normal to the axial direction over a distance 34 d 34 as shown in fig2 b and 2c it is noted from the illustration that as compared with the moving distance 34 c 34 of the first joint 12 in the axial direction the moving distance 34 d 34 of the first joint 12 in the normal direction is extremely small stated otherwise despite a relatively large moving distance 34 c 34 of the turning links 4 and 5 in the axial direction of the tool their moving distance 34 d 34 in the normal direction is extremely small the reduced sliding resistance between the tool and the tool holder unit in accordance with the present invention assures very smooth movement of the tool during operation and as a consequence the tool holder unit in accordance with the present invention is well suited for even and smooth removal of burrs and beads from a workpiece in practice due to uneven dimensions of burrs and or beads on the workpiece some degree of play in the axial direction is needed to facilitate movement of the tool such play in movement is provided by precise position control of the tool in operation in particular of the rotary shaft 9 smooth movement of the tool is a prerequisite for such a precise position control thus the present invention satisfies the demand for precise position control of the tool as is clear from the foregoing equation 1 a small.