Geometric metrology I. Separation functionals in tolerance assessment

Geometric metrology represents a fundamental shift in viewpoint in regard to the analysis and interpretation of measurement data sets associated with metrological analysis. Geometric metrology is based oil the notion of a separation functional and provides a unifying and conceptual framework to describe the shape variability of manufactured artefacts. The ?methodology is simple and intuitive, provides a complementary perspective to normal metrological analysis, enlarges the class of shapes that can be accommodated in terms of minimum zone separation, and provides a means to classify, categorize and quantify ?manufactured objects. Geometric; metrology allows dimensional tolerances to be generalized and evaluated in a geometric ?framework, and includes the normal "one-number" compliance test as a first-order approximation in shape differences. The separation functional is the basic object of interest in geometric metrology, and is useful to visualize, interpret, and analyze the measurement data, as well as to extract (additional) information from the measurement process not available using normal techniques. The minimum zone separation functional for a metrological artefact is computed for-a ?simple planar region representing the measurement data and an arbitrary convex polygon as the perfect form. The zone separation functional? for a perfect form nz is then introduced and computed in closed-form for several special cases. The perfect form functional allows several new measures associated with the manufactured artefact to be completed and compared with its nominal form. An equivalence class of artefacts is defined using the separation functional?, and a description of form based on a compliance vector generalizes the usual tolerance inspection test. A global measure of shape difference between the actual and nominal artefact is described using the separation functional. (C) 1997 The Franklin Institute. Published by Elsevier Science Ltd.