WHITEPAPER – HEXAPODS HELP MEASURE STRESS IN A MODEL
Birgit Bauer

Precise Positioning with Six Degrees
of Freedom in Measurement Setups
Hexapods Help Measure Stress in a Model

Physik Instrumente (PI) GmbH & Co. KG_Auf der Roemerstrasse 1_76228 Karlsruhe, Germany
Tel. +49 721 4846-0, Fax +49 721 4846-1019 Email info@pi.ws, www.pi.ws

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WHITEPAPER – HEXAPODS HELP MEASURE STRESS IN A MODEL
Birgit Bauer

Today many new and further developments would not be

Depending on the requirements of the application, they

possible in the absence of computer-aided simulation

are driven by high-precision drive screws and precisely

processes. This is one of the reasons why the finite

controllable DC motors or directly by linear motors, e. g.

element method has become a standard tool in solid-

based on piezo actuators, instead of using hydraulicstate simulation. It can be used to calculate solutions todrives.

problems from a wide range of physical disciplines. Not
only

automobile

manufacture,tool

makingandmechanical engineering, but also medical technology
and the manufacturers of musical instruments canbenefit from the results thus obtained. However, despite
their simulation of reality, they can only provide
calculated and thus fictitious values. This is why inparticular for biomechanical and biomedical problems
also hardware models are readily used for simulation.

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 islow, enabling better dynamic performance, which is thesame for all motion axes. Moreover, cable managementis no longer an issue, because cables are not moved,
and, last but not least, the system features a much morecompact design. Nowadays a wide range of applications
benefit from these advantages. These applications range

Hexapods, which provide high-precision positioning withfrom metrology and mechanical engineering to medical

six degrees of freedom, offer interesting options fortechnology and research. For the latter, dentistrymeasurement setups used to test how well the models

provides a recent example:

reproduce reality. Hexapods have a parallel kinematic
structure, i. e. six drives act together on a single moving
platform (Fig. 1).

Adaptation of Orthodontic
Apparatuses
In orthodontics, the behavior of the tooth elasticallyembedded in the bone must be investigated, forexample, 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 ortest person. Moreover, the anatomic conditions in theoral cavity are rather unsuitable for investigations andtests that allow verifiable statements regarding the active
force system in tooth motions.

Fig. 1 Hexapods are parallel-kinematic systems (a).
Their design is much more compact than that of seriallystacked multi-axis systems (b), and their moving mass ismuch lower (Image: PI)

Nevertheless, the question that always needs to beDepending on their design, Hexapods can position loads

practice they have only had limited success, because,from a few kg to several tons with high precision in any

due to the complex generation of suitable FE models,spatial orientation in three linear and three rotationalthe values calculated by computer are unfortunatelyaxes. The best-known application of six-axis parallel-always fictitious. Thus, for example, the calculation of thekinematicsystems

areprobablysimulators.

biomechanical behavior of the connective tissue of theHexapods,

suitableforapplications

metrology,

periodontal ligament (PDL) has not yet provided a clear

flightinindustry or research, are however much more accurate.

answered is which forces and torques occur and inwhich magnitude. This is where simulations using thefinite element method can provide answers. However, insolution.

Physik Instrumente (PI) GmbH & Co. KG_Auf der Roemerstrasse 1_76228 Karlsruhe, Germany
Tel. +49 721 4846-0, Fax +49 721 4846-1019 Email info@pi.ws, www.pi.ws

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WHITEPAPER – HEXAPODS HELP MEASURE STRESS IN A MODEL
Birgit Bauer

Realistic Simulations Using a Model
This is why scientists from the University of Ulm haveused a different approach and developed a new solution,
designed to answer the question how the tooth

For simulation, the Hexapod was combined with a force
sensor mounted on a rigid rotary table. The phantom
tooth (Fig. 3), essentially an orthodontic bracket like thaton a human tooth, is mounted directly at the sensor.

embedded elastically in the jawbone behaves understress.

The

resultisanumericallycontrolledexperimental setup that allows measurements of theclinically relevant forces acting on the tooth during theorthodontic tooth motion. In this way, FE models can becheckedandmodifiedon

thebasisofrealmeasurements.
The biomechanical structure of the simulation system isbased on a parallel-kinematic Hexapod (Fig. 2) from theextensive product range of PI (Physik Instrumente).

Fig. 3 The force sensor is mounted on the top platform ofthe Hexapod. It simulates a real tooth and registers theforces and torques acting there. The platform iscontrolled by an especially developed algorithm thatsimulates the elastic behavior of the periodontal ligament(Image: University of Ulm)
The standardized elastic behavior of the periodontal
ligament is simulated by means of a program especiallydeveloped for this purpose. The forces and torques
generated by the orthodontic apparatus to be studied act
Fig. 2 The biomechanical structure of the simulation
system is based on a parallel-kinematic Hexapod ofseries H-850 (Image: PI)
At a diameter of 348 mm and a height of 328 mm, theHexapod has a very compact design. At a repeatabilityof±1 µm(Zaxis)

and±2 µm (X and Y axes) and thanks to the high stiffness ofthe overall system, this system turns out to be the idealon the phantom tooth via the orthodontic bracket.
The Hexapod moves the test specimen in small steps, inorder to measure the different stresses, depending on
the tooth position. The required commanding of theHexapod system is very easy. The digital Hexapod
controller allows the user to set a pivot point as thecenter of rotation anywhere inside or outside theHexapod work space. This freely definable pivot point issolution for simulating the small motions of a tooth in themaintained, independently of the motion.

jawbone. In addition to that, its pivot point inside and

The user specifies all motion commands in Cartesian

outside the tooth root can be freely defined, a necessary

coordinates, whereas all transformations to the individual

prerequisite for biomechanical simulation.

drives are performed by the controller.

Physik Instrumente (PI) GmbH & Co. KG_Auf der Roemerstrasse 1_76228 Karlsruhe, Germany
Tel. +49 721 4846-0, Fax +49 721 4846-1019 Email info@pi.ws, www.pi.ws

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WHITEPAPER – HEXAPODS HELP MEASURE STRESS IN A MODEL
Birgit Bauer

Thanks to the high positioning accuracy, the force

For optimum measurement of both plane as well as

applied to the specimen can be exactly assigned to aspherical and aspherical test specimens, the positioning

position, allowing the stress points at the tooth to beof the interferometer requires five degrees of freedom:accurately determined (Fig. 4). The high stiffness of theThe interferometer must travel in the direction of the x, y

Hexapod ensures a real simulation of the tooth motion.

and z axes.
For orientation perpendicular to the test axis, additionalrotation around the x and y axes and, in the case of
cylindrical lenses, also around the z axis is required. The
Hexapod that is in charge of positioning tasks ismounted on 20-mm thick aluminum plate.
The interferometer located inside the Hexapod does notinterfere with its motion. The CCD camera takes thepicture. It is digitized, saved in the computer andevaluated. A control program written in MatLab sends

Fig. 4 The tooth reconstructed from radiological data
is embedded in the red-colored periodontal ligament(shown without the bone). The loads act on the points
shown in the middle portion of the tooth crown as yellow
spheres (image: University of Ulm)

suitable control commands to the Hexapod.

The results obtained with the simulation model thus
contribute to a better evaluation of orthodontic processes
in the oral cavity and a more effective design ofcorrective measures. Similar results can also be
achieved in other areas, for example in dental and hip
implants or the like, using suitable test setups. Thanks to
the versatility and large number of variants of parallelkinematic Hexapods, industrial applications are also
possible.

Ultraprecise Measurement System
for Optical Surfaces
Mold inserts used for manufacturing optical lenses placeextreme demands on the accuracy of the test methods.
Interferometric measuring equipment can now be used
to automate these requirements and integrate them
directly

intoproduction.

Here,too,high-precision

Hexapods have found a typical area of application:

Fig. 5 Ultraprecise measurement system for opticalsurfaces In this application, too, Hexapods are themethod of choice (Image: PI / Fraunhofer Institute for
Production Technology IPT)

Authors
Birgit Bauer, Business Development Manager HealthCare at PI (Physik Instrumente) GmbH & Co. KG
Martin Geiger, Research Assistant at the University
Hospital of Ulm, Hospital for Orthodontics,
Ellen-Christine Reiff, M.A., Editorial Office Stutensee

Physik Instrumente (PI) GmbH & Co. KG_Auf der Roemerstrasse 1_76228 Karlsruhe, Germany
Tel. +49 721 4846-0, Fax +49 721 4846-1019 Email info@pi.ws, www.pi.ws

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WHITEPAPER – HEXAPODS HELP MEASURE STRESS IN A MODEL
Birgit Bauer

About PI (Physik Instrumente)
In the past four decades, PI (Physik Instrumente) with
headquarters in Karlsruhe, Germany has become theleading manufacturer of nanopositioning systems withaccuracies in the nanometer range. With four company
sites in Germany and ten sales and service offices
abroad, the privately managed company operates
globally. Over 700 highly qualified employees around theworld enable the PI Group to meet almost any
requirementin

positioningtechnology.

thefieldAllofinnovative

key

precisiontechnologies

aredeveloped in-house. This allows the company to control
every step of the process, from design right down toshipment: precision mechanics and electronics as well
aspositionsensors.

The

requiredpiezoceramicelements are manufactured by our subsidiary PI Ceramicin Lederhose, Germany, one of the global leaders forpiezo actuator and sensor products. PI miCos GmbH in
Eschbach near Freiburg, Germany, is a specialist for
positioning systems for ultrahigh vacuum applications aswell as parallel-kinematic positioning systems with six
degrees of freedom and custom-made designs.

PI headquarters in Karlsruhe, Germany: More than 350
employees work on high-resolution drive systems andpositioning systems

Physik Instrumente (PI) GmbH & Co. KG_Auf der Roemerstrasse 1_76228 Karlsruhe, Germany
Tel. +49 721 4846-0, Fax +49 721 4846-1019 Email info@pi.ws, www.pi.ws

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