Computational Geometry on the Sphere With Application to Automated Machining

[+] Author and Article Information
Lin-Lin Chen, T. C. Woo

Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI 48105-2117

J. Mech. Des 114(2), 288-295 (Jun 01, 1992) (8 pages) doi:10.1115/1.2916945 History: Received August 01, 1990; Online June 02, 2008


Based on observations made on the geometry of the cutting tools and the degrees of freedom in 3-, 4-, 5-axis numerical control machines, a new class of geometric algorithms is induced on the unit sphere. Spherical algorithms are useful for determining the type of tool, its path, workpiece fixturing, and the type of machine. Basic to these algorithms are four that are presented here: detection of convexity on the sphere, computation for spherically convex hull, determination of the spherical convexity of a union, and the intersection of hemispheres. These four algorithms are related by duality and the sharing of partial results.

Copyright Ā© 1992 by The American Society of Mechanical Engineers
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