BIOMECHANICS FORCES IN ORTHODONTICS

BIOMECHANICS IN ORTHODONTICS
Orthodontic therapy depends on the reaction of the teeth
and more generally the facial structures to gentle but
persistent force.
In orthodontics, biomechanics is commonly used in
discussion of the reaction of the dental and facial structures
to orthodontic force, whereas, mechanics is reserved for the
properties of the strictly mechanical components of the
appliance system.
COMMON TERMINOLOGIESCOMMON TERMINOLOGIES::
 FORCE
 MASS
 CENTER OF MASS (C.M.)
 CENTER OF RESISTANCE (Cres)
 CENTER OF ROTATION (Crot)
 MOMENT
 COUPLE
 MOMENT OF FORCE (MF
)
 MOMENT OF COUPLE (MC
) Main Menu
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FORCEFORCE::
A load applied to an object that will tend to move the object to
different position in space.
Units: Newton
Force equal to mass times acceleration.
F = ma
In metric system, it is usually measured in grams or ounces.
In orthodontics forces are obtained in a variety of ways.
Deflection of wires, activation of springs, elastics and magnets
are the common means of producing orthodontic force.
MASS AND WEIGHTMASS AND WEIGHT::
The mass of any body is the quantity of matter it contains.
The quantity of mass of a particle can be measured by
weighing the particle, since mass and weight are proportional
but not the same.
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CENTER OF MASS (C.M.):CENTER OF MASS (C.M.):
The point at which the mass of a body may be considered to be
concentrated is known as center of mass.
In other words the center of mass is an object’s balance point.
E.g. in a space, if one could push a box in line with its center of mass, the
box will translate away as its entire mass is concentrated at that single
point.
Practically speaking one can predict the behavior of any body in space if
one knows forces in relation to their center of mass.

CENTER OF RESISTANCE (Cres):CENTER OF RESISTANCE (Cres):
For an object in free space, the center of resistance is the same as the
center of mass. If the object is partially restrained as in case of tooth
embedded in bone, the center of resistance is equivalent to the balance
point for restrained bodies.
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The center of resistance depends upon,
·       Root length and morphology
·       Number of roots
·       Level of alveolar bone support.
The exact location of Cres for a tooth is not easily identified.
Although Cres for single rooted teeth with normal alveolar bone
levels is about one fourth to one third of the distance from the
cemento-enamel junction, to the root apex. Cres for multirooted
teeth lies just below the furcation area, i.e. 1-2 mm apical to the
furcation. Cres of maxilla lies in the area of postero-superior aspect
of zygomatico-maxillary suture.
Although its precise location is typically unknown, it is important to
have a conceptual awareness of Cres in selecting and activating an
orthodontic appliance. The relationship of the force system acting
on the tooth to the Cres determines the type of tooth movement
expressed. It is the point through which pure force will produce
only translation i.e. all the points on the tooth moving in parallel
straight line.
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CENTER OF ROTATION (Crot):CENTER OF ROTATION (Crot):
It is the point around which rotation actually occurs when an
object is being moved. Depending upon the force system
applied, the center of rotation may vary.
E.g. In case of controlled tipping center of rotation will be at
root apex while in case of perfect translation it will be at
infinity.

MOMENT:MOMENT:
Is product of force times the perpendicular distance from the
point of the force application and to the center of the
resistance.
Moment = Force x Perpendicular distance
from Cres to point of force application
Thus it is measured in the unit of gm-mm.
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COUPLE:COUPLE:
Two forces equal in magnitude and opposite in direction
produce couple. The result of applying two forces in this way
is a pure moment, since translatory effect of the forces cancels
out.
A couple will produce pure rotation, spinning the object
around its Cres. While combination of a force and a couple
can change the way an object rotates while it is being moved.
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MOMENT OF FORCE (MMOMENT OF FORCE (MFF):):
If the line of action of an applied force does not pass through
the center of resistance, the force will produce some rotation.
The potential for rotation is measured as moment and the
magnitude of the moment is equal to the magnitude of the
line of force multiplied by the perpendicular distance of the
line of the action of force to the Cres. The direction of
moment can be determined by continuing the line of action
of the force around the Cres.
Unit of MF
is gm-mm.
Two factors determine MF
.
1) Magnitude of force
2) Distance.
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MOMENT OF COUPLE (MC):MOMENT OF COUPLE (MC):
Another method of achieving rotational movement is through the
MC
. A couple is two parallel forces of equal magnitude acting in
opposite direction separated by a distance.
The magnitude of a couple is calculated by multiplying the
magnitude of force by distance between them.
Unit: gm-mm.
The direction of the rotation is determined by following the direction
of either force around the Cres to the origin of the opposite force.
The moment of a couple is the product of one of the forces times the
distance between the two forces. This distance is called “the
moment arm of the couple”. When the tooth is embedded in
alveolar bone, we cannot apply a couple with one force on the crown
and the other force on the root.
We all know and have experienced that the force required to turn a
bigger wheel is considerably lesser than that required to turn a
smaller wheel. The reason for that being, in the bigger wheel the
moment arm is larger and hence the force to generate a moment of
particular magnitude is less. Main Menu

In order to retract incisor we apply a force on the crown of the
tooth. This force creates a moment, as it is away from the center of
resistance and will cause tipping. To keep tipping of the tooth to a
minimum we have to create a moment on this tooth in a direction
opposite to that created by the force. This can be done easily by
applying a couple having an anticlockwise moment.
A force of 100 gm acting at a distance of 10 mm from the Cres of a
tooth, produces a clockwise or negative moment of 1000 gm-mm which
will cause the tooth to tip.
Since tipping is undesirable, we must generate a counter balancing
moment of 1000 gm-mm so that a bodily movement is obtained.This
can be achieved by twisting the anterior segment of the rectangular
wire and fitting it into a rectangular slot. Once the wire is engaged in
the bracket slot it generates an “Inherent moment of couple”, which is
nothing but the couple produced within the wire itself. In a rectangular
wire, the moment arm is the depth of the bracket,which is very
small. Main Menu

Since moment is force times the distance the force is equal to
moment divided by the distance. Thus it requires a large force to
generate the counter balancing moment.
Inherent
moment
of a couple
Inherent couple acting at
a distance from the Cres
producing secondary
moment of a couple
‘d’
From our clinical experience we know that such heavy
forces are not required to achieve bodily movement. The
reason for that being, the moment of couple generated by
torquing the rectangular wire acts at a certain distance
from the Cres of the tooth. This again produces a moment
of couple called “secondary moment of couple”. This
secondary moment of a couple adds to the inherent
moment of a couple generated by the rectangular wire.
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TYPES OF TOOTH MOVEMENT:TYPES OF TOOTH MOVEMENT:
Basic tooth movements are categories into,
1.   Tipping
2.   Translation
3.   Root movement
4.   Rotation
Each movement is the result of variation of the
applied moment and force (either by magnitude or
point of application).

Tipping: Is greater movement of the crown of the
tooth than that of the root. Crot is apical to the Cres.
Tipping can be further classified on the basis of the
location of the center of rotation as Uncontrolled
tipping and Controlled tipping.
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Uncontrolled tipping
A horizontal force at the level of bracket will
cause movements of the root apex and crown
in opposite directions. This is simplest type of
tooth movement. It requires single force and
no applied moment.
Crot lies just below the Cres.
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Controlled tipping
It is achieved by an application of force to move
the crown, as done in uncontrolled tipping and
application of a moment to control or maintain the
position of the root apex. Crot lies at the root apex
M/F ratio = 7:1
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Translation: This type of tooth movement is also
known as ‘bodily movement’. Translation of a tooth
takes place
when the root apex and crown move the same distance and
in the same direction.
A horizontal force applied at the Cres of a tooth will result
in this type of tooth movement. However, the bracket
where the force application takes place is at a distance from
the Cres. This force alone applied at the bracket will not
result in translation. To achieve translation at the level of
the bracket, a couple of forces are required that are
equivalent to the force system through the Cres of tooth.
Point of force application – Cres
Center of Rotation – Infinity.
M/F = 10:1
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Root movement (TORQUE): Root movement is achieved
by keeping the crown of a tooth stationary and applying a
moment and force to move only the root.
Root movement is termed as ‘torque’.
Point of force application – a point apical to the Cres
Center of Rotation – at the incisal edge or bracket.
M/F = 12:1
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The simplest way to determine how a tooth will move is to
consider the ratio between moments created when a force is
applied to the crown of a tooth (moment of force MF
) and the
counter balancing moment generated by a couple within the
bracket (moment of couple Mc
).

MC
/MF
= 0 Pure tipping (tooth rotates around the
Cres).

0 < MC
/MF
< 1 Controlled tipping (Inclination of tooth
changes but the Crot is displaced away
from the Cres and the root and crown
move in the same direction.)

MC
/MF
= 1 Bodily movement (equal movement of
crown and root)

MC
/MF
> 1 Torque (Root apex moves further than
crown) Main Menu

Pure rotation: This type of tooth movement occurs when tooth
rotates about its center of resistance.
A couple is required to produce pure rotation.
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Intrusion and extrusion: It is tooth movement in axial direction.
Intrusion is the bodily displacement of a tooth along its long
axis in an apical direction.
Extrusion is bodily displacement of a tooth along its long axis
in an occlusal direction.
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FORCE SYSTEMS:FORCE SYSTEMS:
In order to achieve the described tooth movements, the proper force
system is a critical requirement. The following factors related to the
force system are potentially under the control of the clinician.
1.   Moment-to-force ratio
2.   Constancy of forces and moments.
3.   Magnitude of forces and moments.
Moment-to-force ratio:
In order to produce tooth movement other than uncontrolled tipping by
applying a force system only at the bracket, a single force alone is
insufficient; a rotational tendency (a moment) must be applied at the
bracket.
The proportion of rotational tendency (moment) to the force applied at
the bracket will determine the type of tooth movement. This is
represented by M/F at the bracket.
Moment-to-force ratio plays an important role in anchorage control. By
varying the moment-to-force ratio applied to the anterior and posterior
segments during space closure after
bicuspid extractions, the amount of forward displacement of the
posterior segments can be controlled. Main Menu

Force constancy:
If we accept the assumption that a relatively constant force within an
optimal range produces the most desirable type of tooth movement, then
we will have to design the active components of an appliance such that
they have desirable spring properties as follows.
A) Load deflection rate of the spring appliances.
B) Frictionless force application system.
Load deflection rate:
Refers to the amount of force produced for every unit of activation of an
orthodontic wire or spring. The lower this rate, the more constant is the
force as the tooth moves and the appliance is deactivated.
Four major design parameters available to the clinician to vary the load
deflection rate are:
1. Wire cross-section. 2. Wire length.
3. Wire material. 4. Wire configuration.
Load deflection rate varies directly as the fourth power of the diameter
of a round wire and as the third power of the depth of a rectangular wire.
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L.D.R. α wire cross
section.
Therefore, reducing the cross section of the wire can
significantly reduce the load deflection characteristics of an
orthodontic appliance. Also the size must be such as to
prevent permanent deformation during mastication,
thereby restricting the wire cross-section within the
maximal elastic strength of the wire.
On the other hand those parts of the appliance that are
concerned with preservation of anchorage require a
relatively rigid wire with a large cross-section. The effect a
rigid wire attachment between anchorage teeth is to
enhance the anchorage potential of these units by
producing a more advantageous stress distribution in the
periodontal structure and to prevent the movement of the
anchorage unit.
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Wire Length: The wire length changes the load deflection
rate inversely as the third power.
1
L.D.R. α
Wire length
Therefore, small increase in length of wire can also
dramatically reduce the load deflection rate. In continuous
arch multibanded appliance, the inter-bracket distance
between adjacent teeth dictates the wire length to a great
extent, although some length can be added to the wire by
using loops.
Long wire with a longer inter-attachment distance delivers
a more constant force magnitude as well as a more constant
force direction as the teeth move to the new desired
positions.
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Wire material: For designing appliances, stainless steel alloys are
in common use today. In order to improve the characteristics of
the stainless steel wire, multi-stranded wires with greater
flexibility (reduced load-deflection rate) have been introduced.
Alloys such as NiTi and Beta titanium with low modulus of
elasticity and high spring back have radically changed appliance
design.

Wire configuration: In order to best utilize the effect that wire
length has on load deflection rate, the design of the wire
configuration should be carefully considered. By placing more
wire at the regions where bending deflections are the greatest and
at the regions where the bending moment is large, the load
deflection rate can be optimally reduced
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Frictionless force appliance system:
In order to achieve constant force and moment levels, sliding
frictional forces must be eliminated or reduced.

Force and moment magnitude:
The magnitude of force and moment is the third parameter with
respect to force system. The accuracy in determining and
maintaining force and moment levels become more critical in
achieving the desired treatment goals. Thus the appliance with
low load deflection rate is the system of choice in accurately
calibrating these levels. A small error in activation of spring with
a high load deflection rate will result in a larger error in the
activation force. In addition to the consideration of tissue damage,
force and moment magnitude are important in anchorage control.
Distributing the force over more teeth can reduce the stress levels
on the anchor units
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. To achieve a more advantageous pattern of stress
distribution in the periodontium of the anchor units, use of
heavy rigid arch wires is recommended so as to allow all
the teeth in the anchor unit to react uniformly. Applying a
moment there by, preventing the tipping and permitting
the anchor units to translate can further enhance this.
Therefore, carefully monitoring the magnitude and M/F
ratio (of the force system), stress levels in the anchorage
unit can be controlled and thereby reduce the use of an
extra oral appliance which requires patient cooperation.

Biomechanical considerations serve not only to explain the
effect of an orthodontic appliance but also to detect side
effects of therapy and to assist in planning strategies for the
avoidance or therapeutic exploitation of these side effects.
Efficient orthodontic treatment requires that sound
treatment plans be carried with sound mechanical plans.Main Menu

‘V’ BEND MECHANICS
Appliances are being refined and will continue to improve
with the passage of time. This is good, but the danger lies
with the individual who fails to recognize that the
refinement of appliances may reduce the physical effort
put forth in treatment, but will not eliminate the need for
the Orthodontist to think, understand and apply basic
principles of mechanics to his treatment. This means that
regardless of how well we understand mechanics and
regardless of how much the appliance is refined, we are
dealing with a biologic environment whose variation in
response will continue to challenge the Orthodontist in
many ways.

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CENTERED AND OFF-CENTERED ‘V’ BENDSCENTERED AND OFF-CENTERED ‘V’ BENDS
If the bend is located OFF-CENTRE, there will be a
long segment and a short segment. When the short
segment is engaged into the bracket or tube, the long
segment will point in the direction of the force
produced on the tooth that will receive the long
segment. The short segment points in the opposite
direction of the force that will be produced on the
tooth that receives the short segment.
Fig.1 Fig.2
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If the bend is in the CENTRE, there no longer exists a long
or short segment. Therefore, no force is produced because
when the wire is engaged in the brackets, forces cancel
each other leaving pure moments - not a bad situation
when we wish to parallel roots following space closure, or
rotate teeth equally and oppositely.
Fig.3 Fig.4

FORCES AND MOMENTSFORCES AND MOMENTS
Whenever a force passes through the Cres of a body, there
is no moment produced and therefore no rotational
tendency. However, when a force acts away from the Cres,
a moment is produced and a rotational tendency occurs.
The moment produced is equal to the perpendicular
distance from the line of force to the Cres of the tooth.
Cres of a tooth Moment of a force
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CUE-BALL CONCEPTCUE-BALL CONCEPT

No left or right rotation is produced when the force is
applied through the centre of the cue ball. A force off-
centre causes the cue ball to rotate as well as move
forward in a straight line.
Force thro’ Cres- no rotation Force off-centre
- rotation + forward
movement
Equal and opposite
forces (couple)
-pure rotation
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DIFFERENTIAL TORQUEDIFFERENTIAL TORQUE
When the arch wire with the tip back bend is tied into
the brackets and tied back at the molar tubes different
magnitudes of moments are produced which are
referred as differential torque.
But, again that is not all that is taking place. There are
other forces and moments taking place at the same time,
which will produce molar extrusive forces, incisor
intrusive forces, molar mesial root torque significantly
larger than the incisor lingual root torque, and molar
lingual crown torque. Main Menu

Molar – Extrusion + mesial root tip + lingual crown toque
Incisor – Intrusion + labial crown torque
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STATIC EQUILIBRIUMSTATIC EQUILIBRIUM

Understanding the concept of equilibrium is crucial to
understand the mechanics of tooth movement.
Static equilibrium is a valuable application of Newton’s laws
of motion to the analysis of force system delivered by
orthodontic appliances.
Equilibrium is defined as “a state of balance between or
among the opposing forces, resulting in the absence of
acceleration.” The concept has its basis in Newton’s first and
second law of motion.
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1.   LAW OF INERTIA:
“A body at rest remains at rest and a body in motion
remains in uniform motion in a straight line unless acted upon
by the external force”.

2.   Law of acceleration:
“The acceleration of body is directly proportional to the
applied force and is in the direction of the straight line in which
the force acts.”

3.   Law of action and reaction:
“For every action there is always opposing and equal
reaction.”
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Three requirements are automatically fulfilled whenever static
equilibrium is established.
1.The sum of all vertical forces must equal zero. This is why we
must deal with extrusive components of force during overbite
correction. Since we cannot eliminate these forces, we must learn
to control them.
2.The sum of all horizontal forces must equal zero. This is why
we cannot correct a unilateral cross bite with a single
horizontal force.
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3.The sum of moments acting around any point must also
equal zero.
A Symmetric V- bend creates equal and opposite
couples at the brackets with no forces, because the
associated equilibrium forces at each bracket are equal
and opposite, and therefore cancel each other out.
A symmetrical V-bend is not necessarily half way
between two teeth or two groups of teeth. If two teeth
are involved but one is bigger than the other (e.g. a
canine and lateral incisor), equal and opposite moments
would require placing the bend closure to the large
tooth, to compensate for the longer distance from the
bracket to its centre of resistance
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An Asymmetric V-bend creates a greater moment on one
tooth or unit than the other. As the bend moves toward
one tooth, the moment on it increases and the moment on
the distant tooth decreases.
When the bend is one-third of the way along the inter
bracket span, the distant tooth receives only a force, with
no moment. If the v-bend moves closer than the one-third
point to one of the teeth, a moment in the same direction
is created on both teeth, instead of opposite moments
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Step bend is a combination of two off-centre bends with
short sections bent in opposite directions.
It creates two couples in the same direction
regardless of its location between the brackets. The
location of a V-bend is a critical variable in
determining its effect, but the location of a step bend
has little or no effect on either the magnitude of the
moments or the equilibrium forces.
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DETERMINATE Vs INDETERMINATE FORCE SYSTEMSDETERMINATE Vs INDETERMINATE FORCE SYSTEMS

Force systems can be defined as statically determinate,
meaning that the moments and forces can readily be
discerned, measured and evaluated, or as indeterminate.
Statically indeterminate systems are too complex for
precisely measuring all forces and moments involved in the
equilibrium Typically, only the direction of net moments
and approximate net force levels can be determined.
Determinate force systems, therefore, are advantageous in
orthodontics because they provide much better control of
the magnitude of forces and couples.
For all practical purposes, determinate systems in
orthodontics are those in which a couple is created at one
end of an attachment, with only a force (no couple) at the
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other. This means that a wire that will serve as a spring
can be inserted into a tube or bracket at one end, but must
be tied so that there is only one point of contact on the
other. When the wire is tied into a bracket on both ends, a
statically indeterminate, two couple system is created.

In orthodontic applications, one couple systems are
created in two conditions
1) Cantilever spring applications
2) Auxillary intrusion / extrusion arches
Molar – Intrusive force 50 g
Buccal crown torque
Mesial crown tip
(20 mm x 50 g = 1000 g-mm.)
Canine – Extrusion 50 g L
Lingual crown torque
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Two couple systems are created when intrusion utility arch is
tied into the incisor brackets as well as in transpalatal and
lingual arches.
Molar – Extrusion
Distal crown tip
Incisors -Intrusion
Labial crown torque
However the precise magnitude of
forces and couples cannot be known.
The basis of orthodontic treatment lies in the clinical
application of biomechanical concepts, which explain the
mechanism of action of orthodontic appliances. If these
biomechanical principles are applied to mechanotherapy,
not only may treatment time be reduced, but one could also
develop more individualised treatment plans for achieving
more predictable results. Cognitive application of
biomechanical concepts in the delivery of orthodontic care
can be beneficial in achieving efficient and effective
treatment. Main Menu

INTRODUCTIONINTRODUCTION
The three dimensional control of single teeth exhibiting severe positional
anomalies is a common challenge for the Orthodontist. A through clinical
diagnosis, careful treatment planning and appropriate appliance design is
necessary if successful outcome is to be achieved. Super elastic wires, elastic
threads and chain elastics have made the straight-wire appliance technique
very efficient for the correction of minor discrepancies. In contrast, the
segmented arch approach enables the orthodontist to generate well-defined
force systems that lead to highly controlled tooth movement. By segmenting
the appliance, an optimal force system can be applied to the active unit and to
the tooth to be moved, while the reactive forces are transferred to an anchorage
unit consolidated to withstand the undesirable forces. Correction of positional
discrepancies of single teeth is highly predictable, and any undesirable side
effects can be minimized. A low load-deflection rate enables the clinician to
deliver relatively constant forces and moments throughout the orthodontic
treatment, and allows tooth movement to proceed without frequent monitoring
and appliance adjustments. When maximum control of tooth movement is
desired, rectangular loops are the first choice for intra-segmental alignment,
due to their simplicity and large range of activation.
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When a straight wire is inserted into the brackets of malaligned teeth an odd
combination of forces and moments, such as an inconsistent force system
where moments are desirable yet forces detrimental, or vice-versa may develop.
Minor bends, such as step and ‘V’ bends, have been recommended with the
purpose of delivering the desired moment-to-force ratio on one side of the
bend. As the wire is always in a state of equilibrium, a balancing force system
acts on the other side of the bend. The creative bend involves only a minimum
amount of wire. Consequently, the spring-back and the activation range of the
bends are low, and the load-deflection rate high. In addition, the slightest
change in tooth position will lead to change in the desired force system. Only
minor discrepancies, therefore, should be corrected by using such bends.
SECOND ORDER BENDFIRST ORDER BEND
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The simultaneous correction of major discrepancies in three planes of space
requires an appliance that delivers a specific force system, which is relatively
constant and within a large range of activation. This can be obtained by loops
individually designed for the correction of specific irregularities.
ADVANTAGES OF SEGMENTED ARCH TECHNIQUE:
1. Segmentation offers the possibility of using multiple wire cross-sections
and materials within the same arch. This permits a great deal of versatility
in the selection of proper wire for a given tooth movement for an optimal
force.
2. Segmentation increases the distance between points of force application.
This lowers the load-deflection rate of the wire.
3. The active and reactive forces occur between segments so that the forces
can be distributed over many teeth.
4. Alignment can be achieved without initial flaring and hence round
tripping of teeth can be minimized.
5. A segmented arch can be prefabricated so as to not only increase office
efficiency but also give greater accuracy to the Orthodontist in force
control. The force levels can be easily calibrated.
6. All segments need not be routinely replaced as treatment progresses
thereby wire duplication can be kept to a minimum.
7. Early visits may be longer because of the larger number of arch wires
placed at the start of active treatment in the segmented arch technique
hence improving clinical efficiency. Main Menu

ADVANTAGES OF A LOOP:
1. The inconsistency of the force system developed by a
SWA can be avoided by using loops.
2. The addition of wire length into the appliance while
maintaining the wire size reduces the load-deflection
rate.
3. Greater constancy of force.
4. Since the distribution of the wire with respect to the
bracket determines the moment-to-force ratio, and
tooth movement is produced by the deactivation of the
loop itself, friction is not an issue.
5. It is possible to design a loop in such ways that forces
and moments are dissociated to generate many
combinations of moment and force.
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TYPES OF LOOPS USED FOR INTRA-SEGMENTAL
ALIGNMENT:
1. Vertical loop
2. L-loop
3. T-loop
4. Rectangular loop


THE RECTANGULAR LOOP
For a given tooth movement, only one combination of force and moment
can be considered correct. The active components of the orthodontic
appliance must be designed in such a manner that they posses a low load-
deflection rate and a frictionless force application system.
CHARACTERISTICS:
1. Can be used for first, second and third order corrections
2. Since the loop is inserted in at least two brackets, it represents a
statically indeterminate force system.
3. The clinician can determine the moment-to-force ratio delivered to
the active unit.
4. All combination of moments and forces can be produced. The
direction of moment generated at the loop depends on the point of
force application in relation to the horizontal dimension of the
box.
5. The point at which the moment changes sense is called ‘point of
dissociation’. At this point, no relationship exists between moment
and force. The localization of this point depends on the length as
well as the dimension of the wire.
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A B C
A B C
6.The desired combination of moments and forces can be reached by
choosing different points of force application, controlling the horizontal
dimension of the loop or by angulating the horizontal arm of the loop.
7.The rectangular loop has a low load-deflection rate and a large range of
activation.
8.Combining wires of different dimension can produce composite loops. For
correcting major rotations or tipping, the combination loops are
advantageous as their working range is large.
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FABRICATION OF ‘R’ LOOP:
Fabrication of R loop for the 2nd
premolar correction:
Step 1: Measure the distance between mesial of molar tube and the distal of 2nd
premolar bracket (D)
Step 2: The ‘R’ loop is fabricated using the formula A = B = C each being equal
to half of D.
Note: Distance D for any tooth is measured from the distal of the bracket (of the
tooth to be corrected) to the mesial of the bracket (of the tooth distal to it).
A
B C
A = B = C
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VARIOUS ACTIVATIONS:
‘R’ loop can be effectively used for the corrections of:
Rotation
First order discrepancies
Second order discrepancies
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COMPOSITE LOOPS:
Differences between the stiffness of the active and
reactive units can be varied producing Composite loops.
E.g., Combining 0.017 x 0.025” and a 0.018” TMA wires
Depending on the point of welding, this will displace
the point of dissociation from the geometrical center of
the loop. When correcting major rotations or tipping, the
composite loops are advantageous as their working
range is large. They can also be designed for a correct
moment-to-force combination.
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‘T’ LOOP
Characteristics:
1. Made of 0.017”x 0.025” TMA wire
2. No side determination be made, however, the alpha leg (anterior leg) of
the T loop is longer than beta leg (posterior leg) by 1mm to compensate
for the difference of height between the bracket of the canine and the
auxillary tube of the molar.
3. The central position of the loop can be calculated by the formula
D = L- A
2
Where, D = distance from either the molar auxillary tube or
the canine to the center of the loop
L = distance from the molar auxillary tube to the
canine vertical tube (or center of the bracket)
A = activation of the spring
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αβ
10 mm
5 mm
2 mm
4 mm
ALPHA
(ANTERIOR) SEGMENT
BETA
(POSTERIOR) SEGMENT
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PREACTIVATION CHECK LIST:
1.   Check the neutral position of the loop (0 mm).
2.   Determine the amount of activation.
3.   From the center of the T, mark distance D on both arms
of the spring. Place a vertical bend gingivally 5mm
anterior to the mark on the anterior leg.
4.   Check for comfort and passivity and necessary
adjustments are made to achieve the same.
5.   Placement of Alpha and Beta preactivation bends:
Preactivation bends are placed at six points in the spring
•Bend 1: is at the mesial loop of the T loop. A light wire
plier is placed between the looped gingival arms of the T-
spring with the round beak along the inside of the loop,
which is then opened approximately 300
.
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1
β α
2
3 4
65
•Bend 2: is placed at the distal loop of the T-spring and the
loop is opened by 300
as was done for bend 1.
•Bend 3: is placed 2mm mesial to the anterior leg of the T-
loop, which is bent approximately 250
to the base arch wire.
•Bend 4: is placed 2mm distal to the posterior leg of the T-
loop, which is bent approximately 250
•Bend 5: is made 2mm mesial to the anterior leg of the T-loop,
which is bent approximately 250
•Bend 6: is made 2mm distal to the posterior leg of the T-loop,
which is bent approximately 250
Note: all bends are made around the round beak of the plier.
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Perform trial activation: grasping the spring with two pliers, one just
anterior to bend 5 and other just posterior to bend 6, the activation force
is applied to the spring. The spring is then checked on the template for
superimposition.
Anti-rotation bends: are placed after the trial activation. Anti-rotation
bends are placed at 4 different points, 2 at alpha position and 2 at beta
position.
•Bend 1: is made by placing the plier along the gingival portion of the T-
loop approximately 1 mm from the mesial loop. The lower portion of the
T-loop is then pulled to the buccal so that it makes an angle of 250
to its
original position.
•Bend 2: is placed 2 mm mesial to the anterior leg of the T-loop and the
loop bent approximately by 250
in the same manner as the first bend.
•Bend 3: similar to bend 1, approximately 1 mm mesial to the distal loop.
•Bend 4: similar to bend 2, approximately 2 mm distal to posterior leg.
The number of anti-rotation bends may be based on clinical judgement.
Additionally lingual elastics can be used to prevent rotation of the
canines.
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ANTIROTATION BENDS
1
βα
2
3 4
βα
βα
βα
βα
βα
βα βα
OCCLUSAL VIEW
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ATTRACTION SPRINGTMA 0.017X0.025” R CENTERED
∆
mm
FH
gm
FV
gm
Mα
gm- mm
Mβ
gm- mm
Mβ
gm/mm
Mα/F
mm
Mβ/F
mm
0.0 0.0 4.9 1361.9 -1410.4 00.0 00.0 00.0
0.5 28.4 5.4 1464.0 -1501.8 55.1 52.0 53.4
1.0 50.1 5.5 1556.1 -1583.7 43.6 31.2 31.7
1.5 72.1 6.1 1641.1 -1663.4 44.1 22.8 23.1
2.0 94.7 6.6 1724.1 -1740.3 44.8 18.2 18.4
2.5 116.7 7.2 1801.2 -1815.7 43.7 15.4 15.6
3.0 140.7 8.0 1875.8 -1887.1 47.8 13.3 13.4
3.5 162.7 8.6 1943.5 -1955.1 45.0 12.0 12.0
4.0 185.0 9.4 2009.5 -2019.9 44.6 10.9 10.9
4.5 208.8 10.1 2074.9 -2085.9 46.9 9.9 10.0
5.0 232.9 10.9 2131.2 -2145.6 49.4 9.2 9.2
5.5 257.5 11.6 2187.5 -2206.3 48.9 8.5 8.6
6.0 281.8 12.3 2243.8 -2261.6 48.6 8.0 8.0
6.5 307.3 12.9 2293.8 -2316.6 50.7 7.5 7.5
7.0 333.4 13.6 2348.8 -2367.6 52.0 7.0 7.0
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∆ - ACTIVATION
FH
– HORIZONTAL FORCE
FV
– VERTICAL FORCE
Mα - ALPHA MOMENT
Mβ - BETA MOMENT
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OVERBITE
INTRODUCTION
The deep bite can be defined by the amount and percentage of overlap of lower
incisors by the upper incisors. The overbite may be calculated as a percentage of the
clinical crown height of one of the mandibular central incisors.
Fleming showed that between 9 and 12 years of age the overbite is usually
increasing, whereas in the period between age 12 and adulthood it is decreasing. No
sex differences were noted. More over, the amount of vertical overbite is closely
associated with some craniofacial dimensions. The study also determines that ramus
length is one of most important dimensions associated with the amount of overbite.
Correction of dental overbite can be achieved by:
1. Genuine intrusion of the anterior teeth
2. Extrusion of posterior teeth
3. Combination of anterior intrusion and posterior extrusion.
4. The skeletal vertical dimension, the AB relationship, the occlusal plane cant
desired after treatment, growth and muscular factors, dictate which method
is used to correct the deep bite.
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According to Burstone, there are six principles
governing deep overbite correction by intrusion:
1. Use of optimal magnitude of force and the delivery of
this force constantly with low load-deflection rate
springs.
2. Use of point contacts in the anterior region.
3. Position of force-careful selection of the point of force
application with respect to the Cres of all the teeth to be
intruded.
4. Selective intrusion based on anterior tooth geometry.
5. Control over the reactive units by formation of a
posterior anchorage unit.
6. Inhibition of the eruption of the posterior teeth and
avoidance of undesirable eruptive mechanics.
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BIOMECHANICS OF INTRUSION:
An intrusive force through the center of resistance of
any tooth will intrude the tooth without producing any
labial or lingual rotation of the tooth being intruded.
The center of resistance of anterior teeth can be
estimated to be located near the geometric center of
their roots. Ideally while intruding, we want the
intrusive force through the Cres of the tooth or group of
teeth to be intruded. If the intrusive force is labial to
the center of resistance, a moment is produced which
flares the crowns labially while the roots move
lingually.
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To prevent this flaring, the intrusion arch is tied back posteriorl
Patients presenting with procumbent incisors must be
handled somewhat differently during intrusion, because
the intrusive force is farther from the Cres,
a much greater
moment occurs and much more lingual root movement
occurs. This is contraindicated because the roots are too
far lingually placed initially.
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This situation can be handled in one of the two ways:
1. One approach is to retract the anterior teeth first and
produce more upright axial inclinations and then proceed with
intrusion.
2. The second approach is to apply the vertical force lingual
to the center of resistance either with a continuous intrusion
arch or a three-piece intrusion arch.
Indiscriminate leveling with a continuous arch or with a
sectional wire can produce undesirable side effects. Many
times the overbite is corrected not because intrusion has been
accomplished, but because extrusion and altering the cant of
the occlusal plane has occurred. If this happens, it may be
impossible to achieve intrusion through intra-oral mechanics.
accomplished, but because extrusion and altering the cant of
the occlusal plane has occurred. If this happens, it may be
impossible to achieve intrusion through intra-oral mechanics.
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According to Vanden Bulcke:
1. For an anterior segment comprising two central
incisors, the Cres was located on a projection line
parallel to the mid-sagittal plane on a point situated on
the distal half of the canines.
2. For an anterior segment comprising four incisors, the
Cres was located on a projection line perpendicular to
the occlusal plane between the canines and first
premolars.
3. For a rigid anterior segment that included the six
anterior teeth, the Cres was situated on a projection
line perpendicular to the occlusal plane distal to the
first premolar.
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Control of reaction forces exerted by intrusion arches:
The best control of the anchorage unit is
accomplished by minimizing the forces used for
intrusion. The largest effect upon the anchorage unit
will be a result of the moment produced by the
intrusive force, which is large because of the large
moment arm present.
Two significant side effects are produced:
First side effect alters the plane of occlusion of the
buccal segments. It is caused by the moment
produced by the intrusion arch on the buccal
segments. In the maxilla, the plane of occlusion
steepens and in the mandible it flattens.
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To minimize this side effect several steps can be taken.
1. Keep the forces of intrusion as low as possible.
2. Have as many teeth as possible incorporated in the anchorage
unit.
3. Do as much retraction initially as possible to decrease the
length of the moment arm.
4. An occipital headgear with the force directed anterior to the
Cres of the posterior anchorage unit can negate the moment.
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Second side effect is produced by equal and opposite extrusive force
upon the buccal segments. This force is acting at the auxillary tube
of the molar, which is buccal to Cres of molar and / or buccal
segment.
This force will produce a moment on the molar to tip buccal segment
lingually with the roots moving buccally. This side effect is prevented by
the use of lingual arch, which maintains the axial inclinations and the
arch widths.
RELAPSE AFTER DEEP BITE CORRECTION:
Changing the lower anterior face height in adult patients due to extrusion
of molars is not an advisable clinical procedure. According to some
authors, intrusion of lower incisors may not be the ideal treatment with
respect to stability. Some claim that the establishment of an appropriate
inter incisal angle is advisable in an attempt to prevent deep bite relapse.
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INTRUSION ARCHES
PARTS OF AN INTRUSION ARCH ASSEMBLY:
The posterior anchorage unit
The anterior segment
The intrusion arch itself
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CONTINUOUS INTRUSION ARCH:
Is fabricated from 0.017” x 0.025” / 0.016” x 0.022” TMA
wire. The 0.018” round TMA stops can be welded or
helices may be bent in the wire mesial to the molar tubes,
which serve as tiebacks to prevent flaring of the teeth
undergoing intrusion. A gingival step is placed mesial to
the canine bracket to avoid this bracket upon activation of
the intrusion arch. The step is made no greater than
required to attach the intrusion arch anteriorly without
canine interference. Anteriorly, the intrusion arch is tied to
the wings of the brackets of the incisors, not into the slot
of the bracket itself.
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THREE-PIECE INTRUSION ARCH
Parts:
1. The posterior anchorage unit
2. The anterior segment with a posterior extension
3. The intrusion cantilevers
4. An elastic chain.
The anterior segment is bent gingivally distal to the laterals,
then bent horizontally, creating a step of approximately 3 mm.
The distal part extends posteriorly to the distal end of the
canine bracket, where it forms a hook. This anterior segment
should be made of 0.019” x 0.022” / 0.017” x 0.025” SS wire.
The intrusion cantilevers are fabricated from 0.017” x 0.025”
TMA wire. The wire is first bent gingivally mesial to the
molar tube (and then helix is formed if SS wire is used). On
the mesial end of the cantilever, a hook is bent through which
the intrusive force can be applied to the anterior segment. The
cantilever is then activated by making a bend mesial to the
helix at the molar tube, and then cinched back.
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An elastic chain can be attached to the hook of the
anterior segment to the molar tube to redirect the forces
in a posterior direction.
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CANINE INTRUSION
A cantilever from the auxillary tube of the molar tied
to the canine bracket as a point contact can be used.
Because the intrusive force is applied labial to the
Cresof the canine, the canine can flare labially
during intrusion. To prevent this, the cantilever is
bent to the lingual to give a lingual force.
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FORCE VALUES FOR INTRUSION
TOOTH MOVEMENT FORCE (gm)
INTRUSION PER SIDE TOTAL IN MIDLINE
2 UPPER CENTRAL INCISORS 15 – 20 30 –40
4 UPPER INCISORS 30 – 40 60 – 80
6 UPPER ANTERIORS 60 120
2 LOWER CENTRAL INCISORS 12.5 25
4 LOWER INCISORS 25 50
6 LOWER ANTERIORS 50 100
2 UPPER CANINES 25 -
2 LOWER CANINES 25 -
MOLAR EXTRUSION 60 – 100 120 – 200
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ROLE OF FRICTION IN SLIDING MECHANICS
Friction is the relative roughness of two surfaces in contact. It is the force that resists
the movement of one surface past another and acts in a direction opposite the
direction of movement. When two surfaces in contact slide or tend to slide against
each other, two components of total force arise. One of these is the frictional
component, which is parallel in direction to the intended or actual sliding motion
and opposes the motion. The other component, known as the normal force, is
perpendicular to one or both contacting surfaces. During canine retraction, the
relationship of the bracket to the wire changes at different stages of treatment.
Therefore, the magnitude and direction of the associated frictional and normal
components of contact forces will also vary with time. Once movement has been
initiated, friction does not depend on the surface areas in contact or on the velocity of
their relative motion.

The coefficient of friction can be described mathematically as the frictional force that
resists motion, divided by the normal force that acts perpendicular to the two
contacting surfaces. There are two coefficients of friction for a material. One is the
coefficient of static friction, which reflects the force necessary to initiate movement,
and the other is the coefficient of kinetic friction, which reflects the force necessary
to perpetuate this motion. It takes more force to initiate motion than to perpetuate it.

Therefore when sliding mechanics is used some of the applied force is dissipated as
friction, and the remainder is transferred to supporting structures of the tooth to
mediate tooth movement. Maximum biological tissue response occurs only when the
applied force is of sufficient magnitude to adequately overcome friction and lie
within the optimum range of forces necessary for movement of the tooth
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Variables affecting frictional resistance during tooth movement
A.   Physical
1.   Arch wire
a.   Material
b.    Cross-sectional shape/size
c.    Surface texture
d.    Stiffness
2.   Ligation of arch wire to bracket
a.   Ligature wire
b.    Elastomerics
c.    Method of ligation
3.   Bracket
a.   Material
b.    Manufacturing process
c.    Slot width and depth
d.    Design of bracket
e.   First-order bend
f.      Second-order bend
g.    Third-order bend
4.   Orthodontic appliances
a.   Interbracket distance
b.    Level of bracket slots between adjacent teeth
c.    Forces applied for retraction
B. Biological
1.   Saliva
2.   Plaque
3.   Acquired pellicle
4.   Corrosion
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WALKING OF THE CANINE
Sequence of canine movement during retraction with
sliding mechanics is as follows,
1. The normal component of force (N) and the frictional
resistance to movement (f).
2. The bracket tips until the diagonally opposing corners of
the bracket contact the wire.
3. The wire deflects producing a couple to upright the tooth.
This emphasis why elastomeric chains used for canine
retraction should not be changed frequently.
Thus the canine is retracted bodily by alternate
movements of tipping and root uprighting.
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BYPASS ARCHES MULLIGAN’S BYPASS ARCH
Is fabricated from 0.016” stainless steel wire. Bracketing the anterior teeth may be
delayed, or the anterior section of the wire can be stepped up to avoid interference.
An anchor bend is placed in front of the molar, second bicuspids are sometimes
temporarily not bonded to increase the distance and therefore the differential torque.
Toe-in bends or lingual elastics are placed to offset the tendency for mesiolingual
rotation of the molars.
The tip-back bend is an off-center bend hence produces two unequal moments. The
larger moment (crown distal and root mesial) lies at the bracket / tube containing the
short segment. The moment at the bracket / tube containing the longer segment may
be clockwise, counter clockwise or non-existent. Whatever be the moment at the long
segment, the net effect is dominated by the short segment and is always crown distal
and root mesial.
A power chain is tied directly from the molar to the cuspid, while the second bicuspid
is tied individually with an ‘O’ ring. This allows a greater range of force. The anchor
unit should remain relatively upright, while the non-anchor unit should undergo
tipping until arch wire binding occurs. Once binding occurs, the roots will respond to
the moments produced by the arch wire, until binding stops and crown movement is
resumed. As the cuspid continues to move distally, the bend automatically
approaches the center of the wire, until finally when the extraction site is closed, the
bend is centered.
As the off-centered bend moves towards the center during space closure, the
differential torque begins to gradually disappear, and becomes equal and opposite
torque when the bend is finally centered. Main Menu

BURSTONE’S CANINE-TO-CANINE BYPASS ARCH
Uses,
1. Prevent rotation
2. Actively derotate teeth when there is sufficient space
3. Alter arch width
4. Eliminate side effects from vertical forces.
A rigid wire, preferably 0.021” x 0.025” SS or at least 0.017” x 0.025” SS, is
stepped gingivally 3 to 4 mm mesial to the canine and around the incisors.
This allows for simultaneous bracketing and alignment of the incisors as
the canines are retracted. The vertical step down also incorporates
additional wire length, which allows the step to be bent lingually or
labially, depending upon patient comfort and the need to keep the anterior
wire away from the incisors as the canines retract. In some patients, no
gingival step is made if the incisors are not to be bracketed until canine
retraction is completed. Gradual first order reverse curvature is placed to
produce moments rotating the canines distal-out.
The amount of wire length distal to the canines is determined by the
amount that the canines must be retracted to relieve the anterior crowding.
The increased length provides a means of extending the segment anteriorly
to avoid contacting the incisors during retraction. To avoid lip irritation and
patient discomfort, the wire should only be 1.5 mm labial to the incisors.
This distance can be adjusted each visit by advancing the wire as the
canines retract.
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REFERENCESREFERENCES
Burstone C.J. ‘Rationale of the segmented arch’.
Am.J.Orthod 48:805-822,1962

Burstone C.J. ‘The mechanics of the segmented arch
echnique’.Am.J.Orthod 36:99120,1966

Burstone C.J. ‘Segmented arch approach to space
closure’. Am.J.Orthod 82:361-378,1982

Smith R.J.,Burstone C.J.‘Mechanics of tooth movement’.
Am.J.Orthod 85:294-307,1984

Nelson K.R.,Burstone C.J.,and Goldberg A.J. ‘Optimal
welding of orthodontic wires’.
Am.J.Orthod 92:213-223,1987
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R. Issacson ‘Activating a 2 X 4 Appliance’
Am.J.Orthod 63(1): 17-24,1993

Burstone & Koeing: ‘Creative wire bending’-Force system
from step and V bends. Am.J.Orthod 93:
59-67,1988

T. F. Mulligan ‘Common sense mechanics’ JCO’
Sept.79-Dec 80

Lindaeur S.J., Issacson R.J. ‘One couple system’
Sem.Orthod 1:12-24,1995

Kula K.,Philips C.,Gibilaro A. and Proffit W. R. ‘The
effect of ion implantation of TMA archwires
on the rate of orthodontic sliding space
closure’. Am.J.Orthod 114:577-585,1998
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Issacson R.J. ‘Two couple orthodontic appliance
system’-Torquing arches. Sem.Orthod
1:31-36,1995

Rebellato J. ‘Two couple orthodontic appliance system’-
transpalatal arches. Sem.Orthod 1:44-

Siatowski R.E. “Continuous arch wire closing loop
design,optimization and verification’- Parts I
and II Am.J.Orthod 112:484-495,1997

Burstone. C.J. ‘ Mechanics of segmented arch
technique’.

Graber and Vanersdall. ‘Current principles and
techniques’.
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Nanda R. ‘Biomechanics in clinical orthodontics’.

Marcotte M.R. ‘Biomechanics in orthodontics’.

Proffit W.R. ‘Contemporary Orthodontics’.
Main Menu

Thank You

BIOMECHANICS FORCES IN ORTHODONTICS

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