A roundness and/or dimension measuring device for in-process measurement of crank pins during a machining operation on a grinding machine having a base body, and a measuring head, which is connected to the base body via a rod assembly and which is movable between a neutral position and a measuring position. The measuring head has a measuring probe for contacting the crank pin, and the rod assembly is designed and configured in such a way that the measuring head in the measuring position follows orbital rotations of the crank pin. At least one oscillation damping element is operatively associated with the measuring head for holding it in engagement with the crank pin during the orbital rotation.