Crankshaft rod bearings are pre-ground and finish-ground in a first grinding station and the crankshaft main bearings are then pre-ground and finish-ground in a second grinding station. The crankshaft is first mounted centered between the two points of the rotary drive. The chuck has two support members which can be moved in the radial direction and which are then positioned against the main bearing in a self-equalizing manner. In the engaged position, the support members are locked tightly to the chuck by locking pins. A pivoting clamping member is then clamped with the operating end thereof against the main bearing.