One edge of an elastic rod is inserted into a friction-less and fitting socket head, whereas the other edge is subjected to a torque, generating a uniform twisting moment. It is theoretically shown and experimentally proved that, although perfectly smooth, the constraint realizes an expulsive axial force on the elastic rod, which amount is independent of the shape of the socket head. The axial force explains why screwdrivers at high torque have the tendency to disengage from screw heads and demonstrates torsional locomotion along a perfectly smooth channel. This new type of locomotion finds direct evidence in the realization of a ‘torsional gun’, capable of transforming torque into propulsive force.