Form-finding analysis for a new type of cable–strut tensile structures generated by semi-regular tensegrity

A tensegrity structure is a type of self-balancing tensile structure, which consists of tension cables surrounding compression struts. Based on the geometry and topology of the classic half-octahedron tensegrity, this article presents a form-finding analysis of semi-regular tensegrity units using singular value decomposition of the equilibrium matrix. We propose the design formulas for the unit geometric transformation, obtain its internal self-stress modes and inextensional mechanism modes, and verify its geometric stability. Then, we devise a design method and compute the overall feasible self-stress of a tensegrity torus. A novel cable–strut tensile structural system is generated through combining a tensegrity torus and a Levy-type cable dome. Finally, a physical model is constructed to verify the feasibility of this structural system. This work enriches existing forms of tensegrity structures and contributes to further practical applications of tensegrity systems.