Copy of biomech 01 /certified fixed orthodontic courses by Indian dental academy

INDIAN DENTAL ACADEMY
Leader in continuing dental education
www.indiandentalacademy.com


INTRODUCTION


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.


• 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.


• Thus understanding of the fundamentals
of mechanics must be the starting point for
understanding orthodontics.


• The principles of force analysis are the
basic tools of the mechanical engineer, &
their application is universal.


• 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

BIOMECHANICS
Laws
&
Terminologies

Laws & Terminologies

This chapter is divided into following parts:
• Couple

• Force
–
–
–

– Moment of couple
– Factors controlling the
moment of couple

Direction
Magnitude
Point of application
(Center of Resistance)

• Moment to Force ratio

• Moment
– Moment of force
– Factors controlling the
moment of force
– Center of rotation
– Center of rotation and type
of tooth movement

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.


Force
Definition:
• an act upon a body that changes or tends
to change the state of rest or the motion of
that body.


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.


Point of Application
• Center of Mass
• Center of Gravity
• Center of Resistance


Center of Mass:

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• 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.


Back to Earth


Center of Gravity:
• The same is called center of Gravity in an
environment where gravity is present.


• 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


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.



Center of Gravity


Where is the Center of resistance
of…
•
•
•

Single Tooth ?
Anterior Segment ?
Full Upper Dentition ?

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Moment
Is defined as a tendency to rotate


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.


• In orthodontic terminology we refer to
moment as
– Rotation
– Tipping
– Torquing

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Factors controlling the Moment:
• Moment (M)
• Force (F)
• Perpendicular Distance (d)

M=Fxd

Center of Rotation


Center of Rotation &
• 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

Couple
Two equal and opposite, non-collinear

forces


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.


• 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.


A clinical example

Subtractive

Additive

Explanation
Resultant moment = Fd1 + Fd2
F1

F1

d1

F1 x d1 = Fd1
d2

F2 x d2 = Fd2

F2


d1
d2

F2

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

F1

d
d
F2

F2

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.


• 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.

Stick.swf


• 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.


• I am sure all of you already familiar with the
above mentioned points.
• I will assume that from now onwards you are
familiar with terminologies such as,

– Force
– Moment of a force
– Couple
– Moment of a couple

• 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?


Moment-to-Force ratio
The ratio of counter-balancing moment
produced to net force that is applied to
a tooth.


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

F = Force
d = distance (X)

F x d(X) = M(X)

M(X)

• 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 = Force (X)
d = distance

F(X) x d = M(X)

M(X)

• 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.


Bodily movement of a tooth requires a moment-toforce ratio of 8:1 or 10:1, depending on the length of
the root, BUT WHY?

20 mm
10 mm

M : F
10 : 1

M :
F
20 :
1

Tooth Movement
Orthodontic Application
of
Moment to Force Ratio

• 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.


• 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.


• In addition to the
force applied, a
couple may also be
engaged intentionally
to partially correct,
completely correct, or
over-correct this
tendency.

• 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.


Uncontrolled Tipping
At the
BRACKET

At the
CENTER OF
RESISTANCE

NET
MOMENT


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Controlled Tipping
At the
BRACKET

At the
CENTER OF
RESISTANCE

NET
MOMENT


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Translation
At the
BRACKET

At the
CENTER OF
RESISTANCE

NET
MOMENT

ZER


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Root Movement
At the
BRACKET

At the
CENTER OF
RESISTANCE

NET
MOMENT


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Pure Rotation
At the
BRACKET

At the
CENTER OF
RESISTANCE

NET
MOMENT


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Copy of biomech 01 /certified fixed orthodontic courses by Indian dental academy

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