Recently, nanomechanical devices composed of a long stationary inner carbon nanotube and a shorter, slowly rotating outer tube have been fabricated. In this paper, we study the possibility of using such devices as nanoscale transducers of motion into electricity. When the outer tube is chiral, we show that such devices act like quantum Archimedes screws, which utilize mechanical energy to pump electrons between reservoirs. We calculate the pumped charge from one end of the inner tube to the other, driven by the rotation of a chiral outer nanotube. We show that the pumped charge can be greater than one electron per 360° rotation, and consequently, such a device operating with a rotational frequency of 10 MHz, for example, would deliver a current of ≈1 pAmp.