Proposal of a Mechatronic System
for Reading and Analysis of Jaw Movements and Denture Testing
M. Callegari and P. Marzetti
Department of Mechanics, Polytechnic University of Marche
Via Brecce Bianche, 60131 Ancona, Italy
E-mail [email protected]
Abstract
•
In the odontoiatric field very complex rehabilitation
techniques have been recently developed but they have
so far little support from diagnostic systems able to
record or emulate patient’s situation with acceptable
accuracy. In the paper it is proposed the architecture of
a mechatronic system able to support dentists in the
study of movements of the mandible in order to plan
interventions able to solve actual disorders. The design
of a mechatronic articulator, which is based on a
parallel kinematics machine, is specifically addressed.
•
•
1
Introduction
Due to traumatic or pathological events, correct
chewing movements can be significantly altered. Such
perturbations lead to impaired apparatus functionality
and, in most serious cases, to real incompatibilities
between the trajectories tracked during chewing
behaviour and the morphology of dental arches.
Anomalous trajectories, uneven force distribution,
unnatural contacts between upper and lower teeth cause
the degeneracy get growing, a reduced functionality,
pain and impair to the patient. Seriousness of the
induced handicap can be greatly impairing in some
cases.
The problem is usually tackled through a change in
the geometry of the jaws (by affecting the shape of some
teeth or by prosthetic intervention) making them
compliant with tracked trajectories. Alternatively the
trajectories themselves can be changed through surgical
or re-educating therapies. In any case, the final result
must be the recovery of chewing functionality due to an
enhanced compliance between trajectories and
morphology.
The paper proposes the architecture of a complex
mechatronic system, to be used as a diagnostic and
therapeutic instrument for the study of chewing
disorders, aiming at the morpho-functional and
psychological recovery of the patients. Such an
investigation tool, in order to be effective and be
valuable both for medical practise and for research
studies, must yield a complete support to the described
activities, and therefore:
•
2
take care of dynamical and morphological data
acquisition;
provide tools for their study;
supply an environment for the processing of
different solutions (possibly with some knowledge
based decision support tool);
allow the specialist to simulate and assess the outcoming solutions.
State-of-the-art
Despite interesting studies developed on the subject,
actual state-of-the art is rather far away from
expectations of dentists and physicians and integrated
solutions for diagnosis and restoration do not exist yet.
Off-the-shelf reading apparata, Fig. 1, usually record
only mandibular end positions (open mouth, close
mouth) and yield the followed path by an inferential
process; moreover the data are statically measured and
not in actual chewing movements. The present
mechanical articulators, Fig. 2, on the other hand, are
tuned by making reference to hypothetical simple
movements of patient’s jaw in a single direction but
actually, since jaw is linked to cranium only by muscles
and ligaments, real movements will always have
components in different directions with respect to what
has been guessed. Therefore, complexity of registration
and lack of precision in emulating human behaviour lead
to the fact that such instruments are less and less used in
actual dental practice.
(a)
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(b)
Figure 1. Typical pantograph for the registration of jaw
movements (a) and its mounting conditions (b)
Some research instruments are indeed able to store
dynamical data but they lack of necessary precision and,
most of all, they greatly intrude with patient’s
movements, so that used tools may significantly affect
the measure. Moreover, they are too complex to use and
too expensive with respect to their performances.
Finally, movements of the mandible cannot be described
by simple geometric paths because the biological
structures that are involved have an individual elasticity
and a certain freedom of movements: therefore actual
instrumentation, just like conventional mechanical
articulators, is limited in its accuracy and capability of
describing actual mandibular behaviour.
Figure 2. A manual articulator (Artex by Girrbach)
Among the first studies on electronic recording
process it is worth citing the work of Klett [1] for
innovation and methodology, leading to present
industrial realisations like the opto-electronic measuring
device Condylocomp LR3 by Dentron, the Eliteplus
motion analyser and so on; 3D scanning technology also
provides interesting results (like the integrated product
offered by Orthotel and initially developed by Syrinx
Medical Technologies GmbH) but apparently at high
costs. Photogrammetry seems to be an interesting
technology, like shown by the researches of Miyashita et
al. [2]. Edinger, at the University of Hamburg-Harburg
realised ROSY, a mechatronic device for simulation of
some jaw movements and production of restorations [34]. Takanobu et al., on the other hand, performed
interesting studies on jaw kinematics and developed a
whole series of robotic devices (from model WJ-0 up to
model WY-5, using up to 9 motors) emulating human
chewing behaviour [5-7]. It must be noted, moreover,
that some patents are pending on correlated items [8-10].
3
Proposal of an Innovative System
An innovative system, to be able to meet the
requirements of common orthodontic practice, must
improve actual state of the art with reference to the
following points.
• The mandibular movements must be recorded in all
six degrees of freedom without limiting patient’s
mouth mobility at any rate, i.e. the recording system
must not be intrusive at all.
• The model must be fixed to the articulator by means
of purely mechanical devices, not using cements,
plasters or other gluing means.
• The automated articulator must be able to run in a
dual mode: active mode, i.e. motor driven and
repeating the trajectories generated during recording
or passive mode, i.e. driven manually by the
specialist and, for each point in its workspace,
permitting only the movements that are actually
allowed to real mandible, as constrained by actual
kinematic pair with maxillar surfaces.
The proposed system can be broken down into the
following main modules, that will be described more
deeply:
•
Acquisition of kinematics
•
Acquisition of dental arches morphology
•
Functional analysis
•
Mechanical simulation
3.1 Acquisition of kinematics
The kinematics of jaw movements must be acquired
through in vivo measurements on patients affected by
chewing disorders or gnathological handicaps. The
system of acquisition of jaw movements should be based
on optical technology: such technology is not intrusive
(or is only minimally intrusive) and will therefore allow
to record real chewing movements. Tests have already
been performed by the Authors to assess the feasibility
of stereoscopic vision or laser technology: the results
obtained so far are positive since the target precision of
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50 µm has been overcome. The field is anyhow to
explore further, to be sure to use the most up-to-date
technology, with the aim to simplify acquisition and
calibration techniques and to enhance analysis
algorithms.
3.2 Acquisition of dental arches morphology
As a first instance, an off-the-shelf 3-D scanner
should do the work (e.g. the COMET Plus 400 optical
system by Steinbichler Optotechnik already available at
the Università Politecnica delle Marche): such a system,
in fact, allows geometric acquisitions on dental arches
with accuracy even better than the outcoming data from
the acquisition of kinematics. Even if such kind of tools
are commonly available on the market, due to their high
costs, a further study might lead to lower the posed
requirements and simplify both methodology and
instrumentation.
3.3 Functional analysis
A three-dimensional graphics system for the
evaluation and treatment of orthodontic disorders should
be studied and realised. The analyses should be worked
out by extensive use of IT methodologies. The chewing
movements have to be first emulated in a virtual reality
environment; then, geometric shapes and 3D trajectories
must be studied, giving the dentist the opportunity to
change the ones or the others in order to try to fix
possible disfunctions. Also the final physical models
must be simulated in such VR environment. The
mechanical articulator described in the following section
can be used as a haptic interface for the driving of the
VR model.
Such a module shall be as general as to let further
expansions and allow to tailor specific configurations
according to different users' needs; also easiness of use
shall be taken into account, so that it can become open
to general use among odonthoiatric community.
3.4 Mechanical simulation
A pure VR analysis can not be entirely satisfactory
for dentists’ needs, as they are currently used to
manipulate mechanical articulators and they will
probably like to continue using this approach. Therefore,
a mechatronic articulator should be realised for the
evaluation and treatment of orthodontic disorders, thus
providing a tool that is familiar to orthodontic practise.
Such device would allow an experimental assessment of
designed denture or (by means of a modified plaster
cast) should allow the simulation of resulting kinematics
conditions before actual surgery on the patient.
The core of the whole proposed system is therefore
an automated articulator able to replay chewing
movements: such a device would allow an easy
assessment of manufactured dentures or would allow the
dentist to test real operating conditions before surgery
on the patient. Therefore (at least) two operating modes
must be enabled:
•
playback, to show over and over patient's
mandible movements just as they were
recorded during previous phases
•
human-operated movements, to allow at any
pose only the movements that are actually
permitted by the kinematic pairs of the patient's
mandible/maxilla coupling.
As anticipated before, such a device could be also
used as a haptic interface to drive the VR simulations.
From the mechanical point of view, a parallel kinematics
machine or a hybrid machine, with 6 d.o.f., seems the
most promising architecture to be explored, and this is
done in the following paragraphs.
4
Mechanical Architecture
4.1 Mobility analysis
The kinematics of jaw-motion is determined by the
constraints imposed by the geometry of the contacting
surfaces and the temporomandibular joint (TMJ). As a
result, jaw movements are very complex and can be
decomposed into the following three elemental motions:
•
Opening/Closing, that occurs in two phases:
rotation and translation (both movements are
necessary
for
maximum
opening/closing).
Rotation: condyle rotates with respect to disc in
Lower Compartment (takes place in first 11 to 25
mm of opening); translation: disc/condyle slide
forward in mandibular fossa and articular eminence
in Upper Compartment (total excursion approx. 4050 mm).
•
Deviation: spin of ipsilateral condyle around the
vertical axis and translation of contralateral
condyle (excursion approx. 8 mm); rotation of
ipsilateral
condyle
around
the
A/P
(anterior/posterior) axis and depression of
contralateral condyle.
•
Protrusion/Retraction, that are both realised by an
upper compartment translation. Protrusion:
articular discs and condyles slide downward and
forward (approx. 6-9 mm). Retraction: articular
discs and condyles slide upward and backward
(approx. 3 mm).
Figure 3. Condyles positions during jaw opening
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It is evident that, even if the jaw is actually
characterised by 3 dof’s, the resulting motion is spatial
and very complex and new mechanical models such as
the helical axis and the wrench axis are used to describe
and characterize in a overall and compact way the
kinematics of the mandible and the forces and torques
acting on it [11-12].
Therefore only 5 or even 6 dof’s mechanisms can
properly emulate jaw kinematics and in particular it is
reckoned that PKM’s are the most suitable architectures,
due to the following requirements of the task: high
stiffness (due to the comparatively great chewing
forces); high accuracy (the human mouth is able to
distinguish an hair being bit), good back-drivability (to
use the device as an haptic interface); on the other hand,
only small working volumes are necessary and also
machines’ dexterity is not a premium.
To simplify articulator’s control, which would turn
out to be rather complicated anyway, it is necessary to
separate functionally the complex 6 dof’s task into its
elemental translational and spherical motions: therefore
it is proposed to use a TPM (Translating Parallel
Mechanism) in series with a spherical wrist. The latter
could be a conventional 2 o 3 axes serial wrist, like the
usual RPR (roll-pitch-roll) or PYR (pitch-yaw-roll)
architectures used in industrial applications, or otherwise
a SPM (Spherical Parallel Mechanism) could be used,
e.g. like the one recently proposed in [13]. In the
following paragraphs only the design of the translating
platform will be addressed: it is only anticipated that the
recalled considerations on TMJ mobility lead to the
safety requirements of a useful workspace inscribing a
cube of about 50 mm side.
4.2 Robot kinematics
The TPM is based on the 3-PUU architecture,
whose geometry is shown in Fig. 4. The translating
platform is connected to the base by means of 3 identical
legs: the lower link AiBi, of height h, is actuated by
controlling the linear displacements si of the sliders
along the frame guideways; it is connected to the upper
link BiCi, of length l, by means of a universal joint;
another cardan joint, parallel to previous one, connects
the limb to the travelling platform, whose radius is
indicated with r.
A complete kinematic study of this mechanism is
developed in a companion paper [14], which also
presents the solution of both direct and inverse problems
for the position and velocity analysis. It is there shown
how the workspace shape and position of singularity loci
makes this kind of architecture suitable for the present
application. The actual geometry of the articulator will
be defined after an optimisation process, as described in
following paragraph.
(a)
(b)
Figure 4. Multibody model of the 3-PUU machine (a)
and detailed view of one leg (b)
4.3 Optimisation
The importance of accuracy and stiffness for the
present application suggested that the optimisation
process should be driven by the minimisation of the
condition number:
c 2 (J ) =
λ max (J T J )
λ min (J T J )
(1)
where λmax and λmin are respectively the maximum and
minimum eigenvalue of the matrix JTJ, J being the
Jacobian matrix mapping workspace velocities into
joints velocities:
s& = J p&
(2)
2
Of course the condition number c is a local figure
that varies with the point inside the workspace, so a
global figure must be used instead, e.g. the global
dexterity index:
dw
η=
∫W c 2 (J )
W
(3)
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that simply represents the mean value of the inverse of
local condition numbers inside the volume W of the
workspace (therefore it varies between 0 and 1 and has
to be maximised instead).
The optimisation process is furthermore constrained
by the condition that a cube with a side of 50 mm can be
inscribed inside the workspace and that it includes no
singular points.
4.4 Manipulability
It is well known that the condition number c2 also
represents that ratio between the maximum and
minimum value of mechanism stiffness in a fixed
position, therefore it is a local index of the anisotropy of
dexterity and stiffness of the machine itself. Such
concepts can be well represented graphically by the
resistance ellipsoids, mapping the unit thrusts f at the
joints satisfying:
f T ⋅f = 1
(4)
into workspace forces F, therefore constrained by:
F T J −1 J − T F = 1
Figure 5. Optimisation parameters r, l, h
Due to the particular symmetry of the mechanism,
its geometry is completely defined by the choice of the
value of the 3 parameters h, l and r, see Fig. 5, which are
the same for each leg; on the other hand, a deeper
examination of Jacobian matrix J leads to the conclusion
the platform radius r does not influence the objective
function η, so its value can be chosen by pure practical
considerations (e.g. the dimension of the mechanical
interface with the wrist).
Figure 6 shows the plot of the dexterity index, as a
function of length l, for different values of the height h:
the optimised mechanism will be characterised by the
following geometrical values:
•
r = 150 mm
•
l = 352 mm
•
h=0
(5)
Figure 7 shows such ellipsoids in different points of
the workspace for the optimised mechanism: at the
isotropic point, see Fig. 7a, the ellipsoid becomes a
sphere, while it is flattened or stretched along the
vertical directions in the points lying under or above the
isotropic point, Fig. 7b-c.
(a)
(b)
Figure 6. Plot of dexterity index η
(c)
Figure 7. Resistance ellipsoids on the z axis, at different
heights; isotropic point: (0, 0, 200) (a),
below it: (0, 0, 75) (b) and above it: (0 ,0, 250) (c)
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Such tools are useful for the analysis of the static
properties of the machine and for its design: in this case,
for instance, a proper limitation of sliders’ strokes still
allows the machine the needed workspace jointly with
good stiffness properties (e.g. a force in any point of the
limited workspace yields a maximum thrust in the base
slideways equal to 1.24 times the Cartesian force).
To assess the outcoming stiffness of the machine, it
is useful to assume the legs perfectly rigid (that is a
sensible hypothesis, since in this case the limbs are only
stressed by normal forces) and only consider as possible
sources of compliance the mechanical transmissions, the
actuators and the control loops. Therefore the thrust at ith
actuator fi can be related to its displacement ∆si by:
f i = k ⋅ ∆s i
(b)
(6)
It is noted that, due to the symmetry of the architecture,
a single value k for all legs’ stiffness is assumed. Since
local displacements ∆s are mapped into Cartesian
displacements ∆p by the Jacobian J:
∆s = J ⋅ ∆p
(7)
the global stiffness of the mechanism is expressed by:
F = K ⋅ ∆p
(8)
with the stiffness matrix K defined as:
K = kJ T J
(9)
If the general stiffness χ is defined as the ratio
between external force F at the end-effector and the
resulting displacement ∆p:
χ=
FT F
∆pT ∆p
(c)
(10)
it can be shown that:
kµ min ≤ χ ≤ kµ max
(11)
where µmin and µmax are the minimum and maximum
eigenvalues of the matrix JTJ. Figures 8 shows, as an
example, the values of such eigenvalues on the
horizontal plane passing through the isotropic point.
(d)
Figure 8. Plot of stiffness maps on a horizontal plane
passing through the isotropic point. Minimum stiffness
µmin plot on the entire area (a) and close-up view of
central section (b). Maximum stiffness µmax plot on the
entire area (c) and close-up view of central section (d).
(a)
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5
Conclusions
The complex system that has been proposed in the
paper aims at the realisation of an innovative instrument
that, by using advanced mechatronic technology, can
support dentists in the study of movements of the jaw in
order to plan interventions able to solve actual disorders:
it basically consists of a technology transfer from some
engineering fields (bioengineering, automation, virtual
environments, mechanics) to the medical/dental field.
In fact, it is Authors’ opinion that the implied
technologies are basically already mature in application
fields different from what is here proposed (parallel
kinematics machines, optical systems for complex
movements tracking, 3D scanning, virtual environments,
hybrid position/force control, etc.). It is believed that a
system with such potentialities could be a great support
for medical practise (dental studies, clinics, technicians,
etc.) but also useful for teaching and research goals.
[6]
[7]
[8]
[9]
[10]
Acknowledgment
[11]
The research has been partially supported the Italian
Ministry of Research and Education (MIUR) within the
MiniPAR Project.
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