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In a free-state condition, deformable bodies (or compliant parts) have a significantly different shape than their nominal geometry (CAD model) due to gravity loads and residual stress. Typically, the dimensional metrology of such parts requires a particular approach where expensive and specialized jigs are needed to constrain and follow the component during inspection. This paper proposes a new method to fixtureless inspect deformable bodies by adapting the coherent point drift (CPD) algorithm. This new approach combines the optimization of the smoothness regularization parameters of the CPD powerful non-rigid registration method alongside the Thompson-Biweight statistical test as an identification method to distinguish profile and localization process manufacturing defects from a part's deformation. In other words, a new 'flexible' registration approach that meets the specifications of compliant parts is proposed. The CAD model is smoothly modified to fit the scanned part by minimizing two criteria that belong to deformable bodies. The first criterion is the conservation of the curvilinear distance (isometric transformation). That is to say, the condition that the stretch difference between the original CAD model and the modified one should be very small. The second criterion is the usual minimization of the Euclidean distance between the modified CAD model and its corresponding scanned part. Many case studies were performed on a typical industrial sheet metal which presented profile and localization defects. The estimated values of the defects, as well as their positions, are much closer to their reference ones in most cases, thus reflecting the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Managing geometric part deviations to control their effects on the product function and quality is an important task in the design of physical artefacts. Consequently, computer-aided tolerancing tools are widely applied in industrial practice to evaluate the effects of geometric part deviations on assembly and functional requirements. However, most established models and approaches for the representation of geometric part deviations, geometric tolerances, and geometric requirements in such tools lack of a realistic consideration of form deviations and are often not conform to international standards for the geometric product specification and verification. With the aim to provide a further step towards a computer-aided tolerancing theory employing variational part representatives in discrete geometry, approaches for the generation of such representatives, which conform to pre-defined tolerance specifications, are presented. These approaches ground on algorithms for the evaluation of geometric tolerances from point clouds and are essential for the tolerance analysis employing point based models. We highlight the usefulness of the presented methods for the tolerance analysis in a typical case study. [ABSTRACT FROM AUTHOR]