The article presents a new method for determining the distribution of measurement points, which can be used in the case of contact coordinate measurements of curvilinear surfaces of products. The developed method is based on multi-criteria decision analysis. In the case of the new method, the selection of the distribution of measurement points on free-form surfaces is carried out based on the analysis of five different criteria. The selection of the best model of the distribution of measurement points results from the accuracy of coordinate measurements, the time needed to complete measurement tasks, the number of measurement points, the accuracy of the substitute surface representing the measured free-form surface and the area where measurement points are located. The purpose of using the developed method of the distribution of measurement points is to increase the performance of coordinate measurements primarily by increasing the automation of strategy planning of measurements of curvilinear surfaces and improving the accuracy of measurements of free-form surfaces of products. The new method takes into account various aspects of coordinate measurements to determine the final model of the distribution of measurement points on measured surfaces of products, thereby increasing the probability of the proper determination (i.e., identifying the highest deviations of a product) of the location of measurement points on the surfaces of a measured object. The paper presents an example of the application of the created method, which concerns the selection of the best model of the distribution of measurement points on a selected free-form surface. This example is based on, among others, the results of experimental investigations, which were carried out by using the ACCURA II coordinate measuring machine equipped with the VAST XXT measuring probe and the Calypso measurement software. The results of investigations indicate a significant reduction in time of coordinate measurements of products when using the new method for determining the distribution of measurement points. However, shortening the time of coordinate measurements does not reduce their accuracy.
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