The stiffness of tensegrity structures comes from two sources: the change of force carried by members as their length is changed, and the reorientation of forces as already stressed members are rotated. For any particular tensegrity, both sources of stiffness may have a critical role to play. This paper explores how the stiffness of two example tensegrity structures changes as the level of prestress in a member varies. It is shown that, for high levels of prestress, an originally stable tensegrity can be made to have zero stiffness or indeed be made unstable.

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