A sliding cable element of multibody dynamics with application to nonlinear dynamic deployment analysis of clustered tensegrity

This paper presents a sliding cable element for multibody system analysis. Unlike the existing literature on sliding cables developed using the finite element approach, the novelty of this approach is the use of the configuration of the attached rigid bodies as the generalized coordinates, rather than the traditional nodal displacements. The generalized force vector, and its related tangent stiffness and damping matrix, of the sliding cable and that of the classical cable element are analytically derived. It can also be found that the proposed sliding cable element can degenerate to the existing element formulated using the finite element approach. This allows us to use less generalized coordinates to address a system that contains few rigid or flexible body but with many pulleys. Then, this sliding cable element is employed to investigate the deployment of clustered tensegrity. Both quasi-static and dynamic analyses are carried out. Two representative examples show the effectiveness of the proposed element. The dynamic results also show that the motion characteristics of the system differ from the quasi-static solutions as the actuation speed increases. To achieve a fast actuation speed for deploying such systems, quasi-static analysis seems inadequate, and the dynamic effect must be taken into account. Under this background, the proposed element, coupled with the multibody dynamic methodology used in this work, does provide a powerful tool for analyzing the mechanical properties of such systems.