Topological Design of the Octahedron Tensegrity Family

Abstract

Tensegrity structures have developed greatly in recent years due to their unique mechanical and mathematical properties. In this work, the topology of the Octahedron family is presented. New tensegrity structures that belong to this family are defined based on their topology. As an example, the eleven-time-expanded octahedron is shown, a super-stable tensegrity formed by 12288 nodes, 6144 struts, and 24576 cables (the largest super-stable tensegrity reported in the literature in terms of number of nodes, cables, and struts so far). The values of the force:length ratios which satisfy the super-stability conditions have also been determined based on the topology of the Octahedron family. Consequently, the computational cost of the process of determining a suitable prestress state and its corresponding equilibrium shape (a process called form- finding) is significantly reduced. The members of the Octahedron family could have promising engineering and bioengineering applications.