This paper deals with the problem of 5-axis machining of ruled surfaces. It is well known that a ruled surface may be efficiently machined with a cylindrical cutter using the side milling process. This paper studies the problem of planning the tool motion for side milling of ruled surfaces as a kinematic approximation problem. The goal is to develop a new method for synthesizing a Non-Uniform Rational B-Spline (or NURBS) motion such that the swept surface of such a motion with a cylindrical cutter closely approximates a given ruled surface. First a NURBS motion is used to interpolate or approximate a set of discrete cutter locations for the side milling of a given ruled surface. Then the deBool control positions of the NURBS motion is fine-tuned to minimize the error between the swept surface of the cylindrical cutter under the NURBS motion and the desired ruled surface. In this way, the tool motion is represented by the set of deBoor control positions and associated knot sequence as opposed to a huge set of discrete cutter locations.

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