A grinding machine for finishing turned surfaces of a rotor disc for a gas turbine engine, including a retaining mechanism for retaining the rotor disc and rotatable about a rotational axis corresponding to a central axis of the rotor disc, a spindle engaged to a grinding wheel and rotatable about a rotational axis corresponding to a central axis of the grinding wheel, the grinding wheel having an outer super abrasive surface, a translating mechanism engaged to at least one of the retaining mechanism and the spindle and actuable to provide a relative translational motion between the retaining mechanism and the spindle along three perpendicular axes, and a pivoting mechanism engaged to one of the retaining mechanism and the spindle and actuable to provide a pivoting motion of the rotational axis of one of the retaining mechanism and the spindle around a pivot axis perpendicular thereto.