Analysis and trimming operations in the problem of spatial formation of a family of offset curves given an area with islands

Abstract

Abstract In the present paper an algorithm of determination and trimming of non-working segments of offset curves generated for an area and a number of islands within it is considered. The algorithm is based on cyclographic method of spatial formation of offset curves given curvilinear boundary contours of an area and islands within it. Methods of analysis and corresponding algorithms of trimming of non-working segments of offset curves are considered for the cases of self-intersection of offset curves. The analysis and trimming operations form the basis of the proposed algorithm of spatial formation of offset curves. The calculations that accompany every stage of formation process are exact and not based on iteration algorithms. The acquired analytical solution to the problem of generation of a family of offset curves significantly facilitates cutting tool trajectory calculation and control programming in pocket machining on NC units.