Form-finding for tensegrity structures based on the equilibrium equation

Finding form is a critical step in designing tensegrity structures. On the condition that the partial node coordinates, topology, and a bar/cable attribute (the force density of bar is -1 and the force density of cable is 1.) are known, a form-finding method, which is used to find the remaining node coordinates and the force density relation between elements, is proposed in this paper. Firstly, the equilibrium conditions of the tensegrity system are analyzed, and the equilibrium equation is established. Secondly, the variables that must be solved are set and substituted into the equilibrium equation, and the target equation with the variables is built. The Levenberg-Marquardt method with a damping parameter updating strategy is introduced to solve the least squares problem by transforming the equilibrium equation problem into the least squares problem. The form-finding process is performed by solving the least squares formula. Three examples demonstrate the efficiency and accuracy of searching for self-equilibrium configurations.