Development of Algorithms and Programs for Construction of Reference Circles for the Analysis of Deviations from Roundness

Abstract

A procedure for the construction of reference circles of the profile of the axial section of a test shaft or hole, the maximum inscribed circle and minimum circumscribed circle, along with circles that specify the boundaries of a ring of minimal width, is proposed. The radii and coordinates of the centers of the circles are found through minimization or maximization of a corresponding functional constructed on the basis of the coordinates of the points of the profile. The construction procedures presented are implemented in the Mathcad program package. The results obtained may be used to determine deviations from roundness, in particular, in the development of mathematical software of measuring instruments.