Solutions to the Vector Tetrahedron Equation

[+] Author and Article Information
Milton A. Chace

IBM Systems Development Division, Development Laboratory, Rochester, Minn.

J. Eng. Ind 87(2), 228-234 (May 01, 1965) (7 pages) doi:10.1115/1.3670802 History: Received July 27, 1964; Online December 08, 2011


A set of nine closed-form solutions are presented to the single, three-dimensional vector tetrahedron equation, sum of vectors equals zero. The set represents all possible combinations of unknown spherical coordinates among the vectors, assuming the coordinates are functionally independent. Optimum use is made of symmetry. The solutions are interpretable and can be evaluated reliably by digital computer in milliseconds. They have been successfully applied to position determination of many three-dimensional mechanisms.

Copyright © 1965 by ASME
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