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This paper presents the equilibrium and stiffness study of clusteredtensegrity structures (CTS) considering pulley sizes. We first derive thegeometric relationship between clustered strings and pulleys, where the nodalvector is chosen as the generalized coordinate. Then, the equilibrium equationsof the clustered tensegrity structure with pulleys based on the Lagrangianmethod are given. Since the stiffness of a structure is usually weakened whenusing clustering strings, we formulate the tangent stiffness matrix equationsfor analysis. It is also shown that as pulley sizes go to zero, the governingequations of the clustered tensegrity system with pulleys yield to theclassical clustered tensegrity structure without pulleys, which is consistentwith the existing literature. Three examples are demonstrated to validate thegiven theory. The proposed method allows one to conduct equilibrium, stiffness,and robustness studies of cluster tensegrity structures with pulleys.Nevertheless, the approach developed in this paper is not limited to thetensegrity structures. It can also be applied to a wide range of applicationswith pulley-rope systems, such as drilling rigs, ocean platform anchors, andcargo cranes.

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