Abstract GEOMETRIC TOLERANCES: A NEW APPLICATION FOR LINE GEOMETRY AND SCREWS

A new mathematical model is introduced for the tolerances of cylindrical surfaces. The model is compatible with the ISO/ANSI/ASME Standard for geometric tolerances. Central to the new model is a Tolerance-Map ®1, a hypothetical volume of points which corresponds to all possible locations and variations of a segment of a line (the axis) which can arise from tolerances on size, location, and orientation of the cylindrical surface. Each axis in a tolerance-zone will be represented with the six Plücker coordinates. Cylindrical surfaces in a tolerance-zone for the same hole can then be treated by attaching a size tolerance to each of the lines, thereby forming a screw. Relationships for the content of line-solids for a tolerance-zone are developed to correspond to the variations of locations. These are then used to get a measure for the increment in cost when a more refined tolerance is specified. This model is one part of a bi-level model that we are developing for geometric tolerances. 1