2. 2
Biomechanics
This presentation is divided into following parts:
• Introduction
• Biomechanical Laws &
Terminologies
• Tooth Movement
• Predicting Force
Systems
• Biomechanical
Classification of
Orthodontic Appliances
• Begg and PEA As We
Know Them
3. 3
Biomechanics
This presentation is divided into following parts:
• Introduction
• Biomechanical Laws
& Terminologies
• Tooth Movement
• Predicting Force
Systems
• Biomechanical
Classification of
Orthodontic Appliances
• Begg and PEA As We
Know Them
– Force
• Direction
• Magnitude
• Point of application
(Center of Resistance)
– Moments
• Moment of force
• Factors controlling the moment
of force
• Center of rotation
• Center of rotation and type of
tooth movement
– Couple
• Moment of couple
• Factors controlling the moment
of couple
– Moment to Force ratio
4. 4
Biomechanics
This presentation is divided into following parts:
• Introduction
• Biomechanical Laws &
Terminologies
• Tooth Movement
• Predicting Force
Systems
• Biomechanical
Classification of
Orthodontic Appliances
• Begg and PEA As We
Know Them
– Uncontrolled tipping
– Controlled tipping
– Translation
– Root movement
– Pure rotation
5. 5
Biomechanics
This presentation is divided into following parts:
• Introduction
• Biomechanical Laws &
Terminologies
• Tooth Movement
• Predicting Force
Systems
• Biomechanical
Classification of
Orthodontic Appliances
• Begg and PEA As We Know
Them
– Visual inspection method
– Static Equilibrium
6. 6
Biomechanics
This presentation is divided into following parts:
• Introduction
• Biomechanical Laws &
Terminologies
• Tooth Movement
• Predicting Force Systems
• Biomechanical
Classification of
Orthodontic Appliances
• Begg and PEA As We Know
Them
– Equal and opposite force
system
– One couple appliance
system
– Two couple appliance
system
7. 7
Biomechanics
This presentation is divided into following parts:
• Introduction
• Biomechanical Laws &
Terminologies
• Tooth Movement
• Predicting Force Systems
• Biomechanical
Classification of
Orthodontic Appliances
• Begg and PEA As We
Know Them
– Conventional
– modifications
9. 9
INTRODUCTION
• Orthodontic problems are the result of
mechanical forces, and their correction
depends on mechanical forces.
• The force systems in the face can form or
deform, and their conscious control is a
continuing challenge in orthodontics.
10. 10
• Altering the balance of forces can arrest or
reverse progressive deformities during
growth, and it can correct many of their
effects even in the adult.
11. 11
• Thus understanding of the fundamentals
of mechanics must be the starting point
for understanding orthodontics.
12. 12
• The principles of force analysis are the
basic tools of the mechanical engineer, &
their application is universal.
13. 13
• In applying them to oral environment, one
combines engineering with dentistry,
which requires a mixed terminology that is
partly foreign to each discipline:
BIOLOGY
+
MECHANICS
_______________
BIO-MECHANICS
15. 15
Laws & Terminologies
This chapter is divided into following parts:
• Force
– Direction
– Magnitude
– Point of application
(Center of Resistance)
• Moment
– Moment of force
– Factors controlling the
moment of force
– Center of rotation
– Center of rotation and type
of tooth movement
• Couple
– Moment of couple
– Factors controlling the
moment of couple
• Moment to Force ratio
16. 16
Mechanical Forces
• The two broad classes of mechanical force
are:
– Static
– Dynamic
• At any moment the oral structures can be
considered to be in a state of static
balance.
17. 17
Force
Definition:
• an act upon a body that changes or tends
to change the state of rest or the motion
of that body.
18. • Newton’s Laws :
• First Law: The Law Of Inertia
• Every body continues in its state of rest or uniform motion in a
straight line unless it is compelled to change by the forces
impressed on it.
• Second Law :The Law Of Acceleration
• The change in motion is proportional to the motive force
impressed & is made in the direction of straight line in which the
force is impressed.
• Third Law :The Law Of Action & Reaction
• To every action there is always opposing & equal reaction.
• When a wire is deflected or activated in order to insert it into
poorly aligned brackets the 1st & 3rd laws are apparent
18
19. 19
• Forces are vectors, having both direction
& magnitude.
• Point of application of force is also
important in understanding tooth
movement.
20. • Scalar: When a physical property ( Weight, temperature ) has only
magnitude , its called a scalar quantity.
• ( E.g.. A force of different magnitude such as 20gm,50gm etc)
• Vector: When a physical property has both magnitude and direction its
called a vector quantity.
• (E.g.. A force vector characterized by magnitude, line of action, point of origin
and sense
20
21. Resultant of forces
21
The parallelogram method of determining the
resultant of 2 forces having common point of
application
23. The resultant of 2 force with different point of application
can be determined by extending the line of action to
construct a common point of application
23
24. 24
Force
1. Direction
• Pull
• Push
2. Magnitude
• Heavy
• Light
3. Point of Application
• Center of
Mass
Gravity
Resistance
Force Vector
25. 25
Magnitude of force
• Increasing the amount of force will
increase the amount of a free body
displacement.
• However, it is unclear how force
magnitude is related to the rate of tooth
movement, which is biologically controlled
phenomenon.
27. 27
Center of mass:
• Each body has a point in its mass, which
behaves as if the whole mass is
concentrated at that single point, which
we call it the center of Mass in a gravity-
free environment.
29. Center of mass:
Each body has a point on its mass , which
behaves as if the whole mass is concentrated at
that single point. We call it the center of mass in a
gravity free environment.
29
31. 31
Center of Gravity:
• The same is called center of Gravity in an
environment where gravity is present.
32. 32
• The center of gravity of the tooth is
located more towards the crown of the
tooth as the mass of the tooth is
concentrated more coronally
33. 33
Center of Resistance
• It is a point at which resistance to tooth
movement is concentrated.
• It is at the approximate midpoint of the
embedded portion of the root.
35. 35
Where is the Center of
resistance of…
• Single Tooth ?
• Anterior Segment ?
• Full Upper Dentition ?
Center of Resistance
36. Center of resistance
Center of mass of a free body is the point through which an
applied force must pass to move it linearly without any rotation.
This center of mass is the free objects “Balance Point”
The center of resistance is the equivalent balance point of a
restrained body.
Center of resistance varies depending up on the
- Root length & morphology
- Number of roots
- Level of alveolar bone support
37. Center of resistance of 2
teeth
Center of resistance of maxilla
Center of resistance of Maxillary
molar
AJO DO 90: 29-36, 1986
39. Center of resistance during anterior teeth retraction
Center of resistance of 6 anterior teeth- ± 7mm apical to the
interproximal bone
Center of resistance of 4 anterior teeth- ±5mm apical to the
interproximal bone
Center of resistance of 2 anterior teeth- ±3.5mm apical to the
interproximal bone
The location of the instantaneous center of resistance shifted
apically as the number of dental units consolidated (2, 4, and 6)
increased.
Clinical implication:
They suggest that little difference in the moment/force ratio
(M/F) is required to translate a two- or four-teeth unit. However,
for the retraction of a six-teeth segment, the M/F ratio of a
retraction spring should be calibrated for a higher value to
facilitate translation.
AJO DO 91(5):375-384,1987
41. 41
Moment of force
• We can apply a force only on the exposed
part of the tooth, which is at a distance
from the center of resistance.
• Therefore with a single force in a typical
clinical situation we invariably create a
moment, called as moment of force.
42. 42
• In orthodontic terminology we refer to
moment as
– Rotation
– Tipping
– Torquing
45. 45
Center of Rotation &
Center of Resistance
• Changing the point of force application
and its relation to the center of resistance
of the tooth will create:
Uncontrolled tipping Controlled tipping Root Movement Bodily Movement
Center of
Rotation
at infinity
47. 47
Couple
• The two forces cancel out any tendency for the
center of resistance of the pencil to move, but
the moment created by the two forces does
not cancel each other.
• The pencil therefore, rotates about its center of
resistance regardless of the point of application
of the couple.
Stick.swf
48. 48
• If the two forces of the couple act on
opposite sides of the center of resistance,
their effect is additive.
• However, if they are on the same side of
the center of resistance, their effect is
subtractive.
50. 50
Factors controlling the Moment
of a Couple
• Moment (M)
• One of the forces (F1 or F2)
• Moment arm of the couple (d)
M= F1 x d
OR
M= F2 x d
F1
F2
d
F1
F2
d
51. 51
Couple – Clinical point
• When the tooth is embedded within the
alveolar bone we cannot apply a couple
with one force on the crown and the other
force on the root.
• We can apply a couple only on the
exposed part of the tooth.
52. 52
• Irrespective of point of application of a
couple on a body or a tooth, the body will
experience a moment & it will rotate
around it’s center of resistance.
53. 53
• Depending on the plane in which the
couple is acting, this rotation has been
called “rotation” (first order), “tipping”
(second order), or “torque” (third order) in
orthodontics.
54. COUPLE:
Two equal and opposite, non -
collinear forces are called a couple.
Couple consists of two forces of
equal magnitude, which are parallel
to each other but not coincident and
they face in opposite direction.
55. The moment of this couple is equal to the
magnitude of one of the forces multiplied
by the perpendicular distance between the
two lines of action of force.
56. If the two forces of the couple act on
opposite sides of the center of resistance,
their effect is additive.
However, if they are on the same side of
the center of resistance, their effect is
subtractive
60. 60
• I am sure all of you already familiar with the
above mentioned points.
• I will assume that from now onwards you will
become familiar with terminologies such as,
– Force
– Moment of a force
– Couple
– Moment of a couple
61. We put thinner wires at the beginning of alignment i.e. more play - less applied couple -
less M:F - no root moment only crown moment (tipping)
62. 62
• Next we will cover-
– Moment to Force Ratio
• And I am sure many have this question:
– Which moment?
– Whether moment of force or
moment of couple?
64. 64
An example:
• In order to retract an incisor tooth we apply a
force on the crown of the tooth.
• This force tends to move the center of
resistance of the tooth, however it also creates a
moment of force (clockwise).
F = Force
d = distance (X) F x d(X) = M(X)
F
M(X)
65. 65
• An counter-clockwise moment can be generated
easily by applying a couple. Note couple
generates a moment irrespective of center of
resistance of the tooth.
F(X) x d = M(X) M(X)
F = Force (X)
d = distance
66. We put thinner wires at the beginning of alignment i.e. more play - less applied couple -
less M:F - no root moment only crown moment (tipping)
67. 67
• The two moments (i.e. the moment of force and
the moment of couple) cancel out any tendency
for the rotation of the tooth, thereby allowing
the force to move the center of resistance of the
tooth.
68. 68
Bodily movement of a tooth requires a moment-to-
force ratio of 8:1 or 10:1, depending on the length
of the root, BUT WHY?
10 mm
20 mm
M : F
10 : 1
M : F
20 : 1
70. 70
• As we have seen whenever a force is
applied at the crown of a tooth, a
tendency for the tooth to rotate, tip or
torque (a moment) is also created.
71. 71
• The force at the
bracket is equivalent
to a force at the
center of resistance
plus a moment that
will cause the tooth
to tip.
72. 72
• In addition to the
force applied, a
couple may also be
engaged intentionally
to partially correct,
completely correct, or
over-correct this
tendency.
74. 74
• By varying the ratio of moment to force
applied to teeth, the quality of tooth
movement can be changed among
uncontrolled tipping, controlled tipping,
translation and root movement.
75. 75
• Without a moment to counteract the
tendency of the tooth to tip in the
direction of the force, the center of
resistance of tooth moves in the direction
of the force, the crown moves further than
the center of resistance, and the apex
actually moves in a direction opposite to
the force.
78. 78
Controlled Tipping
Force
Force
+
Moment in the
direction of force
CONTROLLED TIPPING
Couple
Moment in the
opposite direction of force
of
lesser magnitude
At the
CENTER OF
RESISTANCE
Result
At the
BRACKET
82. 82
Root Movement
Force
Force
+
Moment in the
direction of force
ROOT MOVEMENT
Couple
Moment in the
opposite direction of force
of
greater magnitude
At the
CENTER OF
RESISTANCE
Result
At the
BRACKET
86. 86
Moment to force ratio
It is the ratio of counter-
balancing moment produced to
the net force that is applied to
a tooth.
Counter balancing moment is
moment of couple which opposes
the moment produced by force
CM/ Mc
M/ Mf
F
87. 87
By varying the ratio of moment to force
applied to teeth, the quality of tooth
movement can be changed among uncontrolled
tipping, controlled tipping, translation and
root movement or rotation
88. 88
d=10 mm
F=100 gm
M f = F x d
= 100 x 10
= 1000 gm.mm
Mc = 1000gm.mm
Mc:F = 1000:100
= 10:1
89. 89
Tipping
It is type of tooth movement with greater
movement of crown than root of tooth
It is of 2 types:
Uncontrolled tipping
Controlled tipping
90. 90
Uncontrolled tipping
Simplest type of tooth movement in which
crown and root move in opposite direction
Here only a force is applied to the crown of
tooth and with no moment applied to
counteract the tipping tendency in direction
of force ,the Cres moves in direction of force
the crown and root move in opposite direction
91. 91
Uncontrolled Tipping
The countermoment applied
is 0 so M:F is 0. It can vary
between 0:1 to 5:1
M
Mc:F = 0:100
= 0:1
Mc:F = 100:100
= 1:1
Mc:F = 200:100
= 2:1
Mc:F = 300:100
= 3:1
Mc:F = 400:100
= 4:1
Mc:F = 500:100
= 5:1
F=100 gm
M f = F x d
= 100 x 10
= 1000 gm.mm
92. 92
The stresses created in this type of tooth
movement are non uniform with maximum
stresses at root apex and cervical area of
crown
93. 93
• Controlled tipping
Is achieved by an application of a force to
move the crown, as done in uncontrolled
tipping, along with application of a counter
moment to control or maintain the root apex.
When the moment force ratio of 7:1 is
applied at the bracket, we get controlled
tipping
95. 95
In this type of movement the stress at the
root apex is minimal which helps in maintaining
the integrity of root apex and the
concentration of stresses at cervical area
allows timely tooth movement
96. 96
Translation
If the line of action of an applied force
passes through the center of resistance of a
tooth, the tooth will respond with pure bodily
movement
Moment generated by the force is equal to
the counterbalancing moment generated by a
couple at the bracket
M:F of 10:1 typically produces translation
97. 97
d=10 mm
F=100 gm
M f = F x d
= 100 x 10
= 1000 gm.mm
Mc = 1000gm.mm
Mc:F = 1000:100
= 10:1
100. 100
• Root movement
Changing a tooth’s axial inclination by moving
the root apex while holding the crown
stationary is termed root movement
Root movement requires further increasing
the magnitude of applied counter moment
101. 101
M:F of 12:1 or greater result in root
movement
Root movement in orthodontic treatment is
often described as torque. Placing twists in
rectangular wire or the angle of the bracket
slot with the long axis of tooth is often called
torque
102. 102
Root Movement
CM
M
M f = F x d
= 100 x 10
= 1000 gm.mm
100 gm
Mc = 1300gm.mm
Mc:F = 1300:100
= 13:1
103. 103
Stress level is greatest at root apex
requiring significant bone resorption in this
area for tooth movement to take place This
concentration of stresses produce
undermining resorption , which causes a
significant decrease in rate of tooth
movement.This can be advantageously used
for augmenting anchorage
104. 104
Rotation
Pure rotation requires a couple. Since no net
force acts at the centre of resistance only
rotation occurs.
M:F=infinite
Center of rotation and
Cent o resistance
108. 108
In orthodontics we use various
components (wires, elastics, etc.) to
bring about desired tooth movement.
Each component is a system by itself, and
produces its own force(s) and couple(s).
109. 109
• The force systems produced by
orthodontic appliance activation must be
resolved separately from the actual forces
and moments that individual teeth will
experience at their respective center of
resistance.
110. 110
Visual inspection method:
• It is a simple method used by a majority
of orthodontists.
• For determining what forces are present,
the arch wire is fully engaged into a
bracket or tube and possible force
system is evaluated by eyeballing.
113. 113
• This method is based on laws of static
equilibrium and if not understood correctly
can confuse the orthodontists further.
• It is this method that so often leads us
down the road to faulty conclusions.
• Many a times, it is because we don’t apply
the simple concept of static equilibrium.
115. 115
• We know that according to Newton’s third
law, every action has an equal and
opposite reaction.
• In spite of knowing this, many
orthodontists tend to forget to apply this
law in their daily orthodontic mechanics in
a simple and practical manner.
116. 116
Three requirements are accomplished
automatically whenever static
equilibrium is established.
They are:
1. The sum of all forces present must
equal zero.
2. The sum of all moments present must
equal zero.
3. The sum of all forces and moments
(together) present must equal zero.
118. 118
• When we engage an arch wire fully, we
are generating unequal moments.
• Forces are also generated to keep the
system balanced.
• Therefore, all the moments and forces will
sum up to zero (i.e. always results in static
equilibrium).
120. 120
• Looking at the two unequal moments in
2nd figure, it appears that the entire unit
would rotate counter-clockwise.
ZERO
121. 121
• But by considering the forces generated
we see that forces by themselves would
cause the unit to rotate clockwise.
• Actually these are equal and opposite
force and their sum equals zero.
ZERO
122. 122
• It is impossible to design an appliance that
defies (disobey / confront) the laws of
physics.
123. 123
Next …
• Now using the simple method of visual
inspection we can classify the orthodontic
appliance into various groups.
125. 125
• Orthodontic appliances can be divided into
following three categories depending on
their biomechanical mode of action (forces
and moments):
– No couple appliance system
– One couple appliance system
– Two couple appliance system
126. 126
No Couple Appliance System
• Simplest orthodontic appliance.
• An elastic band stretched between two
points of attachment is the best example.
• This produces forces of equal magnitude
on either end but opposite in direction.
• Elastic band (Orthodontic appliance) is in
equilibrium and no moments are
generated.
129. 129
One Couple Appliance System
• One end of the appliance experiences
couple (bracket or tube) and other end is
tied as a point contact (which can not
produce a couple).
• It is statically determinate because the
magnitudes of the forces and moments
produced can be determined clinically
after the appliance is inserted into the
bracket/tube.
131. 131
Biomechanics of Begg Appliance
• All over the world, the Begg appliance is
giving way to the new genre of
appliances.
• In India, we are still churning out a huge
number of Begg cases and all of us are
well aware of the quality of results.
132. 132
• We have managed to make Begg appear
so simple that even non-orthodontists
have tried putting their hand in the “Pie”
(without knowledge).
Who is to blame for this?
133. 133
Biomechanics of Begg Appliance
• As we understand today the Begg
appliance is a good example of single
couple system. Stage I arch wire
134. 134
• It is not just the base archwire which
can be explained in terms of single couple
system, but other components of Begg
appliance works in a similar fashion, such
as
– Torquing auxillaries
– Up-righting
– Rotation springs
Let us see these ….
145. 145
To overcome the problem of uprighting
springs it was suggested to use
– Conventional 0.018” or 0.020” special plus
– Refined Begg0.018” or 0.020” premium wire
• It was thought that such a stiff wire will
prevent bending of archwire, but still it
can rotate the base archwire within the
slot of bracket.
159. 159
Torquing springs (vertical
problem)
• Intrusion forces on the posterior teeth especially the
molars
– Intrusion force buccal to center of resistance of these teeth
lead to intrusion of buccal cusps
– And transverse expansion of posterior teeth
163. 163
Stage III arch-wire
• Incorporation of numerous bends in base
archwire was done to prevent various
side effects of auxillaries.
Upper stage III base archwire
164. 164
• In vertical plane
– Gable bend distal to canine
– Mild anchor bend (in few selective cases)
• In transverse plane
– Constriction of upper arch
– Toe-in bend
– Molar offset bend
• In sagittal plane
– Cinch-back distal to molar tube
166. 166
• After we have Understood the advantages
and side-effects of each individual
components of Begg mechanotherapy, let
us evaluate the whole system.
Let us start with
Stage I & Stage II
of Begg mechanotherapy
167. 167
Stage I & Stage II
“Bio-mechanically, Begg mechanotherapy
is most efficient in the first two stages”.
And I am sure everybody agrees with
me!!!
Why So ?
168. 168
Stage I arch-wire
• Exceptionally good anchorage control
– Couple at molar tube high moment in
posterior segment
• Bite opening mechanics
– Extrusion of posterior anchorage tooth due to
high moment created
– Intrusion forces on anterior segment
170. 170
Stage III
• Very poor anchorage control
– Couple at incisors high moment in anterior
segment
• Bite deepening mechanics
(Advantageous in selected patients e.g.
open-bite cases)
– Side effect extrusion of anterior teeth due
to high moment created by auxillaries
– Side effect intrusion forces on posterior
segment
Why So ?
175. 175
• Scrutinization of the literature, reveals that
there was little or no consideration
provided to counteract the side effects of
the stage III.
• For example the commonest problem of
flaring of the molars and their intrusion
was given no consideration.
176. 176
• Hardly anybody has suggested, the use of
anchor bend in the posterior segment in
order to generate higher moments (in
opposite direction) to the moments
generated in anterior region.
• This simple bend (the trade mark of
Begg appliance) was forgotten when
starting stage III.
177. 177
• And even to control the proclination of the
upper incisors due to horizontal effects of
the auxillaries, a (mild) Class II elastics
was suggested.
• However class II elastic would add up to
the extrusion component of the auxillaries
on the incisors, worsening the bite-
deepening effect.
Let us see…
179. 179
• Anchor bend was suggested in the lower
arch only in cases where a Class II elastic
was to be used.
• What about using anchor bend in upper
arch in stage III?
But first, let us see the effects of anchor
bend..
180. 180
Solution for Problems in Stage
III
• We saw that the moment generated in
stage I and II was in the posterior
segment and therefore excellent
anchorage control.
181. 181
• Let’s apply this basic knowledge to the
stage III which has all of its moments
concentrated in the anterior region,
causing
– Proclination of dentition
– Extrusion of incisors
Let us see this …
185. 185
• Forces and couples are applied to teeth
to move them in the desired directions.
• Tooth movement is monitored regularly to
assure that treatment proceeds smoothly
and positively.
186. 186
• Unwanted effects are corrected by
adjustments along the way.
• The final result is achieved by a series of
well-planned mechanical interventions
that initiate and sustain a controlled
biologic reaction.
187. 187
• The components of comprehensive
orthodontic treatment such as,
– preliminary alignment,
– overbite control,
– space closure,
– root paralleling, and
– finishing,
rely on a series of biomechanical principles
and process which need to be understood.
188. 188
• The choice of appliances and
techniques used by practitioners varies
radically among individuals, but the
fundamental forces and moments
they produce are universal.
• Appliance will always act according to the
laws of physics.
189. 189
• Understanding the basic biomechanical
principles involved in effective controlled
tooth movement makes the final outcome
more predictable and consistent.
191. 191
Visual inspection method:
• It is a simple method used by a majority
of orthodontists.
• For determining what forces are present,
the arch wire is fully engaged into a
bracket or tube and possible force system
is evaluated by eyeballing.