Multi-point machining (MPM) is a tool positioning technique used for finish
machining of sculptured surfaces. Ln 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 m
ethod used to generate the multi-point tool positions was slow and labor in
tensive. The objective of this paper is to present efficient algorithms to
generate multi-point tool positions. A basic multi-point algorithm is prese
nted based on some assumptions about the curvature characteristics of the s
urface underneath the tool. This basic algorithm is adequate for simple sur
faces but will fail for more complex surfaces typical of industrial applica
tions. Accordingly, tool position adjustment algorithms are developed that
combine the basic algorithm with non-linear optimization to achieve multi-p
oint tool positions on these more complex surfaces. (C) 2000 Elsevier Scien
ce B.V. All rights reserved.