The flutes and leaves of a pinion are polished in a pinion polishing tool; it consists of a frame in which the pinion is mounted between centres and free to rotate. The frame is fitted to slide on a base which has a wooden disc pivoted to a block, adjusted so that the edge of the disc is slightly askew to the pinion axis. As the disc is rotated the pinion revolves, cutting a screw thread in the edge of the disc, which is charged with polishing material. During the operation the pinion is made to slide back and forth so that its whole length is polished.