LEAST SQUARES ASSESSMENT OF FLATNESS, CYLINDRICITY AND SPHERICITY THROUGH SURFACE CLASSIFICATION BASED ON CONTINUOUS SYMMETRY OF GEOMETRIC OBJECT
Keywords:
Geometric Dimensioning and Tolerancing (Gd&T), Geometric Product Specification (GPS), Homogeneous Transformation Matrix, Reference Element, Continuous Subgroups Of Rigid MotionAbstract
Dimensional inspection of a manufactured surface by means of a coordinate measuring machine (CMM) produces a set of Cartesian coordinates of points. The coordinates are processed to yield the geometric deviations of the manufactured surface from the nominal one. This paper presents a new approach to the evaluation of flatness, cylindricity and sphericity tolerance based on surface invariance with regard to the rigid motions. The proposed algorithm transforms the coordinates measured, through homogeneous transformation matrices, in order to best fit the reference element (datum) of the class of the surface from which the actual measurements were sampled. The methodology was computer implemented, and numerical simulations were performed to validate the effectiveness of the approach. Compared with the form tolerance a priori known of the used datasets, the obtained results indicate that the proposed algorithm provides accurate and quick assessments
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References
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