Sculptured surface are used in a wide variety of applications in the automotive, aerospace and ship building industries, such as turbine blades, impeller and marine propellers. The original design concept is often embodied in a physical model, perhaps sculpted from clay by a skilled artisan, from which measurement data is scanned. Surfaces are fitted to the scanned data, and a mathematically precise description is then available for subsequent steps in the product-design process. Parametric forms such as the well known Bezier, B-spline and NURBS type usually mathematically define the surfaces. Typically, a design is composed of number of parametric surface patches. This is the highly effective method. In this paper an innovative theory for machining complicated surface is presented. By using an anural milling tool instead of ball-end mill or the flat-ended tool, 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. Through the deduction of differential equation, some theory on partial touching between surfaces and surfaces when manufacturing has been explored. The problem of axis orientation under this condition has also been discussed clearly. The outside of the circular tool is a surface; the surface to be machined is a groove, which can be represented by its transverse line. In this case the problem is attributed to the contact between surface and curve.
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