Dynamics for tensegrity structures based on screw theory

This paper proposes a screw theory-based dynamics formulation that employs the motion of rigid bodies(compressive members) within tensegrity structures as generalized coordinates. The formulation can be applied to classic bar-cable tensegrity, class k tensegrity, general tensegrity and clustered tensegrity. By leveraging screw theory, the formulation describes structural dynamics within a unified global coordinate system, significantly simplifying kinematic representation and constraint handling. A dependency matrix is introduced to characterize the relationships between nodes and rigid bodies, forming the foundation for Jacobian matrices that map rigid bodies to nodes and cables while facilitating wrench analysis. To address potential node coincidences, a constraint matrix is employed to establish constraint equations, whose temporal differentiation yields a constrained dynamics formulation specifically for class k tensegrity. Representative structural examples illustrate the formulation’s applicability and effectiveness across various tensegrity structures.