Abstract: An arrangement for chamfering or pointing of cylindrical workpieces having a head or shoulder, in which a rotary table is coaxial with a cutting tool, and has holding units for receiving workpieces and spindles. The holding units have elements with axes parallel to the rotary table axis, and the holding units are mounted in a frame underneath the rotary table. A counter-ring is fixed to the frame and guides the workpieces. An entrainment disk rotates with the table and has holding grooves for shanks of the workpieces. The counter-ring has an upper surface for guiding the heads of the workpieces, whereas the shanks of the workpieces are guided by the holding grooves of the entrainment disk along an inside surface of the counter-ring. The upper surface of the ring is between feed and removal positions for the workpieces, and has at least one plane inclined in the direction of motion of the workpieces when carried by the rotary table for automatic delivery of the workpieces to the cutting tool.