Inverse form-finding for tensegrity structures

Abstract

In this study we examine the topic of inverse form-finding, also referred to as topology finding, for tensegrity structures. Specifically, the problem addressed is given the specification of final nodal positions for a tensegrity, we seek to find appropriate connectivities, or topologies, that satisfy stability and connectivity constraints. Two new algorithms are presented in the paper. The first may be applied for generating prestress-stable tensegrity structures, while the second can be used to generate super-stable tensegrities. Numerical examples for both 2D and 3D tensegrities are provided to demonstrate that these new algorithms can produce desirable structures with nodal positions being the only prescribed piece of information. We also show that inverse form-finding of a specific Class k tensegrity can be formulated into a graph factorization problem. This is the first time that both the stability property and class can be specified among the few existing inverse form-finding methods. These new methods facilitate the design process in which a desired nodal geometry is prescribed, and viable structural configurations consistent with this geometry can be obtained.