Author:
Myasoedova Tatiana Mikhailovna
Abstract
The object of research is the shaping of a family of displacement curves used in designing the path of a tool that processes pocket surfaces. The subject of the study is the working displacement curves in the case of multiply connected areas. Working displacement curves are lines from which non-working sections have been removed. Non-working areas include self-intersecting loops of displacement curves and sections formed when intersecting displacement curves of opposing fronts. The paper presents methods for analyzing and cutting off non-working sections for cases of self-intersection and intersection of displacement curves of opposing fronts. The spatial geometric model of the formation of displacement curves is based on the cyclographic method of displaying space. As a tool for detecting non-working areas for the case of opposing fronts, a method of a testing beam is proposed. In the case of self-intersections of the displacement curves, non-working sections are cut off by the parameter of these lines at the points of self-intersection. The novelty of the study lies in the fact that the obtained mathematical model of the formation of displacement curves for multiply connected regions with contours of complex handicap curves makes it possible to obtain parametric equations of working lines at the output of the computational algorithm in a more reliable and simple way. This greatly simplifies the solution to the problem of automated design of the trajectory of the cutting tool. A comparative assessment of the proposed method of shaping a family of displacement curves with cutting off non-working sections and known methods using the distance function is performed.
Reference19 articles.
1. Farouki, R .T. Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable. Berlin: Heidelberg Springer Verlag, 2008. – 732 p.
2. Blum, H. A transformation for extracting new descriptors of shape, in Models for the Perception of Speech and Visual Form. Cambridge: MIT Press, 1967. – 380 p.
3. Persson, H. NC machining of arbitrary shaped pockets. // Computer Aided Design, 1978. – 3(10). – P. 169–174.
4. Lee, D. Medial axis transformation of a planar shape. // IEEE Transactions on Pattern Analysis and Machine Intelligence, 1982. – 4(4). – P. 362–369.
5. Srinivasan, V. and Nackman, L. R. Voronoi diagram for multiply-connected polygonal domains I: Algorithm. // IBM Journal of Research and Development, 1987. – 31(3). – P. 361–372.