automatic generation of stiff tensegrity structures
TThis work addresses the design of tensegrity structures, which are lightweight load-bearing assemblies entirely composed by only two types of elements: struts and cables. The form-finding of these structures is well known to be a complex problem, so that most of the existing design methods are based on the repetition of templated modules and are limited to simple shapes. Conversely, the present method creates free-form stable tensegrity configurations that satisfy both fabrication and geometric constraints.
Tensegrity is a combination of the words "tensile" and "integrity", invented by Buckminster Fuller, who firstly introduced this structural system. A tensegrity structure consists of a set of isolated compressed components, incuded in a net of tensioned cable segments ("islands of compression in a sea of tension" as defined by Buckminster Fuller himself). The balancing of tension and compression generates stable elements. Beyond the structural properties, these structures are appreciated in architecture and art contexts for their aesthetics, in particular for the weigthless appearance of the floating struts. However, current design methods are not able to manage complex shapes, and finding the components' arragement within a fixed volume is a complex combinatorial problem. This work aims at bridging the gap between the artistic freedom of designing complex shapes and the practical need to compute a tensegrity system that faithfully approximates these input shapes.
In order to explore the complex tensegrity design space, we used an approach based on the geometric optimization of the positions of the elements. Inputs of the problem are a given shape and some auxiliary geometrical constraints, such as minimal distance between pairs of struts, coplanarity of a subset of nodes (in order to preserve the planarity of a face), original face-shape preservation and forbidden zones. Initially, a non-stable connectivity of the tensegrity is generated. Then in the form-finding step, each node is tested for stability and moved locally searching for a stable configuration that results as close as possible to the initial one. The positions of struts and cables are optimized and the connectivity is revised if needed. Finally, removing all redundant cables that do not contribute to the stability, the structure is simplified.
We validate our method with large-scale physical realizations of two tesegrity design cases. The aim of this test is to prove the practical feasibility and the ability of the structures to preserve their stability if submitted to any external stress.
The first case is a spherical design featuring 7 struts, which is a non-trivial asymmetric variation of the popular icosahedron-based 6-struts tensegrity. The second case is a tripod structure with rotational symmetry that has a noticeable dimension of 2.3m (24 tubes, 145 cables) and weight (about 130 kg). The models are made of stainless steel tubes with 60 mm diameter and steel cables with 4 mm diameter.
Paolo Cignoni email@example.com