Substitute Geometry of the Features of Size: Applications to Multidimensional Features

Abstract

The problems of the substitute geometry for features of size are considered and an algorithm for synthesis of the substitute features (SF) is developed. Three and only three classes of surfaces are proved to have an incomplete set of position and orientation deviations within the SF equation: cylinders with any directrix, surfaces of revolution with any meridian, and helical surfaces with any profile. The form accuracy of multidimensional features relating to these classes is considered: ellipsoid of revolution, epitrochoidal cylinder, and Archimedean screw. The deterministic consideration is accompanied by evaluation of the uncertainty of the standard assessments of the geometric accuracy and capacity of the computing procedure.