Abstract: Clamping device for fixing a wheel rim of a vehicle wheel to the shaft of a balancing machine. The clamping device comprises a locating flange which is to be fixed on the shaft of the balancing machine and has a locating face for the wheel rim; a clamping flange which is positioned on a shaft journal and can be clamped against the locating flange; centering bolts which are concentrically arranged on the clamping flange around its circumference and at equal distances from each other and at their ends facing the locating flange each has a centering cone designed to engage fixing and centering holes in the wheel rim of the vehicle wheel; and pivots which axially protrude outwards from the centering cone. A circular groove is arranged in the locating face of the locating flange. The width of the circular groove corresponds to the diameter of the pivots and the mean radius of the circular groove corresponds to the radial distance of the centering bolts to the axis of rotation of the shaft of the balancing machine.