2011 - dental arch3d direct detection system from the patient s mouth and robot for implant...

8/12/2019 2011 - Dental Arch3D Direct Detection System From the Patient s Mouth and Robot for Implant Positioning

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Journal of Mechanics Engineering and Automation 1 (2011) 331-341

Dental Arch3D Direct Detection System from the

Patients Mouth and Robot for Implant Positioning

Paola Nudo1, Michele Perrelli

1, Mario Donnici

1, Guido Danieli

1, Francesco Inchingolo

2, Francesco Giuzio

3and

Massimo Marrelli4

1. Department of Mechanic, Engineering, University of Calabria, Arcavacata Rende 87036, Italy

2. Department of Dentistry, Faculty of Medicine, University of Bari, Bari 70100, Italy

3. Dentists Office, Cosenza 87100, Italy

4. Dentalia S.r.L, Crotone 88900, Italy

Received: September 09, 2011 / Accepted: September 29, 2011 / Published: October 25, 2011.

Abstract: This paper describes a three-dimensional structured light scanning system to generate a virtual model of a dental arch, from

the patients mouth, and the scheme of a 2 + 1 DOF (degree of freedom) parallel/serial Robot for implant positioning, both positioned

on a platform held in a fixed position with respect to the patients head. Presently, dental prosthesization requires quite a long time to be

completed. This process, in fact, involves the detection of the shape of the dental arch, its plaster model generation, scanning of it,

prosthesis preparation and its implant. The procedure is even longer when use of dental implants is required, while early loading of the

implants is considered a positive solution. Current research effort is focused on the development of devices for the direct intra-oral

determination of the shape of dental prostheses and inserts. These devices, however, are able to detect limited portions of the dental

arch, since they must be hand-held by the doctor without external supports, and this may produce relatively large errors due to the sum

of relatively small ones. Furthermore, to place an implant correctly, the doctor can use a new system to guide the implant position, but

this requires sending the information in Sweden to obtain a special mask in return.

Key words: Calibration, stereovision, structured light.

1. IntroductionDuring the last years, three-dimensional scanning

technologies have evolved rapidly. Several digitizing

systems have been proposed which can be divided into

two main categories: contact systems and non-contact

systems [1]. The contact systems digitize a surface by

means of a mechanical digitizer, so that the acquisition

Michele Perrelli, Ph.D. student, research field: electronics

and robotics.Mario Donnici, Ph.D. student, research field: biomedical.Guido Danieli, full professor, research field: applied

mechanics.Francesco Inchingolo, associate professor, research field:

dentistry.

Francesco Giuzio, dentist, research field: oral surgery.Massimo Marrelli, medical director, research field: oral

surgery.Corresponding author:Paola Nudo, Ph.D., research field:

applied mechanics. E-mail: [email protected].

time may be extremely long. The evolution of optical

sensors and optical devices allowed to development of

a new optical non-contact techniques. These methods,

which may dramatically reduce the acquisition time,

are divided in passive and active techniques. Passive

techniques do not require any additional energy source,

while active techniques require an auxiliary light

source. These systems are commonly used in

orthodontics to create Computer-Aided-Design (CAD)

models of the dental arch.

Nowadays, most dentists approach the process of

dental arch shape detection using a classic procedure,

which consists, at first, in the use of an impression

material to detect the shape of the patients dental arch

and, subsequently, in the creation of a dental cast from

the impression by means of dental stone. As a further


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Dental Arch3D Direct Detection System from the Patients Mouth and Robot for Implant Position ing332

step, the dental cast may be digitalized using different

shape acquisition methods to obtain a suitable virtual

model [2].

For many years researches have been trying to

improve this conventional process to minimize the

acquisition time and to optimize the final result, i.e., the

CAD model. The initial studies were concerned with

the use of intraoral probes, operating either by means of

a laser triangulation technique [3], or by a digitalized

projection pattern [4]. The main disadvantages are the

following: (a) the probes mechanical components are

not sterilizable and (b) the probe itself must be replaced

frequently, thus affecting the overall cost of the

procedure. In recent years, many studies were focusedon the development of new devices to reduce the

production costs and to automate the whole scanning

process [5]. Given the limited success of these

procedures, as a result, nowadays, dentists are provided

with specific mechanical or optical digitizers of

different types, which are able to scan the stone dental

arch and produce a virtual model of it.

In particular, some devices use topometric methods

or laser beam/structured light methods [6] to scan a

dental stone and obtain a CAD model of dental arch [7].

To improve the data acquisition process, new optical

devices were developed, as for instance, the Charside

Economical Restoration of Esthetic Ceramics (CEREC)

[8] or the 3MTM

system [9]. The camera is moved

manually in the patients mouth by the dentist. Being

the scanning process sensible to patients movement, in

the case of absence of such movements the

measurement accuracy in depth reaches up to 19 m.

With few exceptions, all these mechanical and opticaldevices have hence a relatively high precision. On the

other hand some devices may be only used to scan the

dental stone; some others, as the intraoral digital device,

are sensitive to small movements of patient that could

compromise the quality of the final result. Currently, as

far as the authors are aware, no device is able to

automate the scanning process and eliminate the

manual scanning. This would dramatically reduce the

errors during the data acquisition process and eliminate

the impression phase and the use of the stone model.

This paper is concerned with the development of a

novel non-contact scanning system, which allows

obtaining the CAD model of the dental arch without the

use of an impression material, and thus directly from

the patients mouth.

This optical system, which uses a structured light

source and an optical sensor to acquire images, is based

both on the coded light technique and the epipolar

geometry principle. This system allows the suppression

of five steps in the classic procedure: (1) the material

application; (2) the material hardening; (3) sending the

impression; (4) casting the model; (5) scanning it.After obtaining the CAD model of the dental arch, a

new system to guide the doctor in the placement of the

fittings in the oral cavity is needed. Presently dental

prosthesization using implants requires long times

between implant positioning and prosthesis fitting,

beside the problem of correctly positioning of the

implant where enough bone stock exists, and with the

correct inclination to support the load of mastication. It

is in fact necessary first to detect the shape of the dental

arch, then generate a plaster model, which is to be

scanned. On the base of this and of a Computet Axial

Tomography (CAT) or an orthopantomography the

doctor decides the optimal position of the implants and

proceeds manually. Only alternative to free hand

positioning, the use of Nobel Guide masks [10]. In this

case first the doctor, navigating through the CAT

virtual representation of the patients mouth,

establishes where to place the implants taking into

account the amount of bone stock available. Then theseinformation are sent to Nobel Guide, which returns the

mask which presents guiding holes where the implants

are to be positioned.

This paper describes also an implant positioning 2 +

1 degree of freedom (DOF) robotic system, which

should be combined with the 3D scanner, to guide the

doctor in the placement of the fittings in the oral cavity,

according to what previously decided from the exam of


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Dental Arch3D Direct Detection System from the Patients Mouth and Robot for Implant Position ing 333

a CAT representation of the patient mouth.

The paper is organized as follows: Section 2

discusses the scanning system; section 3 introduces the

theory of camera and projector calibration; section 4 is

about the calibration results; section 5 introduces the

implant position; section 6 gives conclusions.

2. The Scanning System

The aim of this research is to develop an innovative

optical scanner which, using a particular coded light

technique, allows to obtain the CAD model of the

dental arch directly. The optical section of the scanner,

as shown in Fig. 1, is composed by a mini-projector

with a resolution of 800 600 pixels, twomicro-cameras with a resolution of 352 288 pixels

and a biconvex lens. This part of the scanner is located

on a planar moving system which is actuated by two

step motors via linear sliders.

The step motors are controlled by a microcontroller,

which allows to perform the automatic handling of the

linear sliders and to memorize the teeth positions.

Projector, lens and cameras locations are fixed to each

other, but movable with respect to the denture to be

examined, through a micrometric position control. A

tilting mechanism of the entire optical system is present

and a mirrors angular control will shortly be added as

well, in order to improve the detection ability of this

system.

A six degree-of-freedom (DOF) self-balanced arm,

whose scheme is shown in Fig. 2, supports the whole

system.

As can be noted in the figure, the plate on which the

system rests is suspended to the point in which at leastthe last two rotational axes (5 and 6) meet. The weight

of the entire system is balanced by a counterweight, (11)

in the figure.

Thus, in order to avoid any disturbance to the patient,

the center of mass of whatever is placed on the plate

must coincide with the point of intersection between

the two last axes. But since the slides are present, than

two suitable sliding counterweights are also present,

driven by the motion of the slides, but in opposite

Fig. 1 Optical system.

Fig. 2 Scheme of the self-balanced arm.

direction. This detail is shown in the picture (Fig. 3).

Note also that this arrangement allows rotating the

entire plate by 180 when the upper dental arch is to be

examined.

The projector, lens and cameras system can also be

tilted in order to detect correctly the collar area of the

molars, and this is controlled rotating a small cam (the

blue element in Fig. 4).

The scanning system is kept in fixed position with

respect to the patients head through a suitable mask

resting on the vestibular area, fixed to a U shaped

external structure, secured with straps to a second

external structure pressing the chin (Fig. 5).

The mask provides a support for the miniaturizeddetection system of the teeth shape. This latter can be

moved in a x-yplane within the oral cavity, allowing

the identification of the teeth position in terms of their

coordinates.

There are two phases of the process: during the first

phase the doctor, once positioned the mask in the

patients mouth, drives the system along the teeth to be

scanned, observing them through the cameras, so that

the device records the trajectory imposed by the doctor.

Cameras

Lens

Projector


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Fig. 3 Sliding counterweights.

Fig. 4 Mechanism to tilt laterally the detecting device.

Fig. 5 Photo of the system used to block the patient.

In the second phase the control algorithm give the

signals needed to allow the intra-oral feature to enter

the patients mouth and move according to the

trajectory previously selected by the doctor. To allow

these movements, the microcontroller calculates the

optimal number of steps the motor has to rotate and the

direction of rotation.

During motion, the actual location is monitored by

the sensors and once the selected location is achieved,

its coordinates are memorized in order to be

post-processed by the software during reconstruction.

Finally, Fig. 6 shows the entire dental scanner.

Fig. 6 Dental scanner.

3. Theoretical Analysis of Calibration

Method

In this work a new algorithm to obtain the dental

arch CAD model is developed. The method consists in

the calibration of the optical scanner and in the

subsequent scanning of the dental arch by means of

structured light, whereas a particular calibration

procedure is used to calculate the intrinsic parameters

of the projector.

This technique needs a mini-projector, two

micro-cameras b/n and two planar chessboard with

known size (Figs. 7a-7b). The micro-cameras have to

acquire two image sets to obtain the calibration

parameters. The camera calibration parameters areused for the projector calibration.

Once the camera calibration parameters and

projector calibration parameters are obtained, the

optical scanner with the active triangulation method is

calibrated. The full calibration process is composed by

three steps:

(1) Camera calibration;

(2) Projector calibration;

(3) Scanner calibration.

Second counterweight

First counterweight


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(a) (b)

Fig. 7 Planar chessboard (a) for projector calibration (b)

for camera calibration.

3.1 Camera Calibration

All the micro-cameras are calibrated using the

classic methodology of indirect calibration [11]. The

parameters of the camera are obtained from the

correlation between a set of target points on a

calibration specimen, and the correspondent

coordinates in the image plane [12-13] (Fig. 8).

The calibration process is based on the Direct Linear

Transformation (DLT) method 3D [14-15]. Eq. (1)

describes a CCD camera model.

0v

0u

vyz

fkv

uxz

fku

+

=

+

=

(1)

where (u0, v0)are the principal points coordinates, (u, v)are the image coordinates of the relative points and (ku,

kv) are the pixel reverse effective size in the (u, v)

direction.

An accurate camera model has to consider the radial

distortion of the lens system. A standard model is a

transformation from ideal coordinates, not distorted (u,

v), to real coordinates, distorted (uD, vD).

( ) ( )

( ) ( )

++=

++=

0

2

D10D

0

2

D10D

vrk1vvv

urk1uuu (2)

where

( ) ( )2

v

0

2

u

02

D

vvuur

+

=

vv

uu

fk

fk

=

=

(3)

Eq. (3) shows the focal length in terms of horizontal

and vertical pixels.

Fig. 8 Camera model.

To calibrate the distortion, we consider the distorted

pixel coordinates (uD, vD) in the real image and the

coordinates of the same point (u, v)on the calibration

chessboard. Using Eq. (3), Eq. (2) becomes

( ) ( ) ( )

( ) ( ) ( )

=

+

=

+

vvkvvuu

vv

uukvvuu

uu

D1

2

v

0

2

u

0

0

D1

2

v

0

2

u

0

0

(4)

where the unknown parameters are u0, v0, k1, u, v.

Once known k1, the radial distortion in the acquired

image can be compensated. To calculate the other

intrinsic parameters we use the DLT method. Using

Eqs. (1) and (4), the equation which describes a

standard camera model is obtained.

)zz(c)yy(b)xx(a

)zz(c)yy(b)xx(afvv

)zz(c)yy(b)xx(a

)zz(c)yy(b)xx(afuu

0c30c30c3

0c20c20c2

0

0c30c30c3

0c10c10c1

0

++

++=

++++=

(5)

Here f is an intrinsic parameter; {a1, a2, a3} are the

elements of the Rotation Matrices; (x0, y0, z0) are the

projection centre points; (x, y, z) are the spatial

coordinates.

3.2 Projector Calibration

Also the projector calibration by the DLT method is

defined. The projector is studied as a reverse camera;

note that in Eq. (5) theZcoordinate is set to zero.

)yy(b)xx(a

)yy(b)xx(afvv

)yy(b)xx(a

)yy(b)xx(afuu

0p30p3

0p20p2

0

0p30p3

0p10p1

0

+

+=

+

+=

(6)


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In Eq. (6) (u0, v0, f) are the projector intrinsic

coordinates; (x0, y0) are the projector centre coordinates;

(x, y) are the spatial coordinates; (u, v) are the image

coordinates of the relative points and {a1p,,b1p,..}are

the Rotation Matrices elements. To obtain the intrinsic

and extrinsic parameters shown in Eq. (6) a new

method was used. This method allows to considerer the

projector as an inverse camera, through the use of a

dedicated algorithm that processes the in-plane

coordinates of specific points in a projected calibration

chessboard, acquired by the two micro-cameras. The

two cameras record a set of several images, each

representing a different position of the camera

calibration chessboard. Once acquired the image forthe two cameras, the planar calibration chessboard is

covered with a white paper, and a green and black

chessboard is projected on the white paper. The two

cameras acquire the scene and the algorithm records

this images. During the acquisition phase it is

important not to change the chessboards angulations.

3.3 Scanner Calibration

At this point all the calibration parameters are

processed with an active triangulation system in order

to determine the poses of the two micro-cameras 3D

with respect of the projector pose, in terms of

roto-translational matrix transformation. These

transformation operators allow to describe all points of

interest with respect to a universal coordinate system.

Particularly, the algorithm loads the camera and

projector calibration data. The camera reference

system does not coincide with the projector reference

system, so there is the need to introduce a rigidtransformation which links the two reference systems.

A coordinates change, composed by a rotation (R)

followed by a translation (t), is introduced. If m1c

indicates the plane homogeneous coordinates in the

camera reference system and m1 the same plane

homogeneous coordinates in the world reference, we

can write

1c1cmGm = (7)

where

=

10

tRG

cc

c

=

T

3c

T

2c

T

1c

c

r

rr

R

=

3c

2c

1c

c

t

tt

t

Having assigned the position with respect to the

camera reference system, the same plane position with

respect to the projector reference system is identified.

Also in this case a coordinate change is needed to link

the world reference system with the projector reference

system. The relationship is the same used in Eq. (7),

where m1pare the plane homogeneous coordinates in

the projector reference system:

1pp1mGm = (8)

Knowing Eqs. (7) and (8), the relative position

between camera and projector can be calculated using

the following relationship:1

pcpcGGG

=

3.4 Acquisition Phase

The shape detection is achieved by the structured

light method. To implement this particular technique, it

is necessary to project a Gray-Code pattern together

with the Phase-Shift to avoid the problem of the

matching between the points of the image plane of the

micro-cameras and the points of the image plane of the

projector [16-17]. This codifying process allows to

generate 2nlines with bright and dark pixels, where nis

the number of bits and depends on the projector

resolution. In our particular case we projected 256 lines.

We also used a particular pattern: the Gray-Code

pattern is followed by seven projections shifted by 1/8

phase. The shape detection is achieved by a

multi-vision scanning process, whereas the two cameras

simultaneously acquire a tooth side each (Fig. 9).

3.5 Processing Phase

To obtain a CAD model it is necessary to correlate

the data acquired from the cameras with the projector


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Fig. 9 Gray-code with phase shift.

data. The transformation (R, t) that changes the

coordinates from the camera reference frame to the

reference frame of the projector are derived from the

calibration process and may be given by the following

relation:

tmRm cp += (9)

where mc are the point coordinates acquired from

camera and mpare the point coordinates illuminated by

projector. A generic point mis described on the camera

plane image by the pointpcin Eq. (10):

c

c

cc

cc

c

c

cm

z

1

1

zy

zx

1

v

u

p =

=

= (10)

The projected point vertical coordinate is unknown.

Letppbe the coordinate of the point which illuminates

m. The point mis projected on the pointppon projector

image plane.

p

p

pm

z

1p = (11)

Using Eqs. (9)-(11) the vector equation is obtained:

tRpzpzccpp

= (12)

Decomposing Eq. (12) on a three linear equations

system, the point mdepth (zp)is known [14].

c

T

1

T

3p

p31

c)prr(u

uttz

=

4. Scanner Calibration Results4.1 Camera Calibration

The camera calibration is calibrated using the

Camera Calibration Toolbox for Matlab1. We use a

1http://www.vision.caltech.edu/boughetj/calib_doc/.

surface with a printed checkerboard pattern and

we take about 20 images of it in different position

(Fig. 10).

The results of this calibration is shown in Table 1

where the last element is the calibration error (c).

4.2 Projector Calibration

To calibrate the projector with the novel algorithm,

only three images are needed, one of the chessboard, to

determine its position with respect to the camera and

two images of the projected pattern, a positive and a

negative (Figs. 11a-11b). The actual images that are

used for projector calibration are the result of the

subtraction of the two aforementioned images (Fig.11c). The calibration of the projector is almost

Fig. 10 Specimen calibration in different position.

Table 1 Results from traditional acquisition.

Parameters Left cam Right cam

u 498.24.00 295.76

v 467.09.00 552.39.00

u -0.069 0.041

v -0.066 -0.087

f 6,8861111 -0.3402

u0 304.83 409

v0 248 273

x0 23.633 20.163

y0 14.986 11.293

z0 -0.9916 2,41875

x -224.683 -1.213.483

y 16.953 -591.193

z 4.262.155 3.920.633

u 921 897

v 893 858

ku -2793.93 -2718.18

kv -3307.66 -3177.77

c 1,52052 0,3132


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(a) (b) (c)

Fig. 11 Projected images: (a) positive; (b) negative; (c)

subtracted.

independent of the camera calibration [18], but for the

points projected position, which depends from the

planes orientation, as determined by the camera.

However this dependence is rather weak.

Besides that, the calibration projector process is

similar to that used for cameras. In fact, as in the

camera calibration, 20 images are obtained, one for

each chessboard position (Fig. 12). The projector

parameters are obtained by the correlation of a target

set of coordinates placed on a projected calibration

specimen with its the corresponding coordinates on the

plane image. The results of this process are shown in

Table 2.

4.3 Acquisition Phase

Once the scanner calibration parameters have been

obtained is possible to pass to the acquisition phase for

reconstruction of a model. Using the Gray Code

described in the previously paragraph, is possible to

obtain the follow images (Fig. 13). The process starts

with the 1 bit image, terminating with the 7 bit one. Of

each image both a positive and a negative image are

recorded. At the end of this process the various images

are obtained in binary code (Fig. 14).

4.4 Surface Generation

Once the individual point cloud has been obtained in

the camera system of reference, it has to be converted

in the mechanical slider system of reference, in order to

enable the generation of the entire point cloud.

In order to do so a further calibration is needed,

using a particular new chessboard (Fig. 15), in which it

is possible to correlate motion of the sliders with the

systems of reference established on the chessboard.

Fig. 12 Specimen projector calibration in different

position.

Table 2 Projector and camera calibration parameters

with the novelalgorithm.

Parameters PROJ CAM L PROJ CAM R

u 7.164.829 498.24.00 171.61 295.76

v 4.518.913 467.09.00 461.39.00 552.39.00

u -0.06957 -0.069 0.03837 0.041

v -0.01143 -0.066 -0.0467 -0.087

f -0.451 6,8861111 -0.34 -0.3402

u0 511.05.00 304.83 285 409

v0 383.05.00 248 182 273

x0 -17.055 23.633 20.163 20.163

y0 -21.848 14.986 11.293 11.293

z0 3,1326389 -0.9916 2,41875 2,41875

x -510.221 -224.683 -1.213.483 -1.213.483

y 43.601 16.953 -591.193 -591.193

z 4.981.056 4.262.155 3.920.633 3.920.633

u 975.07.00 921 285.000 897v 1615.03.00 893 182.000 858

ku -2956.66 -2793.93 -863.63 -2718.18

kv -5982.59 -3307.66 -674.74 -3177.77

c 5,4548611 3,73888889

Fig. 13 Projected gray-code.

Next Fig. 16 shows as example the image recorded

by the same camera after a displacement of the slides.

Every scan is registered and properly aligned with

respect to the universal reference coordinate system in

order to obtain the whole three-dimensional dental arch

model (Fig. 17).


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Fig. 14 Images after the subtraction technique.

Fig. 15 Chessboard with identification marks.

Fig. 16 Two chessboard pictures showing the same point

observed from two different positions.

Fig. 17 CAD model of dental arch.

Once the three-dimensional model of the oral cavity

is created, the doctor may decide the best position for

the implants in order to obtain the desired results. A

numerical control milling machine may produce a

prosthesis, which will be then ready to be installed into

the patients oral cavity. The surgeon may then proceed

with surgery, implanting the new artificial roots. Once

this is done, special identifying abutments may be

finally placed on the implants.

5. Implant PositioningOnce obtained the dental CAD model, the dentist

can decide where to place the implants in the patients

mouth. It uses a new system based on a serial/parallel

robot with 2+1 DOF. This system is basically a four bar

link, whose frame may rotate about its longitudinal axis,

actuated by two step motors that, trough two worm

gears, move two rods acting in directions mutually

parallel on the first bar of a four bar link, while on the

third bar a slide allows the doctor to manually control

the motion of the implant micro-motor (Fig. 18). Two

digital encoders measure the angles, in order to

simplify the control. Thus this micro-robot is

essentially a serial robot, whose motion is controlled in

a parallel robot fashion, becoming extremely strong,

but having a minimal impact on the patients mouthsince all the gearing is external.

The procedure to utilize the system is the following.

First step is the acquisition of a CAT record of the

patients mouth. Then the doctor has to decide where to

place the implants navigating within the 3D

representation of the patient mouth, taking into account

all problems connected with implantation in that

particular mouth. Next the intraoral mask for vestibular

support is inserted in the mouth and fixed against a

second mask placed under the chin, if the jaw is to

undergo surgery, otherwise, for the upper denture,

simply putting straps on the head to secure the mask

against the upper vestibular surface.

Once this is done, a complete scanning of the mouth

is to be performed, in order to establish the

correspondence between the CAT representation and

the actual patient mouth, thus locating with precision

the positions in which the implants have to be fitted.


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(a)

(b)

(c)

Fig. 18 Robotic system for guiding implant positioning: (a)

up and down; (b) left and right; (c) forward and backward.

Finally the 3D scanner has to be detached from its

base and substituted with the 2 + 1 DOF parallel robot,

and the system will guide the doctor assuming the

correct x, y position and angles that have been

previously established, and the doctor may proceed

with the implant fixation.

Once the implants are positioned, and relative

abutments installed, it is possible to repeat the scanning

process to determine both which shape the abutments

should assume, and consequently the final prosthesis

form.

6. ConclusionsThe paper presents the first results of a new scanning

device for intra-oral determination of the mouth model

and the associated guiding robot for implant

positioning, both based on a platform which is fixed to

the patients mouth through a self balanced 6 DOF arm

bearing a vestibular supporting mask. More work is

needed to complete the system, but it will be the first

system that allows determining via software the best

position for an implant and immediately positioning it

into the patient mouth.

Acknowledgments

The present work was partially supported by

Tecnologica Srl of Crotone PIA grant C01/0612/P

46548-13.

The authors wish to acknowlwdge the precious help

of Basilio Sinopoli, Sebastiano Meduri, Diego Pulice

and of the Lab personnel of Dipartimento di Meccanica

of Calabria University for their contribution to thiswork.

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