Force, Moments, Couples, Equilibrium, Moment to force ratio, center of rotation, tipping, crown movement, pure translation, toot movement, static equilibrium

1. THE BASICS
of
ORTHODONTIC
MECHANICS
Steven J. Lindauer, 2001 by W.B. Saunders Company
Presented by
Dr S N Das
1st year PGT
(Dept. of Orthodontics,KDDC)Date-02.10.2020

2. CONTENTS
Introduction
Predicting How Teeth Will Move in Response to Application of
Orthodontic Force Systems
Predicting the Force Systems Created by Orthodontic Appliance
Activations
Predicting How Teeth Will Move in Response to Orthodontic Appliance
Activations
Conclusion
Referenses

3. INTRODUCTION
The physical concepts that form the foundation of orthodontic
mechanics are the key to understanding how orthodontic
appliances work and are critical for designing new appliances.
Orthodontic appliances obey the laws of physics and can be
activated to generate the desired force systems to achieve
predetermined treatment goals for individual patients.
Through understanding of the basic mechanics underlying
orthodontic appliance activation is the ultimate goal of this
study.

4. PARAMETERS TO PREDICT
3 sections
"Predicting How Teeth
Will Move in Response
to Application of
Orthodontic Force
Systems,"
"Predicting the Force
Systems Created by
Orthodontic Appliance
Activations,"
“Predicting How Teeth
Will Move in Response
to Orthodontic
Appliance Activations”
described how
moments and
forces displace
individual
teeth.
discussedtheway
inwhichmoments
andforcesare
generatedby
orthodontic
appliances.
shows how these
two steps can be
used together to
predict how teeth
will move when
orthodontic
appliances are
activated.

5. A. PREDICTING HOW TEETH WILL MOVE
IN RESPONSE TO APPLICATION OF
ORTHODONTIC FORCE SYSTEMS
Force
Moments
Couples
Equivalent force system
Moment to force ratio & centers of rotation
# Tipping
# Crown movement
# Pure translation
# Root movement
# Pure rotation

6. FORCE
Forces are vectors, having both direction and magnitude. To move a
tooth predictably, a force needs to be applied in the desired direction,
with the desired magnitude, and at the correct position on the tooth.
 There is only one point on a tooth
through which a force can be applied
that will move the tooth in the direction
of the force without tipping or rotating it.
 This point is the center of resistance and
a force acting through it will cause pure
translation of the tooth

7.  If a tooth were truly a free body
floating in space, the center of
resistance would be coincident with
the tooth's center of mass or gravity.
 However, teeth are restrained by
surrounding tissues, most notably
the periodontal ligament (PDL).
 The location of the center of
resistance,therefore depends on the
size and shape of the tooth as well
as on the quality and level of the
supporting structures.

8. Forces, as vectors, can be combined or
divided mathematically. Two or more
forces acting at a single point can be
added using simple trigonometry or
vector addition and represented as a
single force at that point.

9. MOMENTS
When a force is applied at any point other than through the center of
resistance, in addition to moving the center of resistance in the
direction of the force, a moment is created.

10.  A force applied directly through the center of resistance will cause pure
translation of the tooth in the direction of the force with no rotation.
 If the same force is applied away from the center of resistance, toward the
crown for example, the tooth will move in the direction of the force and there
will be a moment created to tip the crown in the direction of the force

11. COUPLES
Two equal and opposite, noncolinear forces are called a couple. The 2 forces
cancel out any tendency for the center of resistance of the tooth to move, but the
moments created by the 2 forces do not cancel each other.
The moment of a couple is really the sum of the moments
created by each of the 2 forces that make up the couple:
F 1 and F 2 are equal but opposite. Therefore, the magnitude
of a moment created by a couple is F(d 1 + d2) or F times the
distance between the 2 forces, M = Fd.

12. A premolar is rotated by stretching
an elastic in one direction from the
buccal attachment and another
elastic from the lingual attachment
in the opposite direction. Thus, 2
equal and opposite forces are
applied and the tooth rotates around
its center of resistance without
translation.

13. To achieve a first-order
couple, the wire is
angulated to produce equal
magnitudes of force at the
mesial and distal aspects of
the bracket in opposite,
buccal and lingual
directions
A twist or torque in the
wire will produce intrusive
and extrusive forces that
are equal and opposite
acting at the buccal and
lingual aspects of the
bracket slot to produce a
third-order couple
To create a second order
couple, the wire produces
equal but opposite intrusive
and extrusive forces at the
mesial and distal aspects

14. EQUIVALENT FORCE SYSTEMS
A comprehensive way of describing
tooth movement is to express the
components of movement experienced
by the tooth at the center of resistance,
which include both translation and
rotation.

15. MOMENT-TO-FORCE RATIOS AND CENTERS
OF ROTATION
 The goal of orthodontic treatment is to move teeth a
prescribed distance in a predetermined direction to enhance
the esthetic and functional aspects of occlusion and achieve
a stable result.
 By varying the ratio of moment to force applied to teeth, the
quality of tooth movement can be changed among tipping,
crown movement, translation, and root movement.
 By changing the ratio of the moment from the applied
couple to the force applied, the center of rotation of tooth
movement can be varied to produce the type of tooth
movement desired.

16. TIPPING
If the center of resistance is 10 mm apical to the bracket, this moment is 10 mm times
the magnitude of the force.
For example, a distal force of 100 g at the bracket will create an equivalent of 100 g of
distal force at the center of resistance plus a moment of 1,000 g-mm in the direction of
distal crown tip.

17. CROWN MOVEMENT
If the center of resistance is 10 mm apical to the bracket, a force alone will
produce a moment that is 10 mm times the magnitude of the force.

18. PURE TRANSLATION
 When a force to move a tooth is applied at a bracket that is 10 mm away from the center of
resistance, a tendency for the tooth to tip is created that is 10 mm times the magnitude of the force.
 To counteract the tendency for tipping, a couple can be applied intentionally to produce a moment
of equal magnitude in the opposite direction

19. ROOT MOVEMENT
 The couple applied more than negates this tendency to tip, but the center of
resistance still moves in the direction of the force while the crown does not.
 An applied moment-to-force ratio of about 13/1 will result in root movement while
the crown of the tooth remains relatively stationary.

20. PURE ROTATION
The moment-to-force ratio is infinite and the center of rotation is coincident
with the center of resistance. This is referred to as pure rotation.

21. B. PREDICTING THE FORCE SYSTEMS CREATED BY
ORTHODONTIC APPLIANCE ACTIVATIONS
 The force systems produced by orthodontic appliance activations
must be resolved separately from the actual forces and moments
that individual teeth will experience at their respective centers of
resistance.
 To deduce how each tooth will be displaced as a result of the
activation, the equivalent force systems acting at the centers of
resistance must be assessed subsequently.
1. Static Equilibrium
2. Equal and Opposite Forces
3. One Couple Appliances--Statically Determinate Systems
4. Two-Couple Appliances--Statically Indeterminate Systems

22. STATIC EQUILIBRIUM
 Static equilibrium implies that, at any point within a body, the
sum of the forces and moments acting on a body is zero; i.e., if no
net forces or moments are acting on the body, the body remains
at rest(static).
 Statics is the field of mechanics
that examines the action of forces
acting on bodies at rest.
 The orthodontic application is that for every appliance, but not
necessarily for every tooth to which it is attached, the sum of the
forces and the sum of the moments must be equal to zero.

23. EQUAL AND OPPOSITE FORCES
 Perhaps the simplest orthodontic
appliance to analyze is the elastic
band.
 An elastic band stretched between
two points of attachment will
produce a force of some magnitude
at one end and, by the laws of
equilibrium, produce an opposite
force of the same magnitude at the
other end.

24. DETERMINATE VS. INDETERMINATE
FORCE SYSTEMS
Force systems can be defined as:
A. Statically Determinate – in which the moments and
forces can be easily discerned, measured and evaluated.
B. Statically Indeterminate – which are too complex for
precisely measuring all forces and moments involved in the
equilibrium. Only the direction of net moments and
approximate net force levels can be determined.

25. A 1-couple orthodontic appliance is
inserted into a bracket or tube at 1
end and is tied as a point contact at
the other, Because it is not engaged
into an orthodontic bracket, the end
that is tied as a point contact cannot
produce a couple but only a simple
force at that site.
The other end, which is engaged in
the bracket slot, can produce both a
force and a couple at that attachment.
The appliance is a 1-couple system
because a couple is generated only at
the site of full engagement.
ONE COUPLE APPLIANCES
STATICALLY DETERMINATE SYSTEMS

26. 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.
This can be done by inserting
the appliance into the bracket
and measuring the force
required to activate the wire to
the site where it will be tied as a
point contact.

27. An example of a 1-couple orthodontic appliance is a long arm or
cantilever activated to extrude a high maxillary buccal canine
A long arm or
cantilever to
extrude a high
canine
The passive wire
showing the angle
between the molar
bracket and the wire
The force system exerted by
the wire is in equilibrium
with a crown-mesial moment
at the molar, and equal and
opposite extrusive and
intrusive forces at the canine
and molar, respectively

28. TWO-COUPLE APPLIANCES
STATICALLY INDETERMINATE SYSTEMS
 A 2-couple appliance is one that is engaged into attachments at
both ends. A couple, therefore, may be generated by the wire at
either or both attachment sites.
 Because of the inability to measure force systems produced by 2-
couple appliances clinically, they are referred to as being statically
indeterminate.

29. The force systems produced by 2-couple orthodontic appliances
depend on both the wire geometry and bracket angulation
relationships.
Equal and opposite bracket-
wire angle relationships
result in equal and opposite
couples with no forces
Equal bracket-wire angle
relationships in the same
direction result in equal
couples in the same direction
with large forces to maintain
appliance equilibrium
If bracket-wire angle
relationships are unequal, the
attachment with the largest
angle will have the largest
couple and resultant forces will
be in a direction opposite this
moment to maintain equilibrium

30. The forces and
moments produced by
a straight segment of
round wire inserted
into 2 orthodontic
brackets were first
described by Burstone
and Koenig in 1974.

31. Equal and oppositely angled brackets result in equal and
opposite couples
As 1 bracket angulation decreases, the magnitude of the
couple at that bracket decreases and forces result
When the angulation of 1 bracket is half that of the other, no
couple is experienced at the bracket with the smaller angulation
and forces are consequently increased
As the bracket angle continues to decrease at 1 end of the appliance,
the couple at the lesser angled bracket is in the same direction as at the
greater angled bracket and forces are even greater
As the bracket angle continues to decrease at 1 end of the appliance,
the couple at the lesser angled bracket is in the same direction as at the
greater angled bracket and forces are even greater

33. V BENDS & STEP BENDS

34. When the apex of the V bend is halfway between the brackets,
the wire exerts equal and opposite couples at the 2
attachments and no forces
As the V bend is moved off center, the couple nearer the bend
increases and the couple further from the bend decreases.
Forces result to maintain appliance equilibrium
When the V bend is at ½ the distance between the brackets, a
couple is only present at the bracket nearer the bend. No couple is
experienced at the bracket further from the bend, and forces result
to maintain equilibrium
When the V bend is very close to 1 bracket, couples in the same
direction are experienced at both brackets, with the larger couple at
the bracket closer to the bend. Forces increase as the bend is moved
further off center
A step bend, regardless of where it is placed,
results in equal couples in the same direction at
both attachments. Forces are at a maximum

35. C. PREDICTING HOW TEETH WILL MOVE IN
RESPONSE TO ORTHODONTIC APPLIANCE
ACTIVATIONS
It is important to distinguish between the 2 concepts: teeth move in response to
forces and moments applied at their brackets, and orthodontic appliances are
activated to transfer forces and moments to the brackets of teeth.

36. PREDICTING THE RESULT OF APPLIANCE
ACTIVATION
Using the laws of static mechanics, the force systems generated by
an orthodontic appliance are calculated to discern the forces and
moments transferred to teeth at their points of attachment.

37. A 1-couple appliance is used
to move a canine buccally, out
of crossbite. The force system
exerted by the appliance in
the occlusal view
Forces exerted by the appliance
at the brackets (black) and the
equivalent tbrce systems at the
centers of resistance (gray)
from a mesial aspect

38. DESIGNING AN ORTHODONTIC APPLIANCE
The steps of force system analysis are reversed if the
objective is designing an appliance to move teeth
predictably.
First, the desired force systems at the centers of resistance
are determined.
From this, the force systems required at the brackets can be
calculated and an appliance designed to deliver the desired
forces and moments.

39. Designing an orthodontic appliance. Desired force
systems at the centers of resistance to translate 2 teeth
toward each other without tipping
Force systems necessary at the brackets to
achieve the desired force systems
Closing loop designed to deliver the necessary
force systems at the attachments of the 2 teeth
Reanalysis of the appliance's effects shows that space
closing forces placed at the brackets (black) as seen from the
occlusal view will cause the teeth to move toward
each other and rotate (gray)

40. CONCLUSION
The components of comprehensive orthodontic treatment, preliminary
alignment, overbite control, space closure, root paralleling, and
finishing, rely on a series of biomechanical processes.
The choice of appliances and techniques used by practitioners varies
radically among individuals, but the fundamental forces and
moments they produce are universal.
Appliances will always act according to the laws of physics.
Understanding the basic biomechanical principles involved in
effecting controlled tooth movement makes achieving successful
orthodontic treatment outcomes more predictable and consistent.

41. REFERENCES
Hurd JJ, Nikolai RJ : Centers of rotation for combined vertical and transverse tooth
movements. Am J Orthod 1976; 70: 551-558.
Mulligan, TF : Common Sense Mechanics. Part 1,2,3 & 4. J Clin Orthod 1979; 13
number 9, 10, 11 & 12.
Burstone CJ, Pryputniewicz RJ : Holographic determination of centers of rotation
produced by orthodontic forces. Am J Orthod 1980; 77: 396- 409.
Smith RJ, Burstone CJ : Mechanics of tooth movement. Am J Orthod 1984; 77: 396-
409.