From octagonal connection graphs belonging to the Z-Octahedron family to new tensegrity structures

Abstract

A tensegrity family is a group of tensegrity structures that share a common connectivity pattern. The Octahedron, the Z-Octahedron, and the X-Octahedron families are examples of these groups found in the literature. In this work, a new graphical representation of the members of the Z-Octahedron family based on octagonal cells is presented. These new elementary cells are composed of eight nodes and two struts. In addition, a new member of the family is introduced: the Z-triple-expanded octahedron. New tensegrity structures from the Z-Octahedron family are obtained by modifying the connectivity pattern of the elements that make up the octagonal cell. Several element groupings have been considered in order to find different equilibrium configurations. The values of the force density or force:length ratio that lead to stable and super-stable tensegrity forms have been computed analytically. It has been proved that the Z- Octahedron family is a good source of new tensegrity forms.