Deployment of tensegrities subjected to load-carrying stiffness constraints

Abstract

The structural stiffness of a tensegrity is dominated not only by the material stiffness, but also by its internal forces. The deployment of tensegrities with member length actuation is investigated with an emphasis on the variation in the structural load-carrying stiffness. The relationship between the driving elongation of members and the structural displacement is established. The analytical incremental expressions for the elastic stiffness matrix and the geometrical stiffness matrix with respect to the driving elongation of members are given. The variation in the load-induced elastic deformation can thus be evaluated for a tensegrity being deployed. A basic equation that satisfies both the equilibrium condition and the load-carrying stiffness constraints is established and used to trace the equilibrium configurations on the deployment path step by step. The solutions for the driving elongation of members are discussed for the objectives of producing the shortest actuation distance and reducing the driving energy, respectively. A numerical strategy is suggested to correct the errors caused by the linear assumptions that are introduced in the derivation of the basic equation. The proposed method is employed to analyse the deployment of an illustrative cantilever tensegrity subjected to load-carrying stiffness constraint, and the results verify its validity. When the objective of reducing the driving energy is adopted, the cantilever tensegrity exhibits an adaptive deformation capability to maintain the constant load-induced deflection at its end joint throughout the deployment process.