Abstract: The invention relates to a grinding machine in which a workpiece such as a multi-stage compressor or turbine rotor to have grinding operations carried out at different locations along the workpiece at different radii and at different angles is mounted between sensors on a slideway to present the locations on the workpiece to be ground to a motor driven grinding wheel mounted in a grinding head. The grinding head is mounted on a slideway to traverse the grinding wheel towards and away from the periphery of the workpiece at a location where the grinding operation is to be carried out and the grinding wheel is mounted on the slide for rotational adjustment about an axis extending tangentially to the periphery of the grinding wheel at a location where the grinding wheel acts on the workpiece for adjustment of the angle of cut of the grinding wheel.