Moment to force ratio

MOMENT
TO
FORCE
RATIO
www.indiandentalacademy.com

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

FLOW CHART OF THE PRESENTATION
DEFINITION OF THE BASIC CONCEPTS
PAE
Various
stages
EXTRA
ORAL
Head gears
BEGG
Various
stages
COMMON SENSE MECHANICS
MOLAR CONTROL

. 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.
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

The parallelogram method for resolving a force into vertical
and horizontal components.

. The parallelogram method of determining the resultant of
two forces with a common point of application.
F
O
R
C
E

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.
Couple force

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

CENTER OF ROTATION
The point around which rotation
actually occurs when an object is
being moved

M
O
M
E
N
T
Defined as the rotational tendency when force is
applied away from the center of resistance
A force acting at a distance
Mathematically given as M = f x d
Where M is the moment
f is the force
And d is the perpendicular distance of the line of
action to the center of resistance

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.
F
O
R
C
E
Direction of a moment

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.

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

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
Power arm
Counter moment
Tooth remain upright
And move bodily

Various tooth movements
Uncontrolled tipping
Controlled tipping
Translation
Root uprighting
M/F (moment to force ratio) is the relationship
between the force and the counter balancing
couple that determines the type of tooth movement .

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

M/F 5 : 1 Uncontrolled tipping
M/F 8 : 1 Controlled tipping
M/F 10 : 1 Translation
M/F >10 : 1 Root movement
MOMENT TO FORCE RATIO FOR VARIOUS
TOOTH MOVEMENTS

P
A
E
TORQUE
A rectangular wire in
a rectangular slot
Generate the moment
of a couple necessary
to control root
position
Torque acting as the
counter moment
Bracket system

TIP In the PAE bracket system,
the tip incorporated into the
bracket acts as the counter
moment in the mesio distal
direction
This prevents the tipping
of the tooth in the mesio
distal direction
P
A
E
Bracket system

P
A
E
Bracket system
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
Inter bracket span increases
Increase in the length of the wire
Increased flexibility
Decreased forces

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.
Principle of power arm

A
L
I
N
G
I
N
G
Lingually malposed premolar
Aligning wire engaged
Bucally directed simple tipping
First order angular displacements
Of the adjacent teeth
Decrease the magnitude
of the force
To counteract
Broad distribution of
Responsive force

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
Reduce the canine tip (MBT)
Placement of canine lace back
A
L
I
N
G
I
N
G

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).
Arch leveling
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").
L
E
V
E
L
I
N
G

L
E
V
E
L
I
N
G
Highly placed
canine
Continuous arch
wire
Intrusive force on
lateral greater than
the extrusive force
on canine
Lateral intrusion rather
than canine extrusion due
to the increased root
length of canine
Engage a continuous
wire only after
reasonable aligning of
the anterior segment
excluding canine

B
I
T
E
O
P
E
N
I
N
G
Round wire with reverse curve of Spee
Forward tipping of the lower incisors
Tipping of the lower molar
Cinched back
Lower premolars extruded
Roots of the lower incisor thrown forward
Forward mvt of lower molarForward mvt.of lower In.
Class III Elastics
To counteract
To counteract
Eruptive forces on lower In. and upper molars
To counteract
High pull head gear or extractionswww.indiandentalacademy.com

COUNTERACTING
EFFECTS OF
LEVELING WITH
ROUND WIRE

Banding of the second molars
B
I
T
E
O
P
E
N
I
N
G
Extrusion of the first molars
Opening of the bite
Second molars being at a higher level

Bioprogressive Therapy
Typical variations of the mandibular utility arch.

UTILITY ARCHES
DISTAL UPRIGHTING
DISTO LINGUAL ROTATON
BUCCAL EXPANSION
BUCCAL ROOT TORQUE
450
TIP BEND
300
ROTATION
2MM BUCCAL EXPANSION
450
BUCCAL ROOT TORQUE
50
LABIAL ROOT TORQUE ON
LOWER INCISORS

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.
B
U
R
S
T
O
N
E
I
N
T
R
U
S
I
O
N www.indiandentalacademy.com

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.
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.
B
U
R
S
T
O
N
E
I
N
T
R
U
S
I
O

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.
B
U
R
S
T
O
N
E
I
N
T
R
U
S
I
O

.
. 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.
B
U
R
S
T
O
N
E
I
N
T
R
U
S
I
O

Force system of appliance.Note that the posterior
extension allows force to be directed through the center of
resistance of the incisor. No incisor tipping will occur.
A long posterior extension is used to protrusive lower
incisors to prevent flaring. The hook at the intrusive section
is shown.
B
U
R
S
T
O
N
E
I
N
T
R
U
S
I
O

The extrusive force on the molar during incisor
intrusion tends to tip the crown lingually. This
can be prevented by using a lingual arch.
B
U
R
S
T
O
N
E
I
N
T
R
U
S
I
O

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.
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.
T
H
R
E
E
P
I
E
C
E
A
R
C
H
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. .

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.
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.
T
H
R
E
E
P
I
E
C
E
A
R
C
H

C
O
N
N
E
C
T
I
C
U
T
A
R
C
H 16 x 22 or 17 x 25 nickel titanium wire

Intrusion force system consists of anterior intrusive
force, posterior extrusive force,and posterior tip back
moment
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.
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.
C
O
N
N
E
C
T
I
C
U
T
A
R
C
H

A. Force system for incisor extrusion, with CTA is inserted into
molar brackets upside down. Vertical forces shown are ideal for
correction of minor open bites. B. Open-bite patient before
treatment. C. Mechanics shown in A used to close bite, with high-
pull headgear added to prevent forward tipping of molars and
augment intrusive force of CTA on molars.
C
O
N
N
E
C
T
I
C
U
T
A
R
C
H

19 x 25 TMA with
closed U loop 7mm long
and 2mm wide
K
S
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

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.
K
S
I
R
A
R
C
H
20 degree anti rotation
bends distal to the U loop

S
P
A
C
E
C
L
O
S
U
R
E
INDIVIDUAL CANINE
RETRACTION
ENMASSE RETRACTION
FRICTION
FRICTIONLESS

C
A
N
I
N
E
R
E
T
R
A
C
T
I
O
N
Individual canine retraction – friction mechanics
Do not change the power chain for 5 weeks ,let to
comlplete the root uprighting
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

Source: 1993 JCO: Modified Lingual Lever Arm Technique -
GERHARD KUCHER, MD, DDS, FRANK J. WEILAND, DDS,
HANS-PETER BANTLEON, MD, DDS, P.
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.
C
A
N
I
N
E
R
E
T
R
A
C
T
I
O
N

Schematic of force system: moments at lever arm and
bracket cancel each other out, resulting in net translation
force.

Undesirable side effects from distal canine slide along
continuous arch: tipping, binding, lack of vertical
control and risk of anchorage loss, incisor extrusion

Effect of pure horizontal force at the canine
bracket.
C
A
N
I
N
E
R
E
T
R
A
C
T
I
O
N

Antitip and antirotation moment-to-force
conditions necessary for translation of
canines with average dimensions.
C
A
N
I
N
E
R
E
T
R
A
C
T
I
O
N

C
A
N
I
N
E
R
E
T
R
A
C
T
I
O
N
PG retraction spring
Anti tip bend – 150
in
the mesial leg
Beta bend - 300
in the
distal leg
Anti rotation bend – 350

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

C
A
N
I
N
E
R
E
T
R
A
C
T
I
O
N
T LOOP
Mesial leg angulated by150
Distal leg angulated by 300
Preactivation of 400
Increasing the
gingival length of
the wire increases
the m/f ratio and
reduces the
deflection rate

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,..,.
E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
L
E
S

E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
L
E
S
GROUP A ANCHORAGE
Distal force on anteriors Mesial forces on posteriors
Maximum potential for tooth mvt. Miminised or counteracted
Decrease moment Increase moment
Horizontal force acting on both segments are same
Moment to force ratio
Reactive unit Anchor unit

Alpha moment Beta moment
Anteriors posteriors
Vertical forces created
Extrusion
When unequal or unbalanced
Intrusion
alpha
beta
alpha
beta
Intrusion Extrusion
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, CHARLES J. BURSTONE,
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
E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
L
E
S

With retraction spring, alpha moment produces distal root
movement of anterior teeth; beta moment produces mesial
root movement of posterior teeth.
E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
L
E
S

GROUP B ANCHORAGE
Equal potential for tooth mvt.
Alpha moment Beta moment
EQUAL
EQUAL
RETRACTION OF ANTERIOR
PROTRACTION OF POSTERIOR
E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
L
E
S

GROUP C ANCHORAGE
Maximum potential for tooth mvt.Minimized or counteracted
Decrease momentIncrease moment
Reactive unitAnchor unit
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 legs
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
Gradual sweep
Uniform distribution of the
force and no concentration
of the force on a particular
tooth
Force being distributed
molar and premolar
No undesirable
tipping
E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
L
E
S

SLIDING MECHANICS
E
N
M
A
S
S
E
F
R
I
C
T
I
O
N
The hook is soldered at the center of resistance of the anterior
segment and active tie backs are placed from the molar hook to
the soldered hook.

B
E
G
G
Conventional Begg – type of tooth movement is
uncontrolled or free tipping of the tooth
Amount of force required for this is less and
the moment to force ratio is also decreased
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)
Refined Begg – controlled
tipping

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

B
E
G
G
If the intrusive force is decreased
If the elastic force is increased
Inadequate for
Controlled tipping
Thus, for controlled tipping
Keep the class II elastic force very light
Use adequate amount of intrusive force

B
E
G
G
Anchor bend and the class II elastic force
Distal crown
tipping of
molars
Upright the lower
molars
Retract the anterior
teeth
Move the lower molar
forward bodily
Class II elastics
Anchor bend
Intrusion
of anteriors

Torquing auxillary with spurB
E
G
G
When spread along the wider curvature
Lingual torquing
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 larger arc of the
anterior portion of the
wire roll inwards
The tip of spur to press in a
lingual direction against the
gingival portion of the crown
Inter spur span – lift in a labial
direction
Bracket slot
Base arch wireCounter act

Light couple force
acting on each tooth
Lingual crown torque
with the intrusive
couple force
Opposite to the elastic
force
M/F 8:1
Controlled tipping
II stage Intrusive force
reduced
Additional
moment created
by the MAA
Prevents labial tipping of
the lower incisors
Shortens the third stage
B
E
G
G
MAA

Common sense mechanics Thomas F mulligan JCO
1979
Off center bend
Points in the direction
of the force produced
on the tooth
Center bend
Short segmentLong segment
Points in the direction
opposite of the force
produced on tooth
No short or long
segment
No force produced
C
O
M
M
O
N
S
E
N
S
E

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.
C
O
M
M
O
N
S
E
N
S
E

Round wire
Line of action
Buccal to center of
resistance
Lingual crown
torque
Begg stage l
expansion given to
prevent lingual
rolling of molars
Rectangular wire
Line of action
lingual to center of
Resistance
Buccal crown
torque
Beta bend to
Produce buccal
Root torque
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
rotation is
produced when
the force is
applied through
the center of the
cue ball.
When the line
of force acts
through the
center of
resistance,
only
translation
results.
CUE BALL CONCEPT
Equal and
opposite
forces
(couple)
produce
pure
rotation.
C
O
M
M
O
N
S
E
N
S
E

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
ROW BOAT
EFFECT
C
O
M
M
O
N
S
E
N
S
E

With a constant tipback
angle, the deflection doubles
as the wire length doubles,
the force is reduced to one
fourth
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.
DIVING BOARD
CONCEPT
C
O
M
M
O
N
S
E
N
S
E

M
O
L
A
R
C
O
N
T
R
O
L
Source : Thomas Mulligan JCO 2001
Bends placed in the arch wire
Variety of force systems to produce a direct
response
Off set bend
Step bend
Center bend

M
O
L
A
R
C
O
N
T
R
O
L
Short section of the wire points in the direction of
the long arm
OFFSET BEND
Vertical forces acting through the molar tube
Extrusive Intrusive
Lingual crown torque 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

M
O
L
A
R
C
O
N
T
R
O
L
Rotations first displacement second
Rotation correction required
Toe in
Toe out
Represent the short section of the wire of the off
center bend
Bends located just mesial to the molars

M
O
L
A
R
C
O
N
T
R
O
L
Toe out corrects the distal in and/ mesial out
rotation with horizontal lingual force

M
O
L
A
R
C
O
N
T
R
O
L
Toe in corrects the mesial in or distal out with
horizontal buccal force

M
O
L
A
R
C
O
N
T
R
O
L
In bend for the lingual displacement

M
O
L
A
R
C
O
N
T
R
O
L
Out bend for the buccal displacements

M
O
L
A
R
C
O
N
T
R
O
L
Step bend for the mesio lingulal rotation
with a lingual displacement
When 2 bends are involved and each
bend produces a force in the same
direction
Increases the
force
magnitude

M
O
L
A
R
C
O
N
T
R
O
L
Center bend

H
E
A
D
G
E
A
R
S
CERVICAL PULL HEAD GEAR
LOW OUTER BOW Head gear force line of
action mesial to the center
of resisitance
Extrusive component
Distal component
Large moment that
Tends to steepen the
Occlusal plane
Clockwise
Moment

H
E
A
D
G
E
A
R
S
OUTER BOW Head gear force line of
action passing through the
center of resisitance
Extrusive component
Distal component
No moment that
Tends to alter the
Occlusal plane
At the level of the
inner bow

H
E
A
D
G
E
A
R
S
High OUTER BOW Head gear force line of
action distal to the center
of resisitance
Extrusive component
Distal component
Large moment that
Tends to flatten the
Occlusal plane
Anticlockwise
Moment

H
E
A
D
G
E
A
R
S
HIGH PULL HEAD GEAR
SHORT OUTER BOW
Angulated high to create
head gear force line of
action anterior to the
center of resisitance
Intrusive component
Distal component
Large moment that
Tends to flatten the
Occlusal plane
Anticlockwise
Moment

H
E
A
D
G
E
A
R
S
HIGH PULL HEAD GEAR
OUTER BOW
Angulated such that head
gear force line of action
passes through the center
of resisitance
Intrusive component
Distal component
No moment that
Tends to alter the
Occlusal plane
Equal to the inner bow

H
E
A
D
G
E
A
R
S
HIGH PULL HEAD GEAR
LONG OUTER BOW
Angulated to create head
gear force line of action
posterior to the center of
resisitance
Intrusive component
Distal component
Large moment that
Tends to steepen the
Occlusal plane
Clockwise
Moment

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

Moment to force ratio

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