The stability and stiffness analysis of tensegrities is significant for their applications in robotic areas. Generally, tensegrity structures’ stiffness is divided into a non-negative definite material stiffness and an indefinite geometric stiffness. The stability of tensegrities is closely related to the geometric stiffness caused by the prestress of cables. However, the nodal geometric stiffness derived from nodal static equilibrium equations hides the root of instability for tensegrity structures. This article develops a new derivation of the total stiffness for a general tensegrity structure based on rigid bodies’ static equilibrium equations. And then, it subdivides the geometric stiffness into a non-negative definite stiffness and an indefinite stiffness. The indefinite stiffness is purely rotational stiffness and the only root of instability for tensegrity structures, which has remarkable geometrical significance. By analyzing such indefinite stiffness, a set of sufficient and necessary conditions are derived to guarantee tensegrity structures’ stability. Some numerical examples are presented to verify the effectiveness and versatility of the proposed approach.

张拉整体的稳定性和刚度分析对其在机器人领域的应用具有重要意义。通常，张拉整体结构的刚度分为非负定材料刚度和不定几何刚度。张拉整体的稳定性与拉索预应力引起的几何刚度密切相关。然而，从节点静态平衡方程导出的节点几何刚度隐藏了张拉整体结构不稳定的根源。本文基于刚体的静态平衡方程，对一般张拉整体结构的总刚度进行了新的推导。然后，它将几何刚度细分为非负定刚度和不定刚度。不定刚度纯粹是转动刚度，是张拉整体结构失稳的唯一根源，具有显着的几何意义。通过分析这种不定刚度，推导出一组充分必要条件来保证张拉整体结构的稳定性。给出了一些数值例子来验证所提出方法的有效性和通用性。