Segment a cam contour with generalized cross product

Abstract

Cam contour fitting is greatly affected by data segmentation errors. Yet traditional segmentation methods are susceptible to data noise and not able to cope with contour of multiple curve type. Therefore, a new method is proposed based on Generalized Cross Product (GCP), and the segmentation of arc cam contour is taken as examples. Regarding the contour as a series of arc fragments, circular features of each fragment are transformed to a GCP norm by vector mapping. Based on the robustness of GCP, the disturbances of data noises on the GCP norms of a segmented arc are suppressed while those on its adjacent arc are amplified in the mapping. Then there is a sharp contrast in between the GCP norms, i.e. the differences of the features of 2 adjacent arcs are exhibited distinctly. Thus the dividing point between 2 segments can be easily identified. By this way, the cam contour is segmented accurately. Most importantly, the accuracy can be greatly improved through comparing the vector mappings of different mapping parameters. It is validated by experiments that the method can apply to cam contour of various curve type, including spline curves, and has strong robustness against data noise.