Apparatus comprising a measuring device, a regulating device, an actuating element and a controller, wherein the apparatus is suitable for correcting positional deviations between a tool holder and a workpiece holder of a processing machine, wherein the measuring device comprises a first component group (1.1) and a second component group (1.2), and the first component group (1.1) and the second component group (1.2) are rotatable relative to each other about an axis of rotation, wherein ¬ the first component group (1.1) is arranged in a fixed position with respect to a Cartesian coordinate system with a first directional axis (x), a second directional axis (y) and a third directional axis (z), ¬ the second component group (1.2) can be fixed to a structural element that can be rotated about the axis of rotation, so that the axis of rotation runs parallel to the first directional axis (x) in the Cartesian coordinate system, and by means of the measuring device, a measurement of the relative position between the first component group (1.1) and the second component group (1.2) can be carried out in several dimensions, wherein, by means of the measuring device, - it is possible to generate first signals, which include information about the actual orientation of the axis of rotation relative to the first directional axis (x), and - it is possible to generate second signals, which include information about the actual position of the first component group (1.1) relative to the second component group (1.2) in the first directional axis (x) and/or the second directional axis (y) and/or the third directional axis (z), wherein the measuring device is connected to the regulating device for the transmission of the first signals, and the actuating element can be mounted on the structural element such that the orientation of the axis of rotation relative to the first component group (1.1) can be changed by actuating the actuating element, and the regulating device is configured such that, depending on the information about the actual orientation of the axis of rotation relative to the first directional axis (x), the axis of rotation can be moved into a desired orientation with the aid of the actuating element and, furthermore, the measuring device is connected to the controller for the transmission of the second signals to correct the relative position between the tool holder and the workpiece holder. the measuring device comprises a first component group (1.1) and a second component group (1.2), and the first component group (1.1) and the second component group (1.2) are rotatable relative to each other about an axis of rotation, wherein ¬ the first component group (1.1) is arranged in a fixed position with respect to a Cartesian coordinate system with a first directional axis (x), a second directional axis (y) and a third directional axis (z), ¬ the second component group (1.2) can be fixed to a structural element that can be rotated about the axis of rotation, so that the axis of rotation runs parallel to the first directional axis (x) in the Cartesian coordinate system, and ¬ the first component group (1.1) is arranged in a fixed position with respect to a Cartesian coordinate system with a first directional axis (x), a second directional axis (y) and a third directional axis (z), ¬ the second component group (1.2) can be fixed to a structural element that can be rotated about the axis of rotation, so that the axis of rotation runs parallel to the first directional axis (x) in the Cartesian coordinate system, and by means of the measuring device, a measurement of the relative position between the first component group (1.1) and the second component group (1.2) can be carried out in several dimensions, wherein, by means of the measuring device, - it is possible to generate first signals, which include information about the actual orientation of the axis of rotation relative to the first directional axis (x), and - it is possible to generate second signals, which include information about the actual position of the first component group (1.1) relative to the second component group (1.2) in the first directional axis (x) and/or the second directional axis (y) and/or the third directional axis (z), wherein - it is possible to generate first signals, which include information about the actual orientation of the axis of rotation relative to the first directional axis (x), and - it is possible to generate second signals, which include information about the actual position of the first component group (1.1) relative to the second component group (1.2) in the first directional axis (x) and/or the second directional axis (y) and/or the third directional axis (z), wherein the measuring device is connected to the regulating device for the transmission of the first signals, and the actuating element can be mounted on the structural element such that the orientation of the axis of rotation relative to the first component group (1.1) can be changed by actuating the actuating element, and the regulating device is configured such that, depending on the information about the actual orientation of the axis of rotation relative to the first directional axis (x), the axis of rotation can be moved into a desired orientation with the aid of the actuating element and, furthermore, the measuring device is connected to the controller for the transmission of the second signals to correct the relative position between the tool holder and the workpiece holder.