Areal coordinates: The basis of a mathematical model for geometric tolerances

A mathematical model is presented for representing the tolerances of planar surfaces. The model is compatible with the ASME/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map(R)(1) , a hypothetical volume of points which corresponds to all possible locations and variations of a segment of a plane which can arise from tolerances on size, form, and orientation. This model is one part of a bi-level model that we are developing for geometric tolerances. The new model makes stackup relations apparent in an assembly, and these can be used both to allocate size and orientational tolerances and to identify sensitivities. All stackup relations can be met for 100% interchangeability or for a specified probability.