Influence of the level of connectivity on the members of the Octahedron and X-Octahedron families of tensegrities

Abstract

Tensegrity structures based on topological patterns have been developed greatly in recent years. Tensegrities obtained from the same pattern are said to belong to a family. Two examples of tensegrity families are the Octahedron and the X-Octahedron, whose members are composed of rhombic and X-rhombic cells, respectively, which are collected in three groups. The general connectivity pattern of both families consists of three levels of connectivity. This work analyzes the influence of the reduction of the level of connectivity on the members of both families. The connection graphs corresponding to different levels of connectivity are defined based on the new concept of “twin tensegrities”. Analytical computations have been performed to determine the force:length ratios that satisfy equilibrium, stability, and super-stability conditions. In addition, the mathematical sequence that follows the ratio between the force:length ratio of struts and cables of the X-Octahedron family that leads to a super-stable equilibrium configuration is presented. The new tensegrities obtained in this work also belong to the Octahedron and X-Octahedron families and could have promising engineering applications such as modular constructions.