Self-equilibrium analysis and minimal mass design of tensegrity prism units

In this paper, a specific analysis strategy for tensegrity prism units with different complexities and different connectivity is provided. Through the nodal coordinate matrix and connectivity matrix, the equilibrium equation of the structure in self-equilibrium is established, and the equilibrium matrix can be obtained. The Singular Value Decomposition (SVD) method can be used to find the self-equilibrium configuration. The expression of the torsional angle between the upper and bottom surfaces of the prismatic tensegrity structure, which includes complexity and connectivity, can be obtained through the SVD form-finding method. According to the torsional angle formula of the stable configuration, the mechanical analysis of the single node is carried out, and the force density relationship between elements is gained. The mass, as one of the standards, can be used to evaluate the light structure. This paper also studied the minimal mass of the self-equilibrium tensegrity structure with the same complexity in different connectivity and got the minimal mass calculation formula. The six-bar tensegrity prism unit, including the topology, the force density relationship, the rest length of the element, and the minimal mass with constraints (cables yield, bars yield or buckle), is investigated in this work, which shows the feasibility of systematic analysis of prismatic structures. This paper provides a theoretical reference for prismatic tensegrity units.