Constructing tensegrity structures from one-bar elementary cells

Abstract

This study aimed to develop a method to construct tensegrity structures from elementary cells, defined as structures consisting of only one bar connected with a few strings. Comparison of various elementary cells leads to the further selection of the so-called ‘Z-shaped’ cell, which contains one bar and three interconnected strings, as the elementary module to assemble the Z-based spatial tensegrity structures. The graph theory is utilized to analyse the topology of strings required to construct this type of tensegrity structures. It is shown that ‘a string net can be used to construct a Z-based tensegrity structure if and only if its topology is a simple and bridgeless cubic graph’. Once the topology of strings has been determined, one can easily design the associated tensegrity structure by adding a deterministic number of bars. Two schemes are suggested for this design strategy. One is to enumerate all possible topologies of Z-based tensegrity for a specified number of bars or cells, and the other is to determine the tensegrity structure from a vertex-truncated polyhedron. The method developed in this paper allows us to construct various types of novel tensegrity structures.