Parameter-based spiral tool path generation for free-form surface machining

In computer-aided manufacturing systems, generation strategies are classified into two main types according to the generation domain of the tool path: real space and the parametric domain. Although generation methods in the parametric domain defined using a parametric surface, such as a non-uniform rational B-spline surface, have the advantage of rapid calculation, tool path variations are limited because few methods using this type of tool path generation recognize features of the surface in the parametric domain. This study proposes a new algorithm for tool path generation that can generate machining points in the parametric domain without losing information about the distances among the corresponding points in real space. Using this proposed method, a tool path with a constant pitch in real space and an efficient tool path, such as a spiral path, can be rapidly calculated. This paper explains the theory behind this method and describes its implementation using free-form surfaces composed of a single patch. The proposed method was then expanded to surfaces composed of multiple patches. In this case, because correspondence between each surface patch is required, parametric boundary representation using a half-edge structure is also proposed in this paper. Parametric boundary representation can be used to represent connections among the outer and inner trimming boundaries of each surface patch on the parametric domain. Finally, the proposed method was implemented for two surfaces composed of multiple patches, and its effectiveness was confirmed by simulating and machining these surfaces.