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

Basic Biomechanics of
Tooth Movement
INDIAN DENTAL ACADEMY
Leader in continuing dental education
www.indiandentalacademy.com


Introduction
Scalars and vectors
Orthodontic force:



Resultants and
Components

Types of tooth movements
Centers of rotation and resistance
Equivalent systems

Moment of a force
Moment of a couple
Moment to force ratio
Conclusion


Mechanics
An area of study within physical science
that is concerned with the state of rest or
motions of bodies subjected to forces.
Understanding of mechanics is based on
particle mechanics formulated by Sir Isaac
Newton


Newtonian Mechanics
Static – body at rest and under action of
forces
Dynamic – moving bodies



Kinematics – study of motion itself
Kinetics – relationship between the force
systems and characteristics of body motion
are explored


Newton's Laws
1st law: particle subjected to balanced system of
forces will remain at rest, if originally at rest, or
move with constant speed in a straight line, if
originally in motion.
2nd law: particle subjected to unbalanced system
of forces will accelerate in the direction of the net
force
3rd law: every action has an equal and opposite
reaction.

Reduce empiricism or trail and error
Relates concepts of stress distribution in
the PDL to that of bone remodeling
Increase efficiency and efficacy of the
appliance.


On a sub clinical level:




Control the centre of rotation of the tooth
To maintain a desirable stress level in the pdl
To maintain a relatively constant stress level

On a clinical level:




The M:F ratio
The load deflection rate
The maximal forces or moment of any
component of an appliance


Scalars and Vectors
Scalars---- completely described by
their magnitude alone.
Eg. Mass, distance , temperature.
Vectors---- described by magnitude and
direction.
Eg. Force

Force
Is defined as an act on a body that
changes or tends to change the state of
rest or motion of the body.
As per Newton's laws two bodies are
always associated with a force i.e. one
that exerts the force and the other that
receives the force


Smith and Burstone (1984)


Resultants form a single point


Resultant form two point of application

R2 = a2 + b2 – 2ab

p

q
Tan theta = p/q
R2 = p2 + q2 for mutually perpendicular forces
R2 = p2 + q2 – 2pq (cos theta) for not perpendicular to
Each other.


Forces in general can be




Active and reactive (Newton)
Concentrated or distributed
External or internal


Static equilibrium
This states that for every appliance, not
necessarily every tooth, the sum of
moments and sum of forces be equal to
zero, i.e. the net force should be zero,
regardless of the type of appliance that is
being used.


Intrusive force on the incisors is balanced by an extrusive force on the molars


Types of tooth movement

Pure translation

Pure rotation

Combination of both

When a tooth in the mouth move during
orthodontic therapy there is no pure
translation or pure rotation there is always
a combination of the two.
(Hurd and Nikolai)


terminology
Centre of Mass: is that point where all the
mass of a body is concentrated when the
body is in space.
Centre of Gravity: is the same point but
when gravity is acting on the body.
Centre of Resistance: is that point,
through which if a force is applied will
move a object bodily, or produce a pure
translation.

Centre of resistance in tooth
Depends on the root length and
Depends on the height of the alveolar
bone.
In a tooth of paraboloid shape the centre
of resistance lies at h/3 where h is the
length of the root.


C res. Of a
Single rooted tooth---on the long axis
between 1/3rd and
½ of the root
apical to alveolar
crest.
Multirooted tooth--- between the roots,
1 to 2 mm apical to
the furcation.

Effect of forces
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
(translation) in the direction of the line of
action of the applied force.


A moment of a force is the rotational tendency of the force
The moment of a force is equal to the magnitude of the force
multiplied by the perpendicular distance from its line of action to the
center of resistance.
m = f x d (gmm)


(Note that there will be only a single net moment or net force on a tooth)


Couple :


Is a system consisting of two forces that are equal in
magnitude, with parallel but non collinear lines of
action and opposite senses.

M = 50x10 = 500gmm
Net moment = 1000gmm

or

M = f x (distance between the two forces)
M = 50 x 20
M = 1000gmm


M =( f1d1) + ( f2d2)

M =( -50x10 ) + ( 50 x 30)

M = 1000gmm


Center of rotation
a centre of rotation can be defined as that
point about which a body appears to have
rotated as shown by the initial and final
positions of the tooth


Centre of rotation can also be defined as
that point that has the least magnitude of
moment (m = 0) or
Can also be defined as the point that has
moved the least during tooth movement


Changing centre of rotations in A ( Nilkolai and Hurd)
The centre of rotation for a combined translation and rotatory movement
(Hocevar)

Forces within cross hatched areas will produce rotation as well as
translation whereas the blank areas will produce simple tipping


Forces in the shaded areas will produce translation
And rotation at a rate that is continuously
accelerating


Changing the positions of the centers of rotation can bring about
changes in the type of tooth movement but not the extent of tooth
movement


Equivalent systems


Criteria for systems to be equivalent :






(1) the sums of forces in the x direction are
identical,
(2) the sums of forces in the y direction are
identical,
(3) the sums of moments about any point are
identical.
Smith and Burstone(1984)


150gm

1200gmm

What would the force system at the bracket in B be so that
It would be equivalent to the system in A

Moment to Force ratio

The type of tooth movement would be
determined by the ratio of the moment of
the couple and the force applied at the
bracket.


What is the net moment here considering all forces
to be 5 and distances to be 2
The type of movement occuring would depend on the location
Of the center of rotation which is determined by the moment to force ratio
(not their magnitudes)

10/1

Burstone and Pryputniewicz

A = uncontrolled tipping
B = controlled tipping
C = bodily movement
D = bodily movement
E = root movement
F = pure rotation

7/1
0
20/1
12 or 13/1


F3dc > F1d

F1d = F3dc

F1d>f3dc
F3dc >> F1d


Statically determinate systems (one
couple system)


This means that the magnitudes and the
direction of the forces and moments exerted
by the wire can be determined clinically once
the appliance is inserted into the bracket


One couple system-examples
Cantilever springs used to bring severely
displaced teeth into the arch
Auxiliary intrusion or extrusion arches
Begg intrusion arch


Statically indeterminate systems (two
couple systems)




The ,magnitude of the force systems
produced cannot be determined clinically but
the direction can be.
The force systems produced depend both on
the wire geometry and the bracket
angulations


Conclusion
The laws of physics are fundamental, and
though their application in the different
hands may vary the knowledge of the
fundamentals is a necessary prerequisite
to achieve the desired tooth movement in
the most effective and efficient manner.


references
Graber and Swain :Orhtodontics: Current
principles and practice
Smith and Burstone: mechanics of tooth
movement, AJO 1984; 85: 295 – 300.
Hocevar: understanding, planning and managing
tooth movement, AJO 1981; 457 -477
Mulligan: Common sense mechanics JCO – 13;
676 – 683 1979.
Hurd and Nikolai: centers for rotation of
combined vertical and transverse tooth
movements, AJO 1976; 70 : 551

Nikolai : bioengineering analysis of
orthodontic mechanics
Burstone and Koening, Forces in an ideal
arch. AJO; 1974: 65, 2670 – 289.
Demange C: Equilibirium situations in
bend force systems. AJO – DO; 1990: 98,
333 – 339
Marcotte MR: AJO: 1969, 511 – 523,
1976.

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

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