Mechanical stress and conformation of helical elastic rods clamped at both ends were studied upon unwinding. By axial rotation of one end, the winding number was progressively changed from the natural one (n=n_{0}) to complete chirality inversion (n=-n_{0}) while keeping the total elongation fixed and monitoring the applied torque M and tension T. Along the unwinding process, the system crosses three distinct 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 "injected" (nucleated) from one side and travels toward the opposite side where it is eventually "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 which neglects 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. The traveling perversion in helical elastic rods and related topological phenomena are universal, with applications from condensed matter to biological and bioinspired systems, including in particular mechanical engineering and soft robotics.