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ORIGINAL ARTICLE
Pavankumar Janardan Vibhute, Usha Shenoy
Rationalization of Mechanical Factors affecting
Primary Stability of Orthodontic Miniscrew using
Engineering Principles of Simple Machines
1
Pavankumar Janardan Vibhute, 2Usha Shenoy
ABSTRACT
Miniscrews have become the regular components as an anchorage source in orthodontics. Stability and failure of miniscrew is materializing
to be multifactorial with no consensus on causative factors. Factors that influence the load transfer at the bone-implant interface and
miniscrew stability include host factors, biomechanical factors, sterilization protocol and hygiene. Biomechanical influences on bone structure
play an important role in the longevity of bone. Incorrect loading or overloading as a result of ineffective implant geometries may lead to
implant loss. Miniscrews are not an exception for following the mechanical behavior or engineering principles. More certainly, they are
based on the simple machines, which is a mechanical device that changes the direction or magnitude of a force. This article produces an
insight for rationalization of mechanical factors controlling the stability with principles of simple machines, namely (i) lever, (ii) wheel and
axle, (iii) inclined plane, (iv) wedge and (v) screw.
Keywords: Implant, Miniscrew stability, Biomechanics, Simple machine, Mechanical advantage, Lever, Cortical bone.
How to cite this article: Vibhute PJ, Shenoy U. Rationalization of Mechanical Factors affecting Primary Stability of Orthodontic Miniscrew
using Engineering Principles of Simple Machines. J Ind Orthod Soc 2013;47(4):190-198.
INTRODUCTION
Temporary anchorage devices (TAD), in the form of mini- or
microscrew have become regular components as an anchorage
source in orthodontics.1 Multiple factors are involved in stability
and failure of miniscrew with no consensus on the causative
factors.2-10 Specific controlling factors that might enhance
primary stability of miniscrew are not fully understood. Load
transmission and resultant stress distribution are significant in
determining the success or failure of an implant.11,12 Factors
that influence the load transfer at the bone-implant interface
and miniscrew stability include host factors, biomechanical
factors, sterilization protocol and hygiene. Host factors (bone
quality, quantity, attached gingiva width, soft tissue thickness,
gender, age) are invariable for the particular patient and should
be assessed clinically for site and miniscrew selection.13-20
Biomechanical factors related to screw (size, shape, length and
pitch); insertion procedure and loading (force magnitude and
vector) can be made effectual easily for reducing stresses at
implant-bone interface.21-27 Incorrect loading or overloading as
1
Associate Professor, 2Professor
Department of Orthodontics, Sharad Pawar Dental College, Datta
Meghe Institute of Medical Sciences, Wardha, Maharashtra, India
1,2
Corresponding Author: Pavankumar Janardan Vibhute, Associate
Professor, Department of Orthodontics, Sharad Pawar Dental
College, Datta Meghe Institute of Medical Sciences, Swangi
Wardha, Maharashtra, India, e-mail: [email protected]
Received on: 12/1/12
Accepted after Revision: 19/9/12
190
a result of ineffective implant geometry may lead to implant
loss. The key to successful implants is minimum bone damage,
which depends on biomechanical influences on bone structure.
The magnitude and direction of force applied influence the
implant’s prognosis. Collectively these factors control the
primary stability of orthodontic miniscrew and are important
from the perspective of immediate loading. Insertion torque
and pullout tests typically are used to analyze its primary
stability. Both tests provide anchorage estimates for
immediately loaded miniscrews. Pullout tests are commonly
used to measure primary stability in orthopedics, neurosurgery
and maxillofacial surgery. Pullout tests directed vertically, with
forces parallel to the long axis of the screw, typically are used
to evaluate the design of a screw-type implant. In orthodontics
miniscrews most of time loaded approximately perpendicular
to long axis, hence viability of pullout test is uncertain.
Biomechanics followed in orthodontics are based on definite
engineering principles and laws; miniscrews are not an
exception. More certainly, they are based on the ‘classical
simple machines’, the term which was defined by Renaissance
scientists.28 A ‘simple machine’ is a mechanical device that
changes the direction or magnitude of a force. In general, it
can be defined as the simplest mechanism that uses ‘mechanical
advantage’ (MA) to multiply force.29,30 A simple machine uses
a single applied force to do work against a single load force.
Ignoring friction losses, the work done on the load is equal to
the work done by the applied force. They can be used to increase
the amount of the output force, at the cost of a proportional
decrease in the distance moved by the load. The ratio of the
output to the input force is called the MA. This article gives an
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Rationalization of Mechanical Factors affecting Primary Stability of Orthodontic Miniscrew using Engineering Principles
insight for rationalization of mechanical factors controlling its
stability to improve its efficacy, using MA of five definite
engineering principles of simple machines, namely (i) lever,
(ii) wheel and axle, (iii) inclined plane, (iv) wedge and (v) screw.
Work is defined as the force multiplied by the distance it
moves. So the applied force (Fin), times the distance the input
point moves (Din), must be equal to the load force (Fout), times
the distance the load moves (Dout), (Fin–Din = Fout–Dout). So the
ratio of output to input force, the MA, is the inverse ratio of
distances moved: MA = Fout ÷ Fin = Din÷ Dout For an ideal
(frictionless) mechanism, it is also equal to: MA = distance
over which force is applied ÷ distance over which the object is
moved.
There are two types of MA:
Fig. 1A: Beam in static equilibrium around the fulcrum
Ideal Mechanical Advantage
The ideal mechanical advantage (IMA), or theoretical MA, is
the MA of an ideal machine. It is calculated using principles of
physics, because no ideal machine actually exists. The IMA of
a machine can be found with the following formula: IMA= DE
÷ DR where, DE equals the ‘effort distance’ (for a lever, the
distance from the fulcrum to where the effort is applied) and
DR equals the resistance distance (for a lever, the distance from
the fulcrum to where the resistance is encountered).
Actual Mechanical Advantage
The actual mechanical advantage (AMA) is the MA of a real
machine. Actual MA takes into consideration real world factors
such as energy lost in friction. The AMA of a machine is
calculated with the following formula:
AMA = R ÷ Eactual; where, R = resistance force obtained from
machine, Eactual = actual effort force.
Lever Principle
Class 1 lever: The fulcrum is located between the applied force
and the load. Levers can be used to exert a large force over a
small distance at one end by exerting only a small force over a
greater distance at the other.31 The force applied (at end points
of the lever) is proportional to the ratio of the length of the
lever arm measured between the fulcrum (pivoting point) and
application point of the force applied at each end of the lever.
Mathematically, this is expressed by M = Fd, where F is the
force, d is the distance between the force and the fulcrum and
M is the turning force known as the moment or torque.
Beam balanced around a fulcrum exhibit a MA due to the
moment created by vector force ‘A’ counterclockwise (moment
A × a) being in equilibrium with the moment created by vector
force ‘B’ clockwise (moment B × b). The relatively low vector
force ‘B’ is translated in a relatively high vector force ‘A’. The
force is thus increased in the ratio of the forces A:B, which is
equal to the ratio of the distances to the fulcrum b:a, this ratio is
called the MA. This idealized situation does not take into
account friction (Figs 1A and B).
Fig. 1B: A large force over a small distance at one end balanced by
exerting only a small force over a greater distance at the other (A × a =
B × b)
Miniscrew Insertion and Orthodontic Loading
Bone is porous material with complex microstructure.32 The
higher load bearing capacity of dense cortical bone (Young’s
elastic modulus = 1.5 × 104 Pa) compared with the more porous
trabecular bone (Young’s elastic modulus = 150 Pa) is
recognized.32 Greater difference in stiffness of cortical and
trabecular bone produces load reaction which is expressed using
first class lever, where cortical plate of bone acts as fulcrum or
pivot and miniscrew as rigid beam. Presence of cortical plate
thickness of 0.5 to 2.5 mm in maxilla and mandible is reported
to enough for resisting orthodontic forces of average 300 gm
easily. Specific magnitude of loading force on miniscrew head
outside the cortical plate (as fulcrum) is balanced by the inserted
miniscrew shaft inside fulcrum. Thus, either its maintenance in
static equilibrium or deflection of miniscrew is decided by the
compressive force produced in the trabecular bone inside
cortical plate (fulcrum). Ultimately, this force on trabecular bone
(strain) is directly proportional to deflective force (stress) by
threaded portion of miniscrew (which is decided by the loaded
force at other side lever arm/at miniscrew head). Direct,
perpendicular loading to long axis of miniscrew and stress
distribution around entrenched miniscrew in bone at different
situations is explained using Class 1 lever principle.
A 12 mm long miniscrew is inserted through the cortical
bone to four different depths and loaded perpendicular to its
long axis with similar amount of force in four situations (Figs 2A
to D). (i) A 6 mm (half) of screw inserted and remaining 6 mm
(half) outside bone, form the equal lever arm length on both
sides. A total of 250 gm of direct loading force applied on
miniscrew head resisted (theoretically) with 250 gm of
compressive force at inserted miniscrew tip (actually equal
amount of compressive force by the bone on inserted miniscrew
The Journal of Indian Orthodontic Society, October-December 2013;47(4):190-198
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Pavankumar Janardan Vibhute, Usha Shenoy
Figs 2A to D: According to lever principle, 12 mm miniscrew loaded with
250 gm perpendicular to long axis and different insertion depth exhibits
the different compressive load at cortical plate (stress pattern).
(A) 6 mm threaded portion inserted, (B) 8 mm threaded portion inserted,
(C) 10 mm threaded portion inserted, (D) 11 mm threaded portion inserted
shaft to keep the screw in static equilibrium), cortical plate act
as fulcrum, thus, receiving total 500 gm of compressive load
(force). (ii) Insertion of miniscrew increased up to 8 mm (twothird) inside trabecular bone and amount of applied load remain
same, i.e. 250 gm direct loading force, to keep screw in
equilibrium 125 gm of compressive force is necessary at inserted
miniscrew tip and fulcrum receives a total 375 gm force. (iii)
Further, insertion of miniscrew increased up to 10 mm and
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amount of applied force of 250 gm, it balanced with only 50
gm of compressive force at miniscrew tip and resulting 300 gm
of total load at fulcrum. (iv) In case of miniscrew inserted 11
mm inside trabecular bone with 250 gm of force on 1 mm lever
arm outside cortical plate (fulcrum), only 22.7 gm of
compressive force at miniscrew tip is necessary for static
equilibrium and total 272.7 gm of force exerted on fulcrum.
Lever arm outside cortical plate (fulcrum) is a clear distance
between application point of the force on miniscrew head and
cortical plate, while lever arm inside the cortical plate is being
balanced by trabecular bone (distributed throughout the inserted
shaft of miniscrew). Relatively low and reduced magnitude of
force at miniscrew tip indicates low stresses at bone–miniscrew
interface throughout inserted portion of miniscrew (Balancing
force at miniscrew tip is indicative of total amount of force
being produced throughout inserted miniscrew shaft).
Increasing the depth of insertion of 12 mm long
miniscrew from 6 to 10 mm inside bone reduces the stresses
at bone–miniscrew interface by 80% (MA = 10 ÷ 2 mm =
250 ÷ 50 gm = 5).
Farther the perpendicular loading point on miniscrew head
from cortical plate (fulcrum) on one side (i.e. long loading lever
arm), more the stresses on inserted miniscrew shaft. Excessive
soft tissue thickness (which demand longer neck length, Fig.
3), incomplete miniscrew insertion, incomplete insertion due
to obstruction by root, treatment planning with long
superstructures on miniscrew head alter the lever arms ratio
vulnerably (long loading lever arm) which cause unintended
higher stress level at bone-miniscrew interface. To have the
maximum MA, i.e. lowest theoretical stress at implant tip, that
means eventually decreased amount of stress on inserted
(embedded) portion of miniscrew, and lowest possible force
on the cortical plate (fulcrum), implant should be loaded as
much as close to the fulcrum (i.e. cortical plate) and it should
be inserted to its full length. When there is inadequate bone
depth for insertion, instead of selecting longer screw, short
length miniscrew should be chosen, to avoid incomplete
insertion of threaded portion of longer screw, eventually to avoid
unintended excessive stress levels at miniscrew-bone interface
(cortical plate). Although the risk associated with long
Fig. 3: Longer neck implants (long lever arm) which cause unintended
higher stress level at bone-miniscrew interface and at cortical plate
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Rationalization of Mechanical Factors affecting Primary Stability of Orthodontic Miniscrew using Engineering Principles
miniscrew is root approximation, it may be lowered with use of
best possible diagnostic record and guide for miniscrew
placement.33
‘A large force over a small distance (short loading lever
arm) at one end (miniscrew head) is balanced by exerting only
a small force over a greater distance (long inserted portion lever
arm) at the other end’ (first class lever principle) helps to reduce
the strain levels around the inserted miniscrew shaft for attaining
best primary stability. Thus, length of miniscrew and its relative
insertion in to bone is deciding factor from stability point of
view. Cortical bone, which is considered being most important
for primary stability on perpendicular loading may be explained
scientifically with this principle.
Wheel and Axle Principle
A wheel and axle is a modified lever of the first class that rotates
in a circle around a center point or fulcrum. The larger wheel
(or outside) rotates around the smaller wheel (axle). A wheel is
essentially a lever with one arm the distance between the axle
and the outer point of the wheel, and the other the radius of the
axle. Typically this is a fairly large difference, leading to a
proportionately large MA. Examples are screwdrivers,
doorknobs. The form of ‘lifting water from a well’ consists of
a wheel that turns an axle, which turns a rope, which converts
the rotational motion to linear motion for the purpose of lifting
(Fig. 4).
Calculating MA
Ideal MA: The IMA of a wheel and axle is calculated with the
following formula:
IMA = Radius wheel ÷ radius axle
Actual MA: The AMA of a wheel and axle is calculated with
the following formula:
AMA = R ÷ Eactual
Where, R = resistance force, i.e. the weight of the bucket in this
example.
Eactual = actual effort force, the force required to turn the wheel.
Miniscrew Insertion and Drivers used for
Torquing (as Torque Multiplier)
Torque is tendency of force to rotate an object about its axis/
fulcrum/pivot. Torque = r × f, where ‘r’ is length of lever arm
(wheel/handle radius), ‘f’ is magnitude of force vector. Amount
of torque required during miniscrew placement (insertion)
depend on the nature of bone and design of miniscrew (size,
shape, pitch and thread circumference). In the screw, which
uses rotational motion, the input force is torque, and the distance
is an angle that the shaft is turned. An example of the rotational
form, diameter of the handle gives a MA as torque multiplier.
Screw driver handle is essentially a lever with one arm (distance
between axle and outer point of handle) and other the radius of
the axle (miniscrew). Typically this is fairly large difference,
leading to proportionately large MA.
Ideal MA = Radius of screw driver handle ÷ radius of miniscrew.
Actual MA = Resistance by the bone material ÷ actual force
required to turn the screw driver.
In the application of specific amount of torque, bigger
handles reduce the total efforts for rotation of driver or applying
same amount of torque. Reduction in the total efforts helps to
keep control over insertion pressure required during torque
placement (Fig. 5A). Insertion pressure is dependent upon the
lead (amount of screw travelled in 360° rotation) and nature of
bone.
Nonaxial Perpendicular Loading and
Primary Stability of Miniscrew
Detorquing or destabilizing force on miniscrew is more easily
provided with even small loading force on longer power arm of
screw whose point of loading force is more away from
miniscrew head and opposite to the tightening direction
(Fig. 5B).
Inclined Plane Principle
The inclined plane is one of the original simple machines; as
the name suggests, it is a flat surface whose end points are at
different heights. By sliding an object up an inclined plane rather
than completely vertical, the amount of force required is
reduced, at the expense of increasing the distance the object
must travel (Fig. 6).
Fig. 4: The traditional form as recognized in 19th century textbooks, a
well-known application of the wheel and axle shows one of the most
widely recognized applications, i.e. lifting water from a well
MA = length of slope (L) ÷ height of slope (H). E.g. The height
of the ramp = 1 m, the length of the ramp = 5 m, divide 5 by
1 = 5. MA = 5.
The Journal of Indian Orthodontic Society, October-December 2013;47(4):190-198
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Pavankumar Janardan Vibhute, Usha Shenoy
Fig. 5A: Bigger size of handles reduces the total efforts for rotation
of driver or apply same amount of torque
Fig. 7: Cross-section of a splitting wedge with its length oriented
vertically. A downward force produces forces perpendicular to its inclined
surfaces
Fig. 5B: Perpendicular loading of miniscrew away from its head with
different lever arm length. Small amount force with long lever length
may cause detorquing of screw easily than the short lever and same
force
be used to separate two objects or portions of an object, lift an
object or hold an object in place. It functions by converting a
force applied to its blunt end into forces perpendicular (normal)
to its inclined surfaces. The MA of a wedge is given by the
ratio of the length of its slope to its width. Although a short
wedge with a wide angle may do a job faster, it requires more
force than a long wedge with a narrow angle (Fig. 7).
The MA of a wedge can be calculated by dividing the length
of the slope (S) by the wedge’s width (W) (MA = S ÷ W). The
more acute, or narrow, the angle of a wedge, the greater the
ratio of the length of its slope to its width, and thus the more
MA it will yield (Figs 8A to C).
Thickness of Cortical Plate, Pitch, Perpendicular
Loading and Wedge Principle
Fig. 6: Principle of inclined plane
Wedge is a compound inclined plane, consisting of multiple
inclined planes placed so that the planes meet at one point. The
point where the planes meet is pushed into a solid or fluid
substance and overcomes the resistance of materials to separate
by transferring the force exerted against the material into two
opposing forces normal to the faces of the wedge. Principle of
compound portable inclined plane is discussed under wedge
and screw.
Wedge Principle
A wedge is a triangular shaped tool, a compound and portable
inclined plane, and one of the classical simple machines. It can
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Thickness of the cortical bone in perpendicular loading is
considered the most important for primary stability. Since
maximum stresses are seen at cortical plate on perpendicular
loading, the inclined planes of threads act as a wedge in cortical
plate (Figs 9A and B). Primary stability may be compromised
when miniscrew with a pitch of 1.25 mm is inserted into cortical
bone that is only 1.5 mm thick, because of the limited space
available for thread engagement. MA of greater depth threads
augment cortical bone damage. Reduced depth of threads and
decreased pitch reduces the mechanical damage to cortical bone.
Mechanical purchase of cortical bone which has greater density
requires reduced pitch and thread depth. While less dense
trabecular bone requires increased thread depth and more pitch
for greater purchase of bone material.
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Rationalization of Mechanical Factors affecting Primary Stability of Orthodontic Miniscrew using Engineering Principles
Figs 8A to C: Integrity and sharpness of miniscrew tip plays an important
role in traveling of miniscrew inside bone. Insertion pressure is
responsive to the size, shape and integrity of this compound inclined
plane. Tapered shape seems to provide greater MA than a cylindrical
shape, depending upon slope length of inclined plane and width of
screw
Screw
A screw is essentially an inclined plane wrapped helically around
an axis for a number of turns. A screw can convert a rotational
movement to a linear movement, and a torque (rotational force)
to a linear force. When, the shaft of the screw is rotated relative
to the stationary threads, the screw moves along its axis relative
to the medium surrounding it.34
The Archimedean screw or the screw pump is a machine
historically used for transferring water from a low-lying body
of water into irrigation ditches (Figs 10A and B).35
MA of orthodontic miniscrew:
The theoretical MA for a screw can be calculated using the
following equation:
MA = dm ÷ l; where, dm = the mean diameter of the screw
thread and l = the pitch of the screw thread.
From the perspective of immediate loading, primary or
initial stability of miniscrew is more important in orthodontics.
Figs 9A and B: Maximum stresses at cortical plate on perpendicular
loading, inclined plane of threads acts as wedge in cortical plate
Primary or initial stability depends upon initial torque, which
in turn depend on density of bone material.21,36
The screw’s pitch, the distance the screw travels in one
revolution, determines the MA of screw; the smaller the pitch,
the higher the MA. Resistance encountered (by bone) during
the screw placement is reduced by reducing the pitch or
increasing the thread circumference. MA can be estimated by
dividing the diameter (or circumference) of the shaft by the
distance between the threads (Fig. 11). Actual MA of a screw
system may be further increased if a screwdriver or other screw
driving system has an additional MA as well. Higher level of
MA is usually required for insertion in very hard material, but
with bone moderate initial pressure is required to pass through
cortical plate with several threads, but after that, insertion
pressure should be reduced. Significantly increased pull out
strength with reduced pitch is reported.37 A lesser pitch provides
a greater surface area than the greater pitch, which increases
torque as the result of increased friction at the bone-to-screw
interface.38 This increased torque level is overcome with MA,
and thus increased MA helps to increase pullout strength.
The Journal of Indian Orthodontic Society, October-December 2013;47(4):190-198
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Pavankumar Janardan Vibhute, Usha Shenoy
Figs 10A and B: Archimedes’ screw was operated by hand and could
raise water efficiently. Since the screw is rotated in relative stationary
position instead of forcing screw itself downward, surrounding medium
is raised or glided in opposite, upward direction
Fig. 11: MA can be estimated by dividing the outer diameter (d) of
the shaft by the distance between the threads (pitch)
Torquing of Miniscrew in a Stationary
Position and Primary Stability
Mechanism of screw loosening (loss of initial stability) is
explained by the principle of Archimedes screw. Complete
insertion of miniscrew is indicated by contacting its collar to
cortical plate. With further rotation of screw (shaft) around its
long axis in same stationary position causes stripping of treads
and loss of primary stability. This can also happen with
continued torquing of screw when insertion is obstructed by
roots. Like Archimedes screw principle, instead of forcing screw
in to surrounding medium (bone), medium is raised or glided
in opposite direction. When the mechanically anchored portion
196
Figs 12A to C: Torquing of screw in stationary position causes the
bone material to glide in opposite direction along the threads, a possible
cause for the loss of mechanical integrity of cortical bone, bone
purchased in between threads from surrounding bone
of bone between the threads is pushed/glided toward the cortical
plate, it gets accumulated, the integrity of cortical bone is lost
(Figs 12A to C). This phenomenon is faster with the screws
having less thread circumference and more pitch distance [i.e.
with the screws having less MA (more pitch), or which convert
the rotational movement of screw shaft to faster linear movement
of bone between threads]. Portion of bone between the threads
drawn toward the cortical plate will loose its mechanical
integrity from peri-implant bone, thus causing the loss of primary
stability and failure. Sudden drop of insertion torque occur in
same situation.
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Rationalization of Mechanical Factors affecting Primary Stability of Orthodontic Miniscrew using Engineering Principles
More denser the bone, lesser the chance of initial instability,
because more firm the attachment between peri-implant bone
and bone being grabbed in between threads expected no overrotation of screw in stationary position.
Insertion pressure during placement is decided by the bone
density, implant’s wedging shape (tapered or cylindrical) and
its synchronization with rotational movement and screw design
(thread circumference, pitch). Amount of rotational movement
converted to the linear distance travelled inside the bone is
decided by the pitch of screw (same as followed in expansion
screw, but half of the linear movement since expansion screws
have mirror image thread pattern on either side of it).
Pitch (Symmetrical/Asymmetrical) and
Primary Stability
An effect of pitch type on the primary stability of miniscrew is
important. In cylindrical miniscrew with symmetrical pitch, first
thread on cylindrical shaft is engaged through the cortical bone
and is guided towards the trabecular bone, then, every thread
on the cylindrical miniscrew shaft follows and passes through
the path or crater created by the first thread, thus the
topographical integrity of the bone between the every adjacent
crater is maintained consistently. This integrity is of prime
importance in primary stability. While in case of asymmetrical
pitch, every thread does not follow the track or path created by
the preceding thread. Thus, instead of a definite single path of
crater, several other paths are created which were eventually
not occupied by the subsequent threads, and left blank. This
cause loss of mechanical integrity of bone lied in between threads,
leading to cause of miniscrew failure (Figs 13A and B).
CONCLUSION
Learning the engineering principles based on simple machine
does helps in understanding mechanical and biomechanical
aspects about the screws and its anchorage application in
orthodontics.
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