The parametrization of geometric form
This report covers one of the most important and fundamental aspects of the assessment of the geometric form of workpieces measured with a coordinate measuring machine (CMM). It describes how basic geometric elements - lines, circles, planes, spheres, cylinders and cones - can be represented reliably in terms of a set of algebraic parameters, that is parametrised. In addition, it provides recommended ways of algebraically representing the distance of a point from each of the main geometric elements. These distance formulae are presented in terms of the recommended parameters. Two sets of parametrisations are recommended. The first set applies to full elements, i.e. elements that are to be derived from measurements distributed throughout the feature. The second applies to partial elements derived from (a) measurements distributed over a relatively small portion of a feature (perhaps due to access difficulties), or (b) measurements over features that are naturally incomplete, e.g. a spherical cap or a cylindrical gusset. The relationship between recommended parametrisations and algorithms used to determine numerical values of geometric element parameters is considered. The parametrisations provided have optimality properties with great significance for such numerical computations.
Bibliographic Reference: EUR 13517 EN (1991) 102 pp., MF, ECU 8, blow-up copy ECU 13.75
Record Number: 199110743 / Last updated on: 1994-12-02
Original language: en
Available languages: en