A tetrahedral three-spring system under a single load has been analyzed and a closed-form solution for the equilibrium positions is given. Each of the three springs is attached at one end to a fixed pivot in space while the other three ends are linked by a common pivot. The springs are assumed to behave in a linearly elastic way. The aim of the paper at hand was to find out what the maximum number of equilibrium positions of such a system might be, and how to compute all possible equilibrium configurations if a given force is applied to the common pivot. First a symmetric and unloaded system was studied. For such a system it was shown that there may exist a maximum of 22 equilibrium configurations which may all be real. Second the general, loaded system was analyzed, revealing again a maximum of 22 real equilibrium configurations. Finally, the stability of this three-spring system was investigated. A numerical example illustrates the theoretical findings.
An Inverse Force Analysis of a Tetrahedral Three-Spring System
Institute for Mechanics, Technical University Graz, Graz, Austria
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Dietmaier, P. (June 1, 1995). "An Inverse Force Analysis of a Tetrahedral Three-Spring System." ASME. J. Mech. Des. June 1995; 117(2A): 286–291. https://doi.org/10.1115/1.2826136
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