On-line Journal of the IASS

Using Symmetry for Tensegrity Form-Finding

< Table of Contents for Vol. 47 (2006) No. 3 December n. 152

• Journal Name: Journal of the International Association for Shell and Spatial Structures (J. IASS)
• ISSN: (Electronic Version) 1996-9015, (Print Version) 1028-365X
• Issue: Vol. 47 (2006) No. 3 December n. 152
• Pages: 245-252
• Title: Using Symmetry for Tensegrity Form-Finding
• Author(s): R. Pandia Raj and S. D. Guest
• Keywords: Tensegrity structures, form-finding, stress matrix, group representation theory, symmetry-adapted

Abstract
Symmetry can simplify the form-finding process for tensegrity structures; and this paper will describe one simplification technique. Our method is based on the commonly used force density method, but the calculations are done using a symmetry-adapted coordinate system. The standard force-density method assumes a known connectivity for the structure. A tension coefficient (tension divided by length) must then be found for every member so that an equilibrium solution is possible. Finding the nodal coordinates is straightforward once a suitable set of tension coefficient is found; but finding suitable tension coefficients may be non-trivial. In this paper we simplify the correct choice of tension coefficients by the use of symmetry – in addition to the connectivity of the structure, we assume that the structure has certain symmetry properties, greatly reducing the difficulty of finding possible configurations. The paper will show simple examples of the method where a simple analytical solution gives all possible symmetric tensegrities with a given connectivity.

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