Tolerance-Maps Applied to the Straightness and Orientation of an Axis

Among the least developed capabilities in well-developed mathemati cal models for geometric tolerances are the representation of toleranc es on form, orientation, and of Rule #1 in the Standards, i.e. the coupling between form and allowable var iations for either size or position of a feature. This paper uses Tolerance-Maps ®1 (T-Maps ®1 ) to describe these aspects of geometric tolerances for the straightness and orientation of an axis within its tolerance-zone on position. A Tolerance-Map is a hypothetical poi nt-space, the size and shape of which reflect all variational possibilities for a targ et feature; for an axis, it is constructed in four-dimensional space. The Tolerance-Map for straight ness is modeled with a geometrically similar, but smaller-sized, four-dimensional s hape to the 4D shape for position; it is a subset within the T-Map for position. Another interna l subset describes the displacement possibilities for the subset T-Maps that limits for m. The T-Map for orientation and position together is formed most reliably by trun cating the T-Map for position alone.