A machine tool for the machining of rotary parts with groove-shaped profiles, in particular gears, by a generating method, comprising: a machine bed; a Y-slide, which is linearly displaceable along a Y direction relative to the machine bed; a workpiece spindle which is arranged on the Y slide and which is configured to clamp a workpiece thereon and to drive it to rotate about a workpiece axis, the workpiece axis extending transversely, preferably perpendicularly, to the Y direction; and a tool spindle which is configured to clamp a generating machining tool, in particular a gear-shaped generating machining tool, on it and to drive it to rotate about a tool axis; and a controller which is configured to establish a positive coupling between the rotation of the generating machining tool and the rotation of the workpiece, characterized in that the machine tool further comprises: a Z slide which is arranged on the machine bed and is linearly displaceable along a Z direction relative to the machine bed, the Z direction running parallel to a center plane defined by the Y direction and the workpiece axis, and the Z direction extending at an angle of less than 45°, preferably parallel, to the workpiece axis; and an X slide arranged on the Z slide and linearly displaceable along an X direction relative to the Z slide, the X direction being perpendicular to the center plane; and in that the tool spindle is arranged on the X slide and is pivotable relative to the X slide about a first swivel axis. a machine bed; a Y-slide, which is linearly displaceable along a Y direction relative to the machine bed; a workpiece spindle which is arranged on the Y slide and which is configured to clamp a workpiece thereon and to drive it to rotate about a workpiece axis, the workpiece axis extending transversely, preferably perpendicularly, to the Y direction; and a tool spindle which is configured to clamp a generating machining tool, in particular a gear-shaped generating machining tool, on it and to drive it to rotate about a tool axis; and a controller which is configured to establish a positive coupling between the rotation of the generating machining tool and the rotation of the workpiece, characterized in that the machine tool further comprises: a Z slide which is arranged on the machine bed and is linearly displaceable along a Z direction relative to the machine bed, the Z direction running parallel to a center plane defined by the Y direction and the workpiece axis, and the Z direction extending at an angle of less than 45°, preferably parallel, to the workpiece axis; and an X slide arranged on the Z slide and linearly displaceable along an X direction relative to the Z slide, the X direction being perpendicular to the center plane; and in that the tool spindle is arranged on the X slide and is pivotable relative to the X slide about a first swivel axis. a Z slide which is arranged on the machine bed and is linearly displaceable along a Z direction relative to the machine bed, the Z direction running parallel to a center plane defined by the Y direction and the workpiece axis, and the Z direction extending at an angle of less than 45°, preferably parallel, to the workpiece axis; and an X slide arranged on the Z slide and linearly displaceable along an X direction relative to the Z slide, the X direction being perpendicular to the center plane; and in that the tool spindle is arranged on the X slide and is pivotable relative to the X slide about a first swivel axis.