This paper applied the concept of “contact” in Differential Geometry into the machining of the sculptured surface. I presented the contact principle of the machining of complicated surfaces, using the circumference circle of the cylindrical cutter to sweep the curved surface instead of ball-end mill. This is highly effective method. In this paper an theory for machining complicated surface is presented. By using a flat-end mill instead of ball-end mill, and adjusting the axis relate to the surface, the two surfaces, The swept surface and the required surface, has the same curvature, up to as high as 3th order
