An Approach to Swept Volume Generation for NC Machining using Gauss Map

Abstract

This article presents a novel method for modeling swept volumes of milling tools that undergoes a translational motion by extending the basic idea behind Gauss maps. The main idea is that it 1) transforms the tool shape and the moving direction of the tool from Euclidean space into an unit sphere by means of Gauss function and gets the spherical domains which are called Tool map (T-Map) and Contact map (C-Map) respectively 2) finds an intersection region of T-Map with C-Map and 3) transforms intersected region inversely into Euclidean space to get the envelope profile of the tool at prescribed instant time. The proposed approach is intuitive to understand the cutting behavior of generalized tool shape, simple to implement the swept volume and extendible up to a piecewise C -continuous convex set following translational motion.