Abstract: A method for positioning and rotating a workpiece shaped like a body of rotation and having a plane face, comprising the following steps: positioning the workpiece on an axial and a radial supports; transmitting the torque from a rotary driving member to the workpiece due to the forces of friction developed therebetween; and feeding ultrasonic mechanical vibrations to at least one of the supports, said vibrations being fed to any one of the supports in the direction substantially parallel to or at an angle not exceeding 10 degrees with the line of contact between the workpiece and said support. An arrangement implementing this method comprises separate axial and radial supports, the radial support being constituted by two parts spaced apart through a certain angle and having the profile, in the working portion, congruent to the cylindrical profile of the workpiece surface.

Abstract: The device has a base mounting a support which constantly contacts the surface of an object being measured, the object having a nominally circular cross-section. The support is a plurality of essentially self-adjusting balance beams arranged in steps or in a staggered order. The swing axles of the balance beams of a first step are secured to the base, while the swing axles of the balance beams of a subsequent step are secured to the ends of the balance beams of a preceding step. The balance beams of a last-in-succession step contact the profile of the cross-section of the object being measured. The central angles at which the balance beams are mounted are chosen on the basis of a condition of maximal stabilization of the position of the center of the profile of the cross-section of the object being measured relative to the base in the direction of the disposition of a sensing element of a displacement transducer secured to the base.