Generalization of the imprint method to general surfaces of revolution for NC machining

This paper presents a method of determining the shape of the surface swept by a generalized milling tool that follows a 5-axis tool path for machining curved surfaces. The method is a generalization of an earlier technique for toroidal tools that is based on identifying grazing points on the tool surface. We present a new proof that the points constructed by this earlier method are in fact grazing points, and we show that this previous method can be used to construct grazing points on (and only on) the sphere, the cone, and the torus. We then present a more general method that can compute grazing points on a general surface of revolution. The advantage of both methods is that they use simple, geometric formulas to compute grazing points.