The concept of “contact” in differential geometry is creatively applied into the machining of the sculptured surface; the contact principle of the machining of complicated surfaces is presented. The circumference circle of the cylindrical cutter instead of ball-end milling cutter is used to sweep the curved surface. This is the highly effective method. In this paper an innovative theory for machining complicated surface is presented. By using a flat-end mill instead of ball-end mill, and by adjusting the axis of cutter relative to the surface, the two surfaces, the swept surface and the required surface, have the same curvatures, up to as high as 3rd order. It shows how aspects of 5-axos machining can be achieved through 3-axis methods. This is useful as not all shops can afford 5-axis machining.

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