Control of geometry and stability of tensegrities in the Octahedron and X-Octahedron families

• Tensegrity geometry is controlled by their force:length ratio matrix null space vectors. • Different shapes are obtained depending on the linear combination of those vectors. • Tensegrity bars are always clustered in three groups of parallel equal elements. • Length and orientation of the three groups of struts are controlled by the designer. • Stability of folded forms is controlled by means of the tensegrity shape. Tensegrity structures obtained from the same connectivity patterns are said to belong to families. The Octahedron and X-Octahedron families are examples of these. In the literature, little attention has been paid to how the final geometries of the equilibrium forms of the members of both families are obtained. A compact formulation for controlling the equilibrium shapes of members of the Octahedron and X-Octahedron families is proposed in this article allowing the designer to get any geometry for the super-stable members of both families. Controlling the stability of folded forms is achieved by using the shape of the structure, and a detailed explanation of the formulation is provided here, as well as several examples that clarify the formulation. The geometrical control of the equilibrium shape is fundamental when applying it to tensegrity structures in an engineering context.