Machining apparatus for machining a workpiece, in which a demecanizacion unit (2) is held a machining tool (2a) rotatably, and demecanizacion tool (2a) can be aligned with its axis rotation (X) with respect to the surface of the piece of amecanizar work, so that the rotation axis (X) coincides with the perpendicular geometry (N) in the demecanizacion point on the surface of the workpiece, comprising - a pressure plate (6) mounted on a bearing device (4) freely movably in the demecanizacion installation, wherein both the bearing device (4) as the pressure plate (6) have, respectively, hole (4a; 6a) for the tool (2a), and - a measuring (8) for detecting a deviation between the rotational axis (X) and perpendicular lasuperficie (N) machining point through the alignment of the pressure plate (6) on the surface of Lapieza working in the region of the machining, characterized in that - the bearing (4) has a bearing body (40b) having the superficialesferica least one area and a bearing (40a) surrounding the bearing body (40b) in positive engagement in the spherical zonassuperficiales.