A system for grinding solid workpieces includes a grinding wheel, a bearing for rotatable mounting of the grinding wheel about an axis of rotation, and a grinding wheel drive for rotating the grinding wheel. The system allows the production of freely-definable surfaces on the face of the rigid workpiece that comes into contact with the grinding wheel. The bearing is fastened to a pivotable and displaceable bearing carrier. The bearing plane is pivotable in any desired direction with respect to an initial plane and is displaceable in a direction perpendicular to the initial plane. Actuators are coupled to the bearing carrier to pivot and displace the bearing carrier. A digital control unit controls and synchronizes the actuators such that the surface of the grinding wheel creates a freely-definable face about a positionally fixed reference point which is at a radial distance from the center point of the grinding wheel.