Keynote: The Stiffness of Tensegrity Structures

Tensegrity frameworks form remarkable structures: they frequently do not have enough members to satisfy Maxwell's 1864 rule for the rigidity of frameworks, and yet form stable structures. Commonly, tensegrity frameworks are both statically and kinematically indeterminate, and rely on prestress to achieve stiffness.  Here, I will describe the stability of tensegrity structures using the remarkably simple 'stress' matrix, which captures the effect of prestress on the stiffness of pin-jointed structures. 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 will explore 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.