A Laboratory Project on the Design and Machining of Bezier Surfaces

Abstract

This paper describes a six-hour laboratory project on the design and machining of Bezier surfaces. Students are required to design a pair of mutually orthogonal Bezier surfaces. In both cases, the surface is to lie completely within the stock material provided. In addition, C⁰ and C¹ continuity has to be enforced at the common boundary. The coordinates of the second surface have to be rotated by 90 degrees so that the surface can be aligned to the axis of the cutter. The principal issues relating to the machining of multiple Bezier surfaces are discussed, viz. the determination of the cutter diameter and orientation, and the generation of the NC toolpath (i.e. the spacing between adjacent curves and their incremental movement) to achieve the specified scallop height and machining tolerance. An algorithm incorporating these aspects for the generation of the NC toolpath is presented.

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