Generation of planar tensegrity structures through cellular multiplication

Abstract

Tensegrity structures are frameworks in a stable self-equilibrated prestress state that have been applied in various fields in science and engineering. Research into tensegrity structures has resulted in reliable techniques for their form finding and analysis. However, most techniques address topology and form separately. This paper presents a bio-inspired approach for the combined topology identification and form finding of planar tensegrity structures. Tensegrity structures are generated using tensegrity cells (elementary stable self-stressed units that have been proven to compose any tensegrity structure) according to two multiplication mechanisms: cellular adhesion and fusion. Changes in the dimension of the self-stress space of the structure are found to depend on the number of adhesion and fusion steps conducted as well as on the interaction among the cells composing the system. A methodology for defining a basis of the self-stress space is also provided. Through the definition of the equilibrium shape, the number of nodes and members as well as the number of self-stress states, the cellular multiplication method can integrate design considerations, providing great flexibility and control over the tensegrity structure designed and opening the door to the development of a whole new realm of planar tensegrity systems with controllable characteristics.

Cellular morphogenesis of three-dimensional tensegrity structures

“…Cellular morphogenesis reflects the reverse process of the tensegrity decomposition proposed by de Guzmán and Orden 2006 [6]. A corollary to a Proposition by Fernández and Orden (2011) [51], which allows one to combinatorically calculate the number of self-stress states by decomposing tensegrity structures into cells, was proposed by Aloui et al (2018) [30] and is adapted here for three-dimensional tensegrity structures:…”

“…For three-dimensional tensegrity structures, the number of added or removed states can take any integer value from 0 to 10 depending on the change in the number of edges and nodes of the structure, with each state reflecting the contribution of a single unicellular organism. These unicellular organisms can be tensegrity cells if they are complete graphs on five nodes or virtual cells [30]: subgraphs with one self-stress state formed by the interactions between cells. For cells, the self-stress state can be calculated through Equation 13.…”

“…de Guzmán and Orden [6] characterized tensegrity topologies through their decomposition into elementary stable topological units. Aloui et al (2018) [30] proposed a generative method for the design of planar tensegrity structures based on the elementary stable topological units defined by de Guzmán and Orden [6]. However, the method cannot be directly extended to three-dimensional structures, as the constitutive topological units for the planar and the spatial case differ and the number of topological combinations to be considered increases.…”

Geometric criteria for realizability of tensegrities in higher dimensions

“…, v n ). We choose a nonzero tension w 1,2 on the edge (v 1 ; v 2 ) which immediately determines the tension wn,1 on the edge (v n ; v 1 ) due to the equilibrium condition shown in Equation (2). See also Figure 2 (right).…”

“…Tensegrities form an essential part of modern architecture and in arts, they serve as a light structural support (like in a recent sculpture TensegriTree in the University of Kent). Tensegrities are traditionally used in the study of cells [11,1,2], viruses [5,24], deployable mechanisms [26], etc.…”