Evaluation of form data using computational geometric techniques—Part I: Circularity error

The present work deals with evaluation of form error from the measured profiles obtained using a form tester, namely roundness/cylindricity measuring instrument. In Part I, details of circularity evaluation are presented. Due to eccentricity in component setting and radius-suppression inherent in the measurement, circularity error has to be evaluated with reference to a limacon. A computational geometry-based algorithm is proposed for establishing minimum circumscribed, maximum inscribed and minimum zone limacons. A new type of control hull for directly constructing equi-angular diagrams and a new procedure for updating are introduced. Validation has been done with bench-mark data set and corresponding results available in the literature. Being geometry-based algorithm, it is simple to follow and each iteration can be visualized and interpreted geometrically. On comparison with simplex search method, the proposed algorithm is found to be computationally efficient in terms of accuracy and time taken. The proposed methods can be easily implemented in computer-aided roundness measuring instruments. Extension of this work for evaluation of cylindricity error has been dealt in Part II.