Copy of biomechanical principles of orthodontics

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INTRODUCTION
MECHANICAL CONCEPTS IN ORTHODONTICS
-SCALAR
-VECTOR
-FORCE
-RESULTANTS & COMPONENTS OF ORTHODONTIC
FORCE SYSTEM
-CENTER OF MASS
-CENTER OF GRAVITY
-CENTER OF RESISTANCE
-CENTER OF ROTATIONS
-SIGN CONVENTIONS
-MOMENT OF THE FORCE
-COUPLE


-TORQUE
-SYSTEMS EQUIVALENT FORCE
-MOMENT TO FORCE RATIO & TYPES OF TOOTH
MOVEMENT
-NEWTON’S LAWS
-STATIC EQUILIBRIUM
-INTRUSION ARCH
-CENTERED ‘V’ BEND
-OFFCENTERED ‘V’ BEND
-STEP BEND
-NO COUPLE SYSTEM
-ONE COUPLE SYSTEM(DETERMINATE FORCE)
-TWO COUPLE SYSTEM(INDETERMINATE FORCE)
LEVELLING & ALLIGNING
-MOLAR ROTATIONS
-UNILATERAL
-BILATERAL
-SIMULTANEOUS INTRUSION & RETRACTION
-CLASS II & III ELASTICS
SPACE CLOSURE
-FORCE SYSTEMS FOR
-GROUP B SPACE CLOSURE

-GROUP A SPACE CLOSURE
-GROUP C SPACE CLOSURE
TORQUING
-WITH THE MOMENT OF A COUPLE
-WITH THE MOMENT OF A FORCE
CONCLUSION
REFERENCES


INTRODUCTION
The biologic cascade of events that ultimately results in bone
remodeling and orthodontic tooth movement begins with the mechanical
activation of an orthodontic appliance. The force systems produced by
orthodontic appliances, consisting of both forces and moments, displace
teeth in a manner that is both predictable and controllable. By varying the
ratio of moment to force applied to teeth, the type of tooth movement
experienced can be regulated by the orthodontist. 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.
Likewise, any orthodontic appliance can be analyzed to define the
mechanical force systems it produces. Understanding the biomechanical
principles underlying orthodontic appliance activations is essential for
executing efficient and successful orthodontic treatment.


Mechanics is the discipline that describes
the effects of forces on bodies
Biomechanics refers to the science of
mechanics in relation to biologic system.


MECHANICAL CONCEPTS IN
ORTHODONTICS

An understanding of several
fundamental mechanical concept is
necessary to understand clinical
relevance of biomechanics in
orthodontics.


Scalar:

When a physical property ( Weight, temperature ,force) 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)


Force

Force is equal to mass times
acceleration

F= ma
Forces are actions applied to bodies


RESULTANTS AND COMPONENTS OF ORTHODONTIC
FORCE SYSTEMS
Teeth are often acted upon by more than one force. Since the movement of a
tooth (or any object) is determined by the net effect of all forces on it, it is
necessary to combine applied forces to determine a single net force, or
resultant.
At other times there may be a force on a tooth that we wish to break up into
components. For example, a cervical headgear to maxillary molars will move
the molars in both the occlusal and distal directions. It may be useful to resolve
the headgear force into the components that are parallel and perpendicular to
the occlusal plane, in order to determine the magnitude of force in each of
these directions.


h
a
ø
b
sin ø= a/h
cos ø = b/h

a = h sin ø
b = h cos ø


Resultant of forces

F1

F1
ø

F

2

F2

F1 cos ø + F2 cos ø

The parallelogram method of determining the resultant of 2 forces
having common point of application


Components of a force
F sin ø
F

ø

F cos ø


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

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.

Center of gravity
The same is called the centre of
gravity in an environment when
gravity is present.


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


Center of resistance of
2 teeth

Center of resistance of maxilla

Center of resistance of Maxillary
molar


AJO DO 90: 29-36, 1986

Center of resistance depending upon the level of alveolar bone.


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
Center of resistance of 2 anterior teeth- ±3.5mm apical to
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

Center of resistance during anterior teeth intrusion
For an anterior segment comprising two central incisors, the
center of resistance was located on a projection line parallel
to the midsagittal plane on a point situated at the distal half of
the canines
For an anterior segment that included the four incisors, the
center of resistance was situated on a projection line
perpendicular to the occlusal plane between the canines and
first premolars.
For a rigid anterior segment that included the six anterior
teeth, the center of resistance was situated on a projection
line perpendicular to the occlusal plane distal to the first
premolar.

AJO DO 90(3):211-220,1986

The center of resistance was found in different occlusoapical
positions, depending on the direction of the force. Thus the
location of the center of resistance cannot be considered to be
constant, independent of the direction of loading, for a tooth with a
given support.

A force always acts to displace the center of resistance in the
direction the force is acting (support being the same) .


AJO DO 1993 May (428 - 438)

AJO DO 99(4):337-


JCO28(9):539-546,1994

Center of rotation
If a model of a tooth is attached to a piece of paper by a pin, the point with the
pin in it cannot move, and this point becomes the center of rotation about which
the tooth can spin. If the pin is placed at the incisal edge, only movement of the
root is possible if it is placed at the root apex, movement is limited to crown
tipping. In each case, the center of rotation is determined by the position of the
pin. Thus, in two dimensional figures, the center of rotation may be defined as a
point about which a body appears to have rotated, as determined from its initial
and final positions.


The more nearly translational the movement, the farther apically the center of
rotation would be located. In the extreme case, with perfect translation, the
center of rotation can be defined as being an infinite distance away.

A simple method for determining a
center of rotation is to 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


AJO DO 85(4):294-307,1984

Burstone stated in his simple formula:
y × (M/F) = 0.068 h2 where
y = Distance from center of resistance to center of rotation
M/F = Distance from center of resistance to point of force application
h = Root length
Thus, in this special case of a two-dimensional parabolic root, 0.068 is a
constant for a given root length.


AM J ORTHOD 1969;55:351-69.

Two important parameters σ2 and γ, which measure the
resistance of the tooth to tipping, were found to be constants
for loading in one plane of space, independent of the position of
occlusoapical force.
Using experimental σ2 or γ values, one can calculate the
location of the center of rotation of the tooth for a given force
position or, conversely, when a center of rotation is desired, the
position of the force (or the equivalent moment/force ratio at the
bracket) can be calculated.
Because the γ values differed as the load was changed from
one plane to another through the long axis of the tooth, it was
shown that different centers of rotation would be produced for a
given force location if the direction of loading was changed.
The center of rotation located more apically to the center of
resistance with forces directed labiopalatally than mesiodistally.

AJO DO 99(4):337-345,1991

More is the value of σ2 & γ
more is the resistance to
tipping or rotation


AJO DO 99(4):337-345,1991

Sign Conventions
A universal sign convention is available for forces & moments in dentistry &
orthodontics.
Forces are positive when they are in :
-Anterior direction
-Lateral direction
-Mesial direction
-Buccal direction
-Extrusive forces
Moments are positive when they move the crown in a mesial, buccal or
labial direction.

Moment of the force :It is the tendency of a force to produce rotation.
The force is not acting through the Cres
It is determined by multiplying the magnitude of force by the perpendicular
distance of the line of action to the center of resistance.
Unit– Newton . mm ( Gm. mm)


The direction of moment of force can be determined by continuing the line
of action around the Cres


Couple
A couple consists of two forces of equal magnitude, with parallel but
noncolinear lines of action and opposite senses.
The magnitude of a couple is calculated by multiplying the magnitude of forces
by the distance between them
Unit :- Newton . mm (Gm . mm)

1000gm.mm


Moment of a couple
The tendency of a couple to produce pure rotation around the Cres

Direction of rotation is determined by following the direction of either force
around the Cres to the origin of opposite force.

Cres


Irrespective of where on a rigid object a couple is applied; the external effect
is the same.
50g

50gm

-500gm.mm
50gm
50gm

1000gm.mm


1500gm.mm

The moment of force is always relative to a point of reference. The
moment of a force will be low relative to a point close to the line of action
and high for a point with a large perpendicular distance to the line of action.

A couple is no more than a particular configuration of forces which have an
inherent moment. This moment of couple is not relative to any point.


In orthodontics depending up on the plane in which the couple is acting they
are called as

Rotation-1st order

Tipping- 2nd order


Torque- 3rd order

Torque
Torque is the common synonym of moments

Moments of forces moments of couples


Systems Equivalent force
A useful method for predicting the type of tooth movement that will occur with
the appliance activation is to determine the “ equivalent force system at tooth’s
center of resistance.
It’s done in three steps
First- Forces are replaced at the Cres maintaining its magnitude and direction
Second- The moment of force is also placed at the Cres.
Third- Applied moment ( moment of couple in bracket wire combination) is also
placed at Cres.


MC-MF

F

F

MC

MF

Moment to force ratio & types of tooth movement
The type of movement exhibited by a tooth is determined by the ratio between
the magnitude of the couple (M) and the force (F) applied at the bracket.
The ratio of the two has units of millimeters (this represents the distance away
from the bracket that a single force will produce the same effect).


AJO 85(4):294-307,1984

AJO DO 90: 127-131, 1986

Tipping
-Greater movement of crown of the tooth than of the root

Uncontrolled tipping:
-Movement of the root apex and crown in opposite direction
-Crot – Between Cres and apex
-Mc/F ratio 0:1 to 5:1
-0<Mc/MF<1

Controlled tipping:
-Movement of the crown only
- Crot – At the root apex
-Mc/F ratio 7:1
-0<Mc/MF<1

JCO13:676-683,1979

AJO 85(4):294-307,1984

Translation
-Bodily moment occurs
-Crot – At infinity
-Mc/F ratio 10:1
-Mc/MF=1

-Root movement
-Root movement occurs with the crown being stationary
-Crot – at the incisal edge or the bracket
-Mc/F ratio 12:1 - Mc/MF>1

Pure rotational movement
-Root & crown move equally in opposite direction
- Crot – Just incisal to Cres
- Mc/F ratio 20:1 - Mc/MF>1
JCO13:676-683,1979

AJO 85(4):294-307,1984

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.

Static Equilibrium
It is a valuable application of Newton’s Laws of motion to the analysis of the
force system delivered by an orthodontic appliance.
Static Equilibrium implies that, at any point within a body , the sum of forces &
moments acting on a body is zero; i.e., if no net force or moments are acting on
the body the body remains at rest (static).
The analysis of equilibrium can be stated in equation form
Σ Horizontal forces = 0
Σ Vertical forces = 0
Σ Transverse forces = 0
AND
Σ Moments ( Horizontal axis ) = 0
Σ Moments ( Vertical axis )= 0
Σ Moments ( Transverse axis ) = 0

Intrusion arch


Centered ‘V’ bend


AJO DO 98(4):333-339 1990

Off Centered ‘V’ Bend


AJO DO 98(4):333-339 1990

Step bend

It is easy to understand that the forces
generated in this type of situation are
stronger than those generated in an offcenter V bend. Indeed, for a given angle
between the wire and the brackets, the two
moments, C1 and C2, add up in the step
bend, yielding a stronger reactional
moment, as well as stronger vertical forces.


AJO DO 98(4):333-339 1990

No Couple System

d

d
F

F

MF

One Couple System (Determinate force system)


Two Couple System (Indeterminate force system)


Leveling & Aligning

Wider bracket

Narrower bracket

More Mc

Less Mc

Less contact angle

More contact angle

More the play more is the Mc
It was found that a predictable ratio of the moments produced between two
adjacent brackets remained constant regardless of interbracket distance or the
cross section of the wire used if the angles of the bracket remained constant to
the interbracket axis.
AJO DO 1988 Jan (59 – 67)

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)


MC

MC

MC

Am J Orthod
1974;65:270-289

MC

MC

The 2 central incisors are rotated
mesial in creating a symmetric V
geometry. The
desired corrective force system
involves 2 equal
and opposite moments as illustrated


Semin Orthod 2001;7:16-25.

The force system developed by inserting a straight wire into the brackets of
the 4 anterior teeth will create counterclockwise moments on the 2 central
incisors as well as lingual movement of the left central incisor and labial
movement of the right central incisor. The initial geometry is not favorable for
alignment.


shows a lingually placed right lateral incisor. In this case, the geometric
relationship between the right lateral and central incisors is a step geometry
and the placement of a straight wire into the brackets of the 4 anterior teeth will
align the teeth and also shift the midline to the right side


In the maxillary arch shown in Figure, the relationship between the central
incisors is a step geometry and an asymmetric V geometry is observed
between the central and lateral incisors on the right side. Analysis of the force
system shows that, although correction of the 2 central incisors will occur as
a result of straight wire placement, the right lateral incisor will be displaced
labially, which is an undesirable side effect .

The relationship between the right lateral and central incisors is
recognized as an asymmetric V geometry. Analysis of the force system
shows that, although the left lateral incisor will be corrected by rotating mesial
out and moving labially, the right lateral incisor will move further lingually


During extrusion of a high canine
unilaterally. Figure A shows the
force system generated by the
placement of a straight wire through
a high maxillary right canine. The
canine will extrude as desired, but
the lateral incisor and first premolar
on that side will intrude and tip
toward the canine space. An open
bite may result on that side of the
arch, and the anterior occlusal plane
will be canted up on the right side.



Molar Rotations- absence of maxillary molar rotation is highly desirable in
obtaining class-I occlusion of the molars, premolars, & canines.
B/L Molar rotations:
Palatal Arch

Mc

Mc


Headgear

F

F
MF


MF

U/L Molar Rotations:

D

M

MF

MF
Mc

Mc


Simultaneous Intrusion & Retraction:


Cres

MF

MF
MF

MF

Cross bite elastics


Cres

Force vectors in Cl-III elastics

Force Vectors in Cl-II elastics

Favorable in low angle deep www.indiandentalacademy.com
bite
Favorable in low angle cases
cases

Space Closure

Group A Anchorage

Group B Anchorage

Group C Anchorage

Force system for Group B space closure
M/F Ratio 10/1in anterior & posterior – Translation of anterior & posterior

Mc


Mc

Force System for Group A space closure
M/F ratio 12/1 or more in posterior & 7/1 or 10/1in anteriors – Root moment of
posteriors & tipping or bodily moment of anteriors

IDEAL


Forces Differ


Moments Differ


Force system for Group C space closure mirrors that of group
A.

The anterior teeth becomes the effective anchor teeth.

The anterior moment is of greater magnitude & the vertical force side
effect is an extrusive force on the anterior teeth.


TORQUING WITH THE MOMENT OF A COUPLE
System equilibrium

Torquing arch
Incisor movements

AJO DO1993 May (428 – 438)

TORQUING WITH THE MOMENT OF A FORCE
System equilibrium

Base arch
Incisor movements

AJO DO1993 May (428 – 438)

CONCLUSION

Various mechanics can often be used to achieve the tooth movements
desired for orthodontic treatments. It is important however to understand
the mechanics involved and to recognize when the appliance will not achieve
adequate results or may result in undesirable side effects. This can help us
to prevent prolonged overall treatment time and/or compromise in the final
orthodontic outcome.
The ultimate result will be a happy post treatment patient , with a
beautiful smile leaving your clinic.


REFFERENCES
1. Smith RJ, Burstone CJ: Mechanics of tooth movement. AJO 85:294307,1984.
2. Burstone CJ, Koenig HA: Creative wire bending- The force system from step
& V bends. AJO DO 93(1):59-67,1988.
3. Burstone CJ, Koenig HA: Force system from the ideal arch. AJO 65(3):270289,1974.
4. Demange C: Equilibrium situations in bend force system. AJO DO98(4):333339,1990.
5. Issacson RJ, Lindauer SJ, Rubenstein LK: Moments with edgewise
appliance e: Incisor torque control. AJO DO 103(5):428-438,1993.
6. Koing HA, Vanderby R, Solonche DJ, Burstone CJ: Force system for
orthodontic appliances: An analytical & experimental comparison. J
Biomechanical Eng102(4):294-300,1980.
7. Kusy RP, Tulloch JFC: Analysis of moment/force ratio in the mechanics of
tooth movement. AJO DO 90; 127-131,1986.
8. Nanda R, Goldin B: Biomechanical approaches to the study of alteration of
facial morphology. AJO 78(2):213-226,1980.

9. Vanden Bulcke MM, Burstone CJ, Sachdeva RC , Dermaut LR: Location of
center of resistance for anterior teeth during retraction using the laser reflection
technique. AJO DO 91(5):375-384,1987.
10. Vanden Bulcke MM, Dermaut LR, Sachdeva RC, Burstone CJ: The center
of resistance of anterior teeth during intrusion using the laser reflection
technique & holographic interferometry. AJO DO 90(3): 211-220,1986.
11. Mulligan TF: Common sense mechanics 2 . Forces & moments. JCO
13:676-683,1979.
12. Siatkowski RE: force system analysis of V-bend sliding mechanics. JCO
28(9):539-546,1994.
13. Tanne K, et al: Moment to force ratios & the center of rotation. AJO 94:426431,1989
14. The basics of orthodontic mechanics. Semin Orthod 2001;7:2-15
15. Leveling & aligning: Challenges & Solutions Semin Orthod 2001;7:16-25.
16. Biomechanics in clinical Orthodontics. Ravindra Nanda, 1 st Edition
17. Biomechanics in Orthodontics. Michael R. Marcotte, 1st Edition

18. Modern Edgewise Mechanics & Segmented Arch Technique, Dr C J
Burstone, 1st Edition
19. Contemporary Orthodontics. W R Proffit 3 rd Edition
20. Orthodontics Current Principles & Techniques. T M Graber, R l
Vanersdal. 3rd Edition
21. Systemized Orthodontic Treatment Mechanics. R P McLaughlin, J C
Bennet, H J Trevisi


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