DOI: 10.14489/td.2014.09.pp.044-048

Nikolaev P.M.
APPLYING MEASURED POINTS TO A MATHEMATICAL MODEL USING LOCAL SURFACE LINEARIZATION
(pp. 44-48)

Abstract. Nowadays, measuring machines are commonly used for manufacturing quality control of products coordinate. The results of measure-ments obtained by products scanning are the ordered sets of points. Measured points are compared with a mathematical model to determine various parameters of manufacturing quality. The main problem in the comparison of measurement results with the mathematical model is the difference of their coordinate systems. It is necessary to produce the combination of measured points with a mathematical model by means of a rotation and translation of the coordinate systems. The criterion of best fit is the least distances sum from the measured points to the surface of the model. Complete solution to the problem of combining points with the model is not currently available. Known algorithms, based on the distance minimization between the measured points and the corresponding points on the surface of the model, work unsatisfactory on surfaces with a small curvature. In the paper a description of the algorithm combining the measured points with a mathematical model of a complex shape is presented. The proposed algorithm is based on minimizing the distance between the measured points and the locally linearized surface. To achieve the best combination an iterative cycle is used. Using of surface linearization significantly increases the speed of convergence and the domain of combining the measured points and model. Algorithm calculates displacement and rotation angles for the best match measured points with the mathematical model.

Keywords: surface linearization, complex shape, manufacturing accuracy, measured points, distance minimization.

 

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