Distance function based algorithm for spatial straightness evaluation

Abstract

This paper focuses on the development of an efficient algorithm for evaluating the spatial straightness error based on the minimum circumscribed cylinder (MCC). A signed point-surface distance function is defined, and its increment with respect to the differential motion of the surface is derived. On this basis, spatial straightness evaluation is formulated as a non-linear constrained optimization problem, and a sequential approximation algorithm, with the magnitude of the differential motion of the reference axis being well controlled at each iteration, is developed to solve it. Also, a simple approach for verification of the optimality of the solution is presented. compared with existing algorithms, it has the advantages of implementational simplicity, computational efficiency and robustness. Examples confirm the validity of the proposed algorithm.