Equilibrium and stiffness study of clustered tensegrity structures with the consideration of pulley sizes

This paper presents the equilibrium and stiffness study of planar clustered tensegrity structures (CTS) considering pulley sizes. We first derive the geometric relationship between clustered strings and pulleys, where the nodal vector is chosen as the generalized coordinate. Then, the equilibrium equations of the planar clustered tensegrity structure with pulleys based on the Lagrangian method are given. Since the stiffness of a structure is usually weakened when using clustering strings, we formulate the tangent stiffness matrix equations for analysis. It is also shown that as pulley sizes go to zero, the governing equations of the planar clustered tensegrity system with pulleys yield to the classical clustered tensegrity structure without pulleys, which is consistent with the existing literature. Three examples are demonstrated to validate the given theory. The proposed method allows one to conduct equilibrium, stiffness, and robustness studies of planar clustered tensegrity structures with pulleys. Nevertheless, the approach developed in this paper is not limited to tensegrity structures. It can also be applied to a wide range of applications with pulley-rope systems, such as drilling rigs, ocean platform anchors, and cargo cranes.