Travelling Perversion as Constant Torque Actuator
Abstract
Mechanical stress and conformation of helical elastic rod clamped at both ends were studied upon unwinding process. By axial rotation of one end, the winding number was progressively changed from the natural one (n = n0) to complete chirality inversion (n = −n0) while keeping the total elongation fixed and monitoring the applied torque M and tension T. Along the unwinding, the system crosses three well distinguished states : natural helix (+), mixed state (+/-) and inverted helix (-). The mixed state involves two helices with opposite chiralities spatially connected by a perversion (helicity inversion). Upon unwinding the perversion is first "injected" (nucleated) from one side, travels towards the opposite side where it finally gets "absorbed" (annihilated), leaving the system in the (-) state. In the mixed state the profile of M (n) is almost flat : the system behaves as a constant torque actuator. The three states are quantitatively well described in the framework of a biphasic model, neglecting the perversion energy and finite size effects. The latter are taken into account in a numerical simulation based on the Kirchhoff theory of elastic rods. It reproduces the clamped rod conformations and the observed profiles M (n) and T (n), including abrupt jumps at nucleation and annihilation of the perversion.
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