Abstract: The device has a base mounting a support which constantly contacts a normal section profile of a part, being measured, the part having the shape of a body of revolution. The support is essentially a system of self-adjusting balance beams arranged in steps. The axles of oscillation of the beams of a first step are secured to the base, while the axles of oscillation in subsequent steps are secured to the respective ends of beams of a preceding step. The beams of a last step contact the profile being measured. The central angles under which the balance beams are mounted are chosen on the basis of the condition of maximal stabilization of the position of the centre of the profile of the part relative to the base in the direction of disposition of a sensing element of a linear-movement dial indicator secured to the base.