From graphs to tensegrity structures: Geometric and symbolic approaches

Abstract

A form-finding problem for tensegrity structures is studied; given an abstract graph, we show an algorithm to provide a necessary condition for it to be the underlying graph of a tensegrity in ${\mathbb{R}}^d$ (typically $d=2,3$) with vertices in general position. Furthermore, for a certain class of graphs our algorithm allows to obtain necessary and sufficient conditions on the relative position of the vertices in order to underlie a tensegrity, for what we propose both a geometric and a symbolic approach.

17 pages, 8 figures; final version

References in corpus (2)

• Expansive Motions and the Polytope of Pointed Pseudo-Triangulations
• Improving DISPGB Algorithm Using the Discriminant Ideal

Cited by in corpus (7)

• Cellular morphogenesis of three-dimensional tensegrity structures
• Generation of planar tensegrity structures through cellular multiplication
• The combinatorial geometry of stresses in frameworks
• On stratifications for planar tensegrities with a small number of vertices
• Analysis of self-equilibrated networks through cellular modeling
• Tensegrities on the space of generic functions
• Geometry of configuration spaces of tensegrities