Linearized vibration analysis of tensegrity structures in rigid-body space

This study presents a unified linearized vibration analysis framework for tensegrity structures that explicitly incorporates both constraint-induced geometric stiffness and gravity-induced stiffness. This approach addresses small, undamped free vibrations around a prestressed equilibrium, models compressive members as rigid bodies, and describes the system dynamics within a screw-theoretic formulation. By considering the effect of geometric constraints on the number of independent rigid-body coordinates, the tensegrity structures were classified into unconstrained and constrained cases for analysis. For unconstrained systems, the mass and stiffness matrices are derived analytically from the Jacobian and Hessian equations of cable-rigid-body interactions, whereas gravity-induced stiffness arises naturally from the screw-theoretic representation of gravitational wrenches. For constrained systems, the constraint Jacobian projects the linearized dynamics into an independent coordinate space, in which geometric constraints additionally contribute a reduced-space geometric stiffness term. The effectiveness and generality of the framework are demonstrated through three examples. Two numerical cases verified its applicability to general tensegrity structures—including generalized compressive members, continuous cables, and class k configurations. An experimental study on a biomimetic tensegrity leg with revolute joints, inextensible cables, and closed-chain constraints further validates the formulation. Across the 0.1–4 Hz frequency range, discrepancies between the identified and computed modal frequencies remain within 0.1–4.9%, confirming the accuracy and robustness of the proposed method. Collectively, the numerical and experimental results show that constraints and gravity play a critical role in shaping the vibration characteristics of tensegrity structures.