Tolerance-based localization algorithm: form tolerance verification application

Current localization techniques have been successfully used for aligning sculptured surfaces with CAD models in inspection applications. However, tolerance specifications are not considered as an integral part of the localization process. The tolerance verification and comparison with measured surfaces occur at a later step to accept or reject the manufactured part. This two-step process prolongs the inspection time. For the first time, this paper presents a novel localization algorithm for inspection that integrates the tolerance specifications as an optimality criterion. A closed-form solution algorithm that applies 3D rigid body transformation using quaternion and uses a minimum acceptable deviation zone approach was developed. The formulation is based on the mathematical definitions from ANSI Y14.5.1 standards (American National Standard Institute) for form tolerances. The new iterative minimum acceptable deviation zone localization algorithm is formulated using four types of form tolerances: straightness of a median line, straightness of a surface line, flatness and cylindricity. It is applied and compared to several benchmark examples for validation. The results demonstrated the ability of the new localization approach to achieve comparable results but with less computation effort due to using a constraint satisfaction problem and a closed-form solution algorithm in the formulation. The merit of the new approach stems from its ability to increase the efficiency of tolerance verification during the inspection process. The applicability of the proposed algorithm to various types of tolerance is highlighted.