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3. INTRODUCTION
Understanding the biomechanics is
essential to determine the working of
an appliance system and more
importantly the undesirable changes
associated with it.
This seminar tells about the basic
concepts of biomechanics and their
importance in clinical application
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4. FLOW CHART OF THE PRESENTATION
DEFINITION OF THE BASIC CONCEPTS
PAE
Various
stages
EXTRA
ORAL
Head gears
COMMON SENSE MECHANICS
MOLAR CONTROL
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BEGG
Various
stages
5. F
O
R
C
E
DEFINED as a load applied to an object that will
tend to move it to a different position in space
. Forces may be treated as vectors and are conveniently
represented as arrows. A force vector is characterized by
four features: magnitude, point of application, line of
action, and sense.
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6. The parallelogram method for resolving a force into vertical
and horizontal components.
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7. F
O
R
. The parallelogram method of determining the resultant of
two forces with a common point of application.
C
E
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8. Couple force
A, Two equal and opposite, parallel, forces form a couple. B, The
translational effects of the forces cancel each other out, but the
moments of each force combine. The result is a moment with no net
force.
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9. CENTER OF RESISTANCE
Center of mass is a point through which an
applied force must pass for a free object to
move linearly without any rotation.
The center of a mass is for a generic free body.
Tooth – not generic free- periodontal support.
The analogus to center of mass for a restrained
body is CENTER OF RESISTANCE
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10. CENTER OF ROTATION
The point around which rotation
actually occurs when an object is
being moved
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11. Defined as the rotational tendency when force is
applied away from the center of resistance
M
O
A force acting at a distance
Mathematically given as M = f x d
Where M is the moment
M
f is the force
E
And d is the perpendicular distance of the line of
action to the center of resistance
N
T
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12. F
Direction of a moment
O
R
C
E
The direction of the moment of a force can be determined by
continuing the line of action around the center of resistance
towards the point of origin.
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13. The force in A, passing
through the center of
resistance, will result in
translation of the tooth. The
force in B, at the bracket,
will also translate the tooth
but, in addition, will cause a
rotation because of the
moment created at the
center of resistance.
Teeth move according to the forces and moments acting at the center
of resistance. Most orthodontic forces are applied to the tooth at the
bracket. Understanding the relationship between force systems at the
bracket and the center of resistance requires using the rules for
equivalent force systems.
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14. Force applied on a tooth
Crown moves more than root
To maintain the inclination
Of the tooth
Overcome the moment
Created by the force applied
to the crown
Counter moment
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15. To maintain axial inclination
Apply the force close to
the center of resisitance
Create a 2nd moment
In the direction opposite
to the first
Practical difficulty
Counter moment
Power arm
Tooth remain upright
And move bodily
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16. M/F (moment to force ratio) is the relationship
between the force and the counter balancing
couple that determines the type of tooth movement .
Various tooth movements
Uncontrolled tipping
Controlled tipping
Translation
Root uprighting
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17. Consider the moment created when force is applied Mf and the
counter balancing moment generated by the couple within the
bracket Mc
Mc/Mf = 0 –Pure tipping Crot and cres same,thus the
tooth rotates around the Cres
0 < Mc/Mf >1- Controlled tipping – Crot displaced away
from Cres – crown and root move in the same direction
Mc/Mf = 0 – Bodily movement – equal movement of crown
and root
Mc/Mf > 1 Torque – root apex moves further than the
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19. MOMENT TO FORCE RATIO FOR VARIOUS
TOOTH MOVEMENTS
M/F
5:1
Uncontrolled tipping
M/F
8:1
Controlled tipping
M/F
10 : 1
Translation
M/F
>10 : 1
Root movement
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20. Bracket system
P
A
A rectangular wire in
a rectangular slot
TORQUE
Generate the moment
of a couple necessary
to control root
position
E
Torque acting as the
counter moment
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21. Bracket system
P
TIP
In the PAE bracket system,
the tip incorporated into the
bracket acts as the counter
moment in the mesio distal
direction
A
E
This prevents the tipping
of the tooth in the mesio
distal direction
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22. Bracket system
P
Bracket width and interbracket span
The width of the bracket
on a tooth determines the
length of the moment arm
for the control of the
mesiodistal root position
A
E
Inter bracket span increases
Increase in the length of the wire
Increased flexibility
Decreased forces
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23. Principle of power arm
The line of action of the force passes through the center
of resistance. This tooth will translate, even though the
point of attachment to the tooth is at the bracket.
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24. A
L
I
N
Lingually malposed premolar
Aligning wire engaged
Bucally directed simple tipping
First order angular displacements
Of the adjacent teeth
G
To counteract
I
N
G
Decrease the magnitude
of the force
Broad distribution of
Responsive force
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25. A
L
I
N
Canine tip
When increased - during aligning there is a
tendency for the canine to be thrown forward
- tends to deepen to the bite
To counter act
G
Reduce the canine tip (MBT)
I
Placement of canine lace back
N
G
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26. L
E
V
E
Arch leveling
Reverse curve of Spee. The
vertical forces cancel out in the
manner shown, but moments
produced at either end of the
archwire result in torques on the
incisors and molars (anterior
lingual root torque or labial crown
torque; posterior mesial root torque
or distal crown torque).
L
I
N
G
Since intrusion is placed on the incisor segment, and
because the molars then become the reciprocal teeth, they
incur eruptive forces. Since extrusive forces acting through
the molar tubes usually result in lingual crown torque on the
molars, we have the potential for lingual crown movement
(lingual "dumping").
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27. L
Highly placed
canine
E
Continuous arch
wire
V
E
Intrusive force on
lateral greater than
the extrusive force
on canine
L
I
N
G
Engage a continuous
wire only after
reasonable aligning of
the anterior segment
excluding canine
Lateral intrusion rather
than canine extrusion due
to the increased root
length of canine
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28. Round wire with reverse curve of Spee
Lower premolars extruded
B
I
T
E
O
P
E
N
I
N
G
Tipping of the lower molar
Forward tipping of the lower incisors
To counteract
Cinched back
Roots of the lower incisor thrown forward
Forward mvt.of lower In.
Forward mvt of lower molar
To counteract
Class III Elastics
Eruptive forces on lower In. and upper molars
To counteract
Highwww.indiandentalacademy.com
pull head gear or extractions
30. Banding of the second molars
B
I
T
E
O
P
E
N
I
N
G
Second molars being at a higher level
Extrusion of the first molars
Opening of the bite
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33. B
U
R
S
T
O
N
E
I
N
T
R
U
S
I
O
N
Segmented approach to
simultaneous intrusion
and space closure
. Comparison of force
system developed on
molar with identical 30
gm intrusive forces. A,
Perpendicular to the
occlusal plane. B,
Parallel to the incisor
long axis and lingual to
CR. Note reduction of
the moment on the molar
in B.
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34. B
U
R
S
T
O
N
E
I
N
T
R
U
S
I
O
N
As the intrusive force is applied
more anteriorly to the center of
resistance of the incisors, a positive
moment is created which tends to
move the root lingually, provided the
incisor is restrained from flaring
labially.
Forces acting on the teeth from an
intrusive arch. The effect on the
molar is extrusion and a negative
rotation (crown-distal-root-mesial).
The moment (M) is equal to the
intrusive force (FA) times the
distance (L) from the incisor to the
center of resistance of the molar.
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35. B
U
R
S
T
O
N
E
I
N
T
R
U
S
I
O
N
Basic mechanism for intrusion; posterior anchorage
unit, anterior segment in the four incisors, and an
intrusive arch. The intrusion arch is placed in the
auxiliary tube on the first molar attachment.
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36. B
U
R
S
T
O
N
E
I
N
T
R
U
S
I
O
N
.
. Intrusive arch has been placed at the level of the
incisors. A double rope tie prevents arch from
being displaced into the mucobuccal fold if a tie
is accidentally lost.
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37. B
U
R
S
T
O
N
E
I
Force system of appliance.Note that the posterior
N
T extension allows force to be directed through the center of
R
resistance of the incisor. No incisor tipping will occur.
U
S
A long posterior extension is used to protrusive lower
I incisors to prevent flaring. The hook at the intrusive section
O
is shown.
N
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39. T
H
R
E
E
P
I
E
C
E
A
R
C
H
A, Intrusive force through CR will intrude incisor
along line of action of this force. B, An intrusive
force perpendicular to the distal extension and
through CR will have the same effect as in A.
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40. T
H
R
E
E
P
I
E
C
E
A
R
C
H
Intrusive force can be directed
along long axis of anterior teeth
and applied lingual to CR. The
farther lingual the force, the
larger will be the moment acting
to tip the incisors lingually.
Direction of net intrusive force
through CR may be changed by
application of a small distal force.
The resulting intrusive force has a
direction parallel to the long axis
of the incisor and is distal to CR. .
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41. T
H
R
E
E
P
I
E
C
E
A
R
C
H
Diagrammatic representation of three-piece base arch.
The anterior segment extends 2 to 3 mm distal to the
center of resistance (CR) of the anterior teeth. Force
acts through center of resistance.
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42. T
H
R
E
E
P
I
E
C
E
A
R
C
H
Diagram of three-piece base arch and Class I elastic
stretched from maxillary first permanent molar to distal
extension of anterior segment. Class I elastics are
needed to redirect force parallel to the long axis of the
incisor.
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45. C
O
N
N
E
C
T
I
C
U
T
A
R
C
H
Force system created by CTA and high-pull headgear. CTA force
system (red) consists of intrusive force on incisors, extrusive force
on molars, and moment tipping molar crowns distally. Headgear
(blue) produces intrusive force on molars and moment allowing
distal root movement. Purple arrow represents combined distal
force of CTA and headgear on molars.
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46. C
O
N
N
E
C
T
I
C
U
T
A
R
C
H
Force system for incisor flaring. CTA is not cinched
back, and can be ligated directly into incisor brackets for
maximum flaring.
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47. C
O
N
N
E
C
T
I
C
U
T
A. Force system for incisor extrusion, with CTA is inserted into
molar brackets upside down. Vertical forces shown are ideal for
A correction of minor open bites. B. Open-bite patient before
R treatment. C. Mechanics shown in A used to close bite, with highC pull headgear added to prevent forward tipping of molars and
H augment intrusive force of CTA on molars.
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48. K
S
19 x 25 TMA with
closed U loop 7mm long
and 2mm wide
I
R
A
R
C
H
90 degree bend placed in the arch wire at the level of the U
loop.centered V bend creates equal and opposite
moment(red) that counter tipping moment(green) produced
by activation forces www.indiandentalacademy.com
49. K
S
I
R
A
Off center v bend 60 degree placed 2mm distal to the loop
This bend creates an increased moment increased molar
anchorage and intrusion of the anterior teeth.
R
C
H
20 degree anti rotation
bends distal to the U loop
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51. C
A
N
I
N
E
R
E
T
R
A
C
T
I
O
N
Individual canine retraction – friction mechanics
Initial controlled tipping of the tooth (m/f 8:1)
Force decay with time
Force level on the tooth decreases
M/f ratio is increased
Root uprighting
Walking of the canine
Do not change the power chain for 5 weeks ,let to
comlplete the root uprighting
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52. C
A
N
I
N
E
R
E
T
R
A
C
T
I
O
N
Lever arm adapted to
palatal vault and
bonded to lingual
surface of cuspid.
Extension soldered to
palatal bar, and
activation achieved
with buccal and
lingual Superelastic
coil springs.
Source: 1993 JCO: Modified Lingual Lever Arm Technique GERHARD KUCHER, MD, DDS, FRANK J. WEILAND, DDS,
HANS-PETER BANTLEON, MD, DDS, P.
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53. Schematic of force system: moments at lever arm and
bracket cancel each other out, resulting in net translation
force.
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54. Undesirable side effects from distal canine slide along
continuous arch: tipping, binding, lack of vertical
control and risk of anchorage loss, incisor extrusion
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58. C
A
N
I
N
E
R
E
T
R
A
C
T
I
O
N
T LOOP
The preactivated spring with the anti tip
and anti rotation is placed
Activation on insertion is 6mm
The m/f is 8:1 – controlled tipping
Now as the tooth moves the activation
reduced to 4mm – the force is reduced
M/f ratio is increased - bodily movement further
The activation is reduced to 2mm – force is
further reduced
M/f ratio increased – 12:1
Root uprighting
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60. E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
L
E
S
Space closure
using a retraction
appliance.
Source: AJO-DO 1997 : Three-dimensional effects in
retraction appliance design D. W. Raboud, MSc, M. G.
Faulkner, MSc, PhD, A. W. Lipsett,..,.
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61. E
GROUP A ANCHORAGE
N
M
A
Distal force on anteriors
Mesial forces on posteriors
S
S Maximum potential for tooth mvt.
Miminised or counteracted
E
F
Increase moment
R
Decrease moment
I
C
Horizontal force acting on both segments are same
T
I
O
Moment to force ratio
N
L
E
Reactive unit
Anchor unit
S
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63. E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
L
E
S
A. Vertical force anterior to center of resistance, producing
clockwise moment. B. Vertical force posterior to center of rotation,
producing counterclockwise moment.
Source: JCO 1990 : Vertical Force Considerations in Differential
Space Closure - BIRTE MELSEN, DO, VASSILI FOTIS, DDS,
MSD,www.indiandentalacademy.com
CHARLES J. BURSTONE,
64. E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
L
E
S
Beta moment greater than
alpha moment, producing net
intrusive force on anterior
teeth and extrusive force on
posterior teeth. B. Alpha
moment greater than beta
moment, producing net
intrusive force on posterior
teeth and extrusive force on
anterior teeth. C. Equal alpha
and beta moments, producing
no vertical component of
force.
Source: JCO 1991 JULIE ANN
STAGGERS, DDS, MS, NICHOLAS
GERMANE, DMD
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66. E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
L
E
S
GROUP B ANCHORAGE
Distal force on anteriors
Mesial forces on posteriors
Equal potential for tooth mvt.
Alpha moment
EQUAL
Beta moment
Horizontal force acting on both segments are same
Moment to force ratio
EQUAL
RETRACTION OF ANTERIOR
PROTRACTION OF POSTERIOR
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67. E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
L
E
S
GROUP C ANCHORAGE
Distal force on anteriors
Minimized or counteracted
Mesial forces on posteriors
Maximum potential for tooth mvt.
Increase moment
Decrease moment
Horizontal force acting on both segments are same
Moment to force ratio
Reactive unit
Anchor unit
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68. E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
L
E
S
Burstone and koenig 1976 AJO
Three primary characteristics of retraction loops
1.moment to force ratio
2.the force at yield
3.the force to deflection rate
Factors that influence m/f
Height of the loop
Horizontal loop length
Apical length of the wire
Placement of the loop
Helix incoporation
Angulation of loop www.indiandentalacademy.com
legs
69. E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
L
E
S
Gradual sweep versus an acute bend
Acute bend
Force concentrated on the premolar
Mesial tipping of the premolar
Undesirable
No undesirable
tipping
Gradual sweep
Force being distributed
molar and premolar
Uniform distribution of the
force and no concentration
of the force on a particular
tooth
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71. B
Conventional Begg – type of tooth movement is
uncontrolled or free tipping of the tooth
E
Amount of force required for this is less and
the moment to force ratio is also decreased
G
Uncontrolled tipping is not desirable as it hastens root
resorption and control of the tooth movement is also
difficult (source: Biomechanical principles and reacions,
Reitan1985)
G
Refined Begg – controlled
tipping
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72. B
E
G
G
Stage 1
Intrusion and tipping of the incisors simultaneously
Intrusive force – crown labial
root
lingual
Retractive force – crown lingual
Root labial
Moment of the intrusive force acts to counter moment the
moment of the elastic force
Moment of the intrusive force to the elastic force ratio
determine the type of tooth movement
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73. B
If the intrusive force is decreased
If the elastic force is increased
E
G
Moment to force ratio
Inadequate for
Controlled tipping
Thus, for controlled tipping
G
Keep the class II elastic force very light
Use adequate amount of intrusive force
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74. B
Anchor bend and the class II elastic force
Anchor bend
E
Distal crown
tipping of
molars
G
Retract the anterior
teeth
G
Class II elastics
Move the lower molar
forward bodily
Upright the lower
molars
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Intrusion
of anteriors
75. B
Torquing auxillary with spur
When spread along the wider curvature
Lingual torquing
E
G
The larger arc of the
anterior portion of the
wire roll inwards
Vertical plane in which the
aux orients when fitted into
the incisor is changed to the
horizontal plane of the arch
wire when tied to it
The tip of spur to press in a
lingual direction against the
gingival portion of the crown
G
Inter spur span – lift in a labial
direction
Counter act
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Bracket slot
Base arch wire
76. MAA
B
Light couple force
acting on each tooth
E
G
Lingual crown torque
with the intrusive
couple force
II stage
Intrusive force
reduced
Additional
moment created
by the MAA
G
Prevents labial tipping of
the lower incisors
Opposite to the elastic
force
M/F 8:1
Controlled tipping
Shortens the third stage
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77. C
O
M
M
O
N
Common sense mechanics Thomas F mulligan JCO
1979
Off center bend
Long segment
Short segment
S Points in the direction Points in the direction
E of the force produced opposite of the force
N on the tooth
produced on tooth
S
E
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Center bend
No short or long
segment
No force produced
79. C
O
M
M
O
N
S
E
N
S
E
Differential torque - the
molar tip back bend
produces a large distal
moment on the molar and
a small labial moment on
the anterior segment in
spite of the force being
equal as the distances
involved are radically
different.
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80. Round wire
C
O
M
M
O
N
S
E
N
S
E
Rectangular wire
Line of action
Buccal to center of
resistance
Lingual crown
torque
Line of action
lingual to center of
Resistance
Buccal crown
torque
Begg stage l
expansion given to
prevent lingual
rolling of molars
Beta bend to
Produce buccal
Root torque
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81. CUE BALL CONCEPT
C
O
M
M
O
N
S
E
N
S
E
A force off
center causes
the cue ball to
rotate as well
as move
forward in a
straight line.
No left or right When the line
of force acts
rotation is
through the
produced when
center of
the force is
resistance,
applied through
only
the center of the
translation
cue ball.
results.
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Equal and
opposite
forces
(couple)
produce
pure
rotation.
82. C
O
M
M
O
N
S
E
N
S
E
ROW BOAT
EFFECT
If the tipback and torque bends produce equal
angular relationships (A), the net forces are zero. If
unequal (B), net forces occur.
This explains why there is extrusion with the
increase in the alpha bend.
Thus the length of the segment and the angulation
determine the tooth movement
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83. C
O
M
M
O
N
DIVING BOARD
CONCEPT
When the length of the diving
board is doubled, only one-eighth
the force is required to produce the
same amount of deflection. B. The
same force acting at twice the
length will produce eight times as
much deflection.
S
E
With a constant tipback
N
S angle, the deflection doubles
E as the wire length doubles,
the force is reduced to one
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fourth
84. M
O
L
A
R
Bends placed in the arch wire
Variety of force systems to produce a direct
response
Off set bend
C
O
N
T
R
O
L
Step bend
Center bend
Source : Thomas Mulligan JCO 2001
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85. M
O
L
A
R
OFFSET BEND
Short section of the wire points in the direction of
the long arm
Vertical forces acting through the molar tube
Intrusive
Lingual crown torque
C
O
N
T
R
O
L
Extrusive
Buccal crown torque
Narrowing of the post
Arch width
Widening of the post
Arch width
Reduction in the curve
of monson
Increase in the curve
of monson
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86. M
O
L
A
R
Rotations first displacement second
Toe in
Rotation correction required
Toe out
C
O
N
T
R
O
L
Represent the short section of the wire of the off
center bend
Bends located just mesial to the molars
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87. M
O
L
A
R
Toe out corrects the distal in and/ mesial out
rotation with horizontal lingual force
C
O
N
T
R
O
L
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88. M
O
L
A
R
Toe in corrects the mesial in or distal out with
horizontal buccal force
C
O
N
T
R
O
L
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89. M
O
L
A
R
In bend for the lingual displacement
C
O
N
T
R
O
L
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90. M
O
L
A
R
Out bend for the buccal displacements
C
O
N
T
R
O
L
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91. M
Step bend for the mesio lingulal rotation
O
with a lingual displacement
L
A When 2 bends are involved and each
Increases the
R bend produces a force in the same
force
direction
magnitude
C
O
N
T
R
O
L
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93. CERVICAL PULL HEAD GEAR
H
E
A
D
LOW OUTER BOW
Head gear force line of
action mesial to the center
of resisitance
Extrusive component
Distal component
G
E
A
R
S
Large moment that
Tends to steepen the
Occlusal plane
Clockwise
Moment
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94. CERVICAL PULL HEAD GEAR
H
E
A
D
OUTER BOW
Head gear force line of
action passing through the
center of resisitance
At the level of the
inner bow
Extrusive component
Distal component
G
E
A
R
S
No moment that
Tends to alter the
Occlusal plane
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95. CERVICAL PULL HEAD GEAR
H
E
A
D
High OUTER BOW
Head gear force line of
action distal to the center
of resisitance
Extrusive component
Distal component
G
E
A
R
S
Large moment that
Tends to flatten the
Occlusal plane
Anticlockwise
Moment
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96. HIGH PULL HEAD GEAR
H
E
A
D
SHORT OUTER BOW
Angulated high to create
head gear force line of
action anterior to the
center of resisitance
Intrusive component
Distal component
G
E
A
R
S
Large moment that
Tends to flatten the
Occlusal plane
Anticlockwise
Moment
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97. HIGH PULL HEAD GEAR
H
E
A
D
OUTER BOW
Angulated such that head
gear force line of action
passes through the center
of resisitance
Equal to the inner bow
Intrusive component
Distal component
G
E
A
R
S
No moment that
Tends to alter the
Occlusal plane
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98. HIGH PULL HEAD GEAR
H
E
A
D
LONG OUTER BOW
Angulated to create head
gear force line of action
posterior to the center of
resisitance
Intrusive component
Distal component
G
E
A
R
S
Large moment that
Tends to steepen the
Occlusal plane
Clockwise
Moment
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99. Conclusion
Newton’s third law states that every action has a
equal and opposite reaction.
Its important to keep this concept in mind working
with any appliance system and give adequate
importance to take steps to prevent the adverse
effects.
In orthodontic terms, the understanding of the
moment and the application of the necessary
counter moment to bring about the optimal tooth
movement is the key to successful treatment results
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100. Thank you
For more details please visit
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