This document provides an overview of biomechanics concepts in orthodontics. It defines biomechanics as the application of mechanics to tooth movement. Key concepts discussed include: - Forces have magnitude, direction, and point and line of application. Force systems generate tooth movements. - The centre of resistance is the point where a force causes translation without rotation and varies depending on root length and bone support. - The centre of rotation depends on the applied force system and can vary from the centre of resistance to infinity. - Different force magnitudes and moments relative to the centre of resistance (M:F ratios) result in different types of tooth movement, such as tipping, translation, and root movement. Couples

1. BIOMECHANICS IN
ORTHODONTICS
PRESENTED BY: DR. ANSHUL MUNJAL
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2. CONTENTS
 INTRODUCTION
 BASIC CONCEPTS
 FORCE
 CENTRE OF MASS
 CENTRE OF RESISTANCE
 CENTRE OF ROTATION
 COUPLE
 MOMENT
 TOOTH MOVEMENTS
 COUPLE SYSTEMS
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3. INTRODUCTION
Mechanics:
Is the branch of physics concerned with the behaviour of physical
bodies when subjected to forces or displacements, and the
subsequent effect of the bodies on their environment.
Biomechanics:
 Biomechanics is the study of mechanics as it affects the biologic
systems.
 It is the application of mechanics to the biology of tooth movement.
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4. BASIC CONCEPTS
 Isaac Newton's (1642-1727) three laws of motion, which analyse
the relations between the effective forces on objects and their
movements, are all applicable to clinical orthodontics.
 LAW OF INERTIA
 LAW OF ACCELERATION
 LAW OF ACTION AND REACTION
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5. Force
 It is the effect that causes an object in space to change its
place or shape.
 It is vector having characteristics of the line of action,
direction, magnitude and point of application.
 For orthodontics – duration and distribution of force is also
important
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6. Point of application
Magnitude
Sense
Line of action
Properties of force
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7.  Force generating components- active elements
 Arch wires
 Springs
 Screws
 Elastics
 Elastomeric chains
 Tension, compression, bending, or torsion in the active
members
 Components try to regain the original forms
 Generate forces
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8. Centre of mass
 Is a point in a body where its entire mass can be considered to be
concentrated in a gravity free environment.
 For homogeneous bodies with a regular geometrical shape, the CM
is located at their geometric center (i.e. the center of a sphere).
 It is the point where if force is applied the body moves linearly
without any rotation.
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9. 9

10. Centre of resistance
 The point where the line of action of the resultant force vector
intersects the long axis of the tooth, causing translation of the
tooth, is defined as the centre of resistance.
 For single rooted teeth:
 Proffit and Nikolai: 50% of root length
 Smith and Burstone at 33%- 50% of root length
 Nanda: 24% - 35% of distance from alveolar crest
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11.  In case of a partially restrained object
such as our teeth that is partially
embedded in the alveolar bone, center of
gravity drifts apically becoming the
center of resistance.
 The CRes is determined by the mass,
shape and form of the tooth, as well as by
the characteristics of the constraining
elements (bone, PDL).
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12. 6mm
apical
4mm
posterior to
a line  to
occlusal
plane
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13.  Center of resistance of a tooth varies depending upon:
 Root length
 Number of roots
 Alveolar bone support
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14. Centre of rotation
Point around which body rotates
Location depends upon the force system applied M:F ratio
If couple is applied: Crot coincides with Cres
Translation: Crot is at ∞ i.e. no rotation
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15. It is not a fixed point , and can be changed depending upon the point
of force application.
It can be at the centre of resistance, apical to the centre of resistance,
at the root apex, or at infinity.
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16. UNCONTROLLED TIPPING CONTROLLED TIPPING
TRANSLATION
ROOT MOVEMENT
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17. How to determine….?
 Take any two points on the tooth and
connect the before and after positions of
each point with a line. The intersection
of the perpendicular bisectors of these
lines is the center of rotation
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18. Couple
 A couple is a system having two parallel forces of equal
magnitude acting in opposite directions.
 No matter where the couple is applied, the object rotates
about its centre of resistance—that is, the centre of resistance
and the centre of rotation superimpose
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19. Moment
Moment is the tendency for a force to produce rotation or tipping of a tooth.
 The potential for rotation
 M = F x d
 Unit = gram x millimeters
 Can be positive(clockwise) or
negative (anti clockwise)
 Extending the line of action around
the Cres will give the
direction of the moment
GREATER
MOMENT
LESSER
MOMENT
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20. Moment of a force
f
d
M = F x d
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21. f1
MOMENT ARM OF COUPLE(d)
f2
The moment of a couple is equal to the magnitude of
one of the forces multiplied by the perpendicular
distance between them.
Moment of a couple
M = f1 or f2 x d
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22. If the 2 forces acting on
opposite sides of the center of
resistance, their effect is
additive.
Additive
+
F1
F1XDM1= F1XD M2=F2XD
D1
D2
M= F X (D1+D2)
Moment of a couple
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23. If they are on the same side of the
center of resistance, they are
subtractive.
Subtractive
F1
F2
M1=F1XD1 M2=F2XD2
D1
D2
M= F X (D1-D2)
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24. A clinical example
Additive
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25.  This moment may be referred in orthodontics as:
 Rotation or first order tooth movement
 Tipping or second order tooth movement
 Torque or third order tooth movement.
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26. FIRST ORDER SECOND ORDER THIRD ORDER
Cres is in occlusal
perspective
Cres is in facial
perspective Cres is in mesial/distal
perspective
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27. Moment
Moment of force
 Crot shifts in the direction of
movement.
 The moment produced
depends on the distance of
application of force from Cres.
 It can be counteracted by
moment of force or moment of
couple
Moment of couple
There is no shift in the
position of Cres
Crot=Cres.
The moment produced does
not depend on the distance
of application of force from
Cres
It can only be counteracted
by moment of couple
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28. d=10 mm
F=10 gm
M= F x d
= 10 x 10
= 100 gm.mm
Moment to force
ratio
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29. UNCONTROLLED TIPPING CONTROLLED TIPPING
TRANSLATION
ROOT MOVEMENT
Lies at infinity
Slightly apical to
center of
resistance
Apex of root
Incisal edge
M:F
0-5:1
M:F
>10:1
M:F
6-9:1
M:F
10:1
MC/MF = 0
MC/MF < 1
MC/MF = 1 MC/MF >1
M:F & Mc:Mf ratio in various types of tooth
movements
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30. F + M = uncontrolled tipping
F + M = controlled tipping
F + M = translation
F + M = root movement
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31. Tooth movements
- tipping
 Easiest type of tooth movement
 Single force is applied to a bracket on a round wire
 Tooth tips around centre of rotation close to Cres.
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32. UNCONTROLLED TIPPING
 Crown and apex move in opposite
direction
 Clinically undesirable
 M:F= 0:1 to 5:1
 Round wire
CONTROLLED TIPPING
 With light counter clockwise moment
with a rectangular wire, while single
distalizing force is still applied.
 Crown tips, root stays in place
 M:F= 6:1 to 9:1
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33. Uncontrolled Tipping
The counter moment applied is 0
so M:F is 0. It can vary between
0:1 to 5:1
M
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34.  The stresses created in this type of tooth movement are non uniform
with maximum stresses at root apex and cervical area of crown.
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35. Controlled Tipping
M
CM
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36.  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
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37. 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
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38.  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
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39. Root Movement
CM
M
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40. When the counter clockwise moment (M2; torque) is
increased to equal the moment of force (M1),
the moments neutralize each other,
no rotation in the system.
the centre of rotation no longer exists (it is infinite)
Tooth undergoes translation, or bodily movement .
M: F = 10:1
TRANSLATION
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41. M
CM
Translation
TRANSLATION CAN OCCUR IN ANY PLANE: HORIZONTAL , VERTICAL OR OBLIQUE,
DEPENDING UPON THE DIRECTION OF THE FORCE APPLIED
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42.  It produces uniform stresses in periodontium
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43. Rotation
 Rotation of a body is the
movement of any straight line
on that body by a change in
the angle with respect to a
fixed reference frame. If the
body rotates about its centre
of resistance, it is called pure
rotation.
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44.  Pure rotation requires a couple. Since no net force acts at the
centre of resistance only rotation occurs.
M:F=infinite
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45. PART TRANSLATION AND PART
ROTATION
 When a force acts away from Cres, it causes part translation
and part rotation.
 Mulligan explained it using the billiards cue ball analogy.
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46. CUE BALL CONCEPT47

47.  Example: when a retractive force acts at the bracket of upper
central incisor
 Eccentric force application
 Tooth retracts (translates) + rotates (crown lingual and root
labial)
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48.  Example: application of medial force on lingual aspect of
molar tooth from lingual sheath
 Force passes through the Cres in an occlusal perspective
causes translation
 But change its inclination i.e. will cause rotation
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