Stability Conditions and Stiffness Variability of General Tensegrity Systems With Kinematic Joints

Tensegrity systems represent promising candidate mechanisms with in situ stiffness variability through changing the cables’ prestress levels. However, prestress-based stiffness behaviors of tensegrity systems with arbitrary kinematic joints have not been analyzed systematically. This paper adopts the natural absolute coordinates for static modeling of tensegrity systems consisting of rigid members and tension elements. Then, a generic stiffness analysis method is developed to formulate the reduced-basis tangent stiffness matrix, which is found to include three parts: positive semi-definite material and geometric stiffness matrices, and an indefinite constraint stiffness matrix. Based on these findings, a systematic stability-checking procedure is derived to determine prestress and super stability, which are qualitative indicators of the softening and stiffening effects in different tensegrity systems. Then, we proceed to quantify the range of prestress-based stiffness variability by formulating semi-definite programming problems that numerically pinpoint the maximum and zero stiffness points. Furthermore, this paper reveals the composable nature of multiple self-stress states, enabling the composability of stiffness properties in mechanism designs. Several numerical examples verify the efficacy and versatility of the proposed method and demonstrate interesting stiffness behaviors of tensegrity systems with kinematic joints.