Machining device for machining workpieces, having at least one first device part and at least one second device part which is arranged separately therefrom, wherein the machining device has in particular only five controllable machining axes, namely four rotational axes (A1, A2, D1, D2) and one translational axis, wherein: - the first device part has a workpiece receptacle and the second device part has a tool receptacle, - the first device part and the second device part each have a first rotational axis (A1; A2) about which the respective device part (10, 20) is able to rotate, - the tool receptacle and the workpiece receptacle are rotatable relative to the respective device part (10; 20) about a second rotational axis (D1; D2), and - the tool receptacle is formed displaceable relative to the second device part, wherein the first and the second rotational axis (A1, D1) of the first device part as well as the first and second rotational axis (A2, D2, T) as well as the translational axis of the second device part are each arranged in succession without the interposition of a further machining axis, wherein the first rotational axis of the second device part runs at least with one directional component in a vertical direction defined perpendicular to the installation base of the machining device, characterised in that the first rotational axis of the first device part runs with one directional component in the horizontal direction of the machining device and thus obliquely to the first rotational axis of the second device part. - the first device part has a workpiece receptacle and the second device part has a tool receptacle, - the first device part and the second device part each have a first rotational axis (A1; A2) about which the respective device part (10, 20) is able to rotate, - the tool receptacle and the workpiece receptacle are rotatable relative to the respective device part (10; 20) about a second rotational axis (D1; D2), and - the tool receptacle is formed displaceable relative to the second device part, wherein the first and the second rotational axis (A1, D1) of the first device part as well as the first and second rotational axis (A2, D2, T) as well as the translational axis of the second device part are each arranged in succession without the interposition of a further machining axis, wherein the first rotational axis of the second device part runs at least with one directional component in a vertical direction defined perpendicular to the installation base of the machining device, characterised in that the first rotational axis of the first device part runs with one directional component in the horizontal direction of the machining device and thus obliquely to the first rotational axis of the second device part. wherein the first and the second rotational axis (A1, D1) of the first device part as well as the first and second rotational axis (A2, D2, T) as well as the translational axis of the second device part are each arranged in succession without the interposition of a further machining axis, wherein the first rotational axis of the second device part runs at least with one directional component in a vertical direction defined perpendicular to the installation base of the machining device, characterised in that the first rotational axis of the first device part runs with one directional component in the horizontal direction of the machining device and thus obliquely to the first rotational axis of the second device part.