A Foundation for a Unified Theory of Analysis of Spatial Mechanisms

[+] Author and Article Information
J. Duffy, J. Rooney

Department of Mechanical Engineering, Liverpool Polytechnic, Liverpool, England

J. Eng. Ind 97(4), 1159-1164 (Nov 01, 1975) (6 pages) doi:10.1115/1.3438718 History: Received July 03, 1974; Online July 15, 2010


In analogy with a spherical (spatial) triangle there are only three fundamental loop equations for any spherical (spatial) polygon, namely the real (dual) sine, sine-cosine, and cosine laws. All other loop equations which fall naturally into groups of subsidiary sine, sine-cosine, and cosine laws can be derived from the three basic laws. Novel half-tangent laws are derived which are expressions for the common root of pairs of sine and sine-cosine laws.

Copyright © 1975 by ASME
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