Dynamics of the shell class of tensegrity structures

A tensegrity structure is a special truss structure in a stable equilibrium, with selected members designated for only tension loading, and the members in tension form a continuous network of cables separated by a set of compressive members. This paper develops an explicit analytical model of the nonlinear dynamics of a large class of tensegrity structures, constructed of rigid rods connected by a continuous network of elastic cables. The kinematics are described by positions and velocities of the ends of the rigid rods, hence, the use of angular velocities of each rod is avoided. The model yields an analytical expression for accelerations of all rods, making the model efficient for simulation, since the update and inversion of a nonlinear mass matrix is not required. The model is intended for shape control and design of deployable structures. Indeed, the explicit analytical expressions are provided herein for the study of stable equilibria and controllability, but the control issues are not treated in this paper.