind of feature and the tolerances that are specified for it, the model may be used to represent variations within tolerance-zones for circular runout, size, position, orientation, and form. In this paper, the Tolerance-Map (T-Map) is a hypothetical volume of points that captures all the circular variations that can arise from these tolerances. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. T-Maps have been generated for other classes of geometric tolerances in which the variation of the feature are represented with a plane or line, and these have been incorporated into testbed software for aiding designers when assigning tolerances for assemblies. In this paper the T-Map for circular runout is created and, for the first time, circles are used to represent the geometric variations of a feature in tolerance-zones.

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