Multi-point machining (MPM) is a tool positioning technique used for finish machining of sculptured surfaces. In this technique the desired surface is generated at more than one point on the tool. The concept and viability of MPM was developed by the current authors in previous works. However, the method used to generate the multi-point tool positions was slow and labor intensive. The objective of this paper is to present efficient algorithms to generate multi-point tool positions. A basic multi-point algorithm is presented based on some assumptions about the curvature characteristics of the surface underneath the tool. This basic algorithm is adequate for simple surfaces but will fail for more complex surfaces typical of industrial applications. Accordingly, tool position adjustment algorithms are developed that combine the basic algorithm with non-linear optimization to achieve multi-point tool positions on these more complex surfaces.
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