Energy harnessing in the snap-through motion of a flexural-tensegrity flagellum

Flexural tensegrity is a structural concept according to which the flexural integrity of a chain of segments in unilateral contact is granted by one prestressing tendon (cable), whose elongation is varied by the relative segmental rotations as a function of the shape of the contact profiles. The elastic strain energy of the tendon, which can be tuned by springs added in series, dictates the constitutive response in bending of the flexural-tensegrity assembly. Here, we show that increasing the internal mobility of the tendon inside hollow segments allows for multi-stable equilibrium configurations. In particular, appropriately designed segmental cavities can induce a complex multi-articulated snap-through motion of long chains of segments, consequent to the harnessing of the elastic energy associated with the relative rotation of only one pair of segments. The motion can be reversed by changing the sign of the relative rotation. The dynamical problem is theoretically solved and results are compared with experiments on 3D printed prototypes for a cantilever configuration, which behaves like a tail that flagellates in response to the cyclic rotation of the pair of end segments. This concept design can find applications in collapsible-deployable micro-and macro-structures, robotics, metamaterials with memory.