HEXAPODS | FEATURE
<< Figure 3: Te force sensor is
mounted on the top platorm of
the Hexapod. It simulates a real tooth and
registers the forces and
torques acting there. Te platorm is
controlled by an especially developed
algorithm that simulates the
elastic behaviour
of the periodontal ligament (image: University of Ulm). >>
Realistic Simulations Using a Model This is why scientists from the University of Ulm have used a different approach and developed a new solution, designed to answer the question of how the tooth embedded elastically in the jawbone behaves under stress. The result is a numerically controlled experimental setup that allows measurements of the clinically relevant forces acting on the tooth during the orthodontic tooth motion. In this way, FE models can be checked and modified on the basis of real measurements.
Their advantages compared with serial, i.e. stacked systems, are that they have much better path accuracy, repeatability and flatness. In addition, the moved mass is low, enabling better dynamic performance, which is the same for all motion axes. Moreover, cable management is no longer an issue, because cables are not moved, and, last but not least, the system features a much more compact design. Nowadays a wide range of applications benefit from these advantages. These applications range from metrology (see text box on the right) and mechanical engineering to medical technology and research.
Adaptation of Orthodontic Apparatuses In orthodontics, the behaviour of the tooth elastically embedded in the bone must be investigated, for example, for corrective measures. To simulate realistic tooth motions using an experimental setup directly on the patient is, however, hardly feasible. Such an ‘in vivo’ experiment would be highly unpleasant for the patient or test person. Moreover, the anatomic conditions in the oral cavity are rather unsuitable for investigations and tests that allow verifiable statements regarding the active force system in tooth motions.
Nevertheless, the question that always needs to be answered is which forces and torques occur and in which magnitude. This is where simulations using the finite element method can provide answers. However, in practice they have only had limited success, because, due to the complex generation of suitable FE models, the values calculated by computer are unfortunately always fictitious. Thus, for example, the calculation of the biomechanical behaviour of the connective tissue of the periodontal ligament (PDL) has not yet provided a clear solution.
The biomechanical structure of the simulation system is based on a parallel-kinematic Hexapod (figure 2) from the extensive product range of PI (Physik Instrumente). At a diameter of 348 mm and a height of 328 mm, the Hexapod has a very compact design. At a repeatability of ±1 µm (Z axis) and ±2 µm (X and Y axes) and thanks to the high stiffness of the overall system, this system turns out to be the ideal solution for simulating the small motions of a tooth in the jawbone. In addition to that, its pivot point inside and outside the tooth root can be freely defined, a necessary prerequisite for biomechanical simulation. The travel ranges of the Hexapod are ±25 mm and ±50 mm in the vertical and horizontal directions at rotating or tilt angles of ±30 degrees (vertical) and ±15 degrees (horizontal). For simulation, the Hexapod was combined with a force sensor mounted on a rigid rotary table. The phantom tooth (figure 3), essentially an orthodontic bracket like that on a human tooth, is mounted directly at the sensor. The standardised elastic behaviour of the periodontal ligament is simulated by means of a program especially developed for this purpose. The forces and torques generated by the orthodontic apparatus to be studied act on the phantom tooth via the orthodontic bracket.
The Hexapod moves the test specimen in small steps, in order to measure the different stresses, depending on the tooth position. The required commanding of the Hexapod system is very easy. The digital Hexapod controller allows the user to set a pivot point as the centre of rotation anywhere inside or outside the Hexapod work space. This freely definable pivot point is maintained, independently of the motion. The user specifies all motion commands in Cartesian coordinates, whereas all transformations to the individual drives are performed by the controller. Thanks to the high positioning accuracy, the force applied to the specimen can be exactly assigned to a position, allowing the stress points at the tooth to be accurately determined (figure 4). The high stiffness of the Hexapod ensures a real simulation of the tooth motion.
<< Figure 4: Te tooth reconstructed from radiological data is embedded in the red-coloured
periodontal ligament (shown without the bone). Te loads act on the points shown in the middle portion of the tooth crown as yellow spheres (image: University of Ulm). >>
36 | commercial micro manufacturing international Vol 7 No.4
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