Abstract: Two superposed and rigidly associated cradles are brought into position opposite a magazine for unmachined workpieces. One of the cradles is loaded by extracting an unmachined workpiece from the magazine. The cradles are moved towards the work axis, the unloading cradle is brought into position beneath the finished workpiece which drops into the cradle under the action of gravity. The two cradles are displaced so as to bring the unmachined workpiece into position along the work axis on which it is clamped between centers, and the two cradles are then moved away from the work axis.