A unified analytical form-finding of truncated regular octahedral tensegrities

• Published in: International journal of mechanical sciences 2023-02, Vol.239, p.107857, Article 107857
• Main Authors: Jiang, Jin-Hong, Yin, Xu, Xu, Guang-Kui, Wang, Zi-Yu, Zhang, Li-Yuan
• Format: Article
• Language: English
• Subjects: Equilibrium matrix method; Force-density matrix method; Self-equilibrium; Super-stability; Tensegrity
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2022.107857

•A novel hybrid truncated regular octahedral (TRO) tensegrity is proposed.•A unified model is established for Z-based, rhombic, and hybrid TRO tensegrities.•The model readily yields the super-stable configurations for each TRO tensegrity.•This work could arouse potential unification between more types of structures. Symmetric configurations are preferred in various application scenarios of tensegrity and the representative examples include Z-based and rhombic truncated regular polyhedral (TRP) tensegrities. A key step in the design of such tensegrities is the determination of their self-equilibrated and stable configurations, known as form-finding, which have been extensively but individually investigated by many research groups. To unify the existing form-finding results of these two types of tensegrities, we propose here a novel hybrid type of the TRP tensegrities that can be readily converted into Z-based and rhombic. Based on this structural transformation, two unified form-finding models of the Z-based, rhombic, and hybrid truncated regular octahedral (TRO) tensegrities are established using the equilibrium/force-density matrix methods. A distribution coefficient for the force-densities of strings is defined for our models to directly yield the self-equilibrium and super-stability conditions for each type of TRO tensegrities, with no need for additional derivation. This work elucidates a connection between the Z-based, rhombic, and hybrid tensegrities in terms of form-finding, and may motivate the exploration of potential unification between more types of structures. [Display omitted]