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Basic Biomechanics ofBasic Biomechanics of
Tooth MovementTooth Movement
www.indiandentalacademy.comwww.indiandentalacademy.com

IntroductionIntroduction
Scalars and vectorsScalars and vectors
Orthodontic force:Orthodontic force:

Resultants andResultants and

ComponentsComponents
Types of tooth movementsTypes of tooth movements
Centers of rotation and resistanceCenters of rotation and resistance
Equivalent systemsEquivalent systems

Moment of a forceMoment of a force
Moment of a coupleMoment of a couple
Moment to force ratioMoment to force ratio
ConclusionConclusion

MechanicsMechanics
An area of study within physical scienceAn area of study within physical science
that is concerned with the state of rest orthat is concerned with the state of rest or
motions of bodies subjected to forces.motions of bodies subjected to forces.
Understanding of mechanics is based onUnderstanding of mechanics is based on
particle mechanics formulated by Sir Isaacparticle mechanics formulated by Sir Isaac
NewtonNewton

Newtonian MechanicsNewtonian Mechanics
Static – body at rest and under action ofStatic – body at rest and under action of
forcesforces
Dynamic – moving bodiesDynamic – moving bodies

Kinematics – study of motion itselfKinematics – study of motion itself

Kinetics – relationship between the forceKinetics – relationship between the force
systems and characteristics of body motionsystems and characteristics of body motion
are exploredare explored

Newton's LawsNewton's Laws
11stst
law: particle subjected to balanced system oflaw: particle subjected to balanced system of
forces will remain at rest, if originally at rest, orforces will remain at rest, if originally at rest, or
move with constant speed in a straight line, ifmove with constant speed in a straight line, if
originally in motion.originally in motion.
22ndnd
law: particle subjected to unbalanced systemlaw: particle subjected to unbalanced system
of forces will accelerate in the direction of the netof forces will accelerate in the direction of the net
forceforce
33rdrd
law: every action has an equal and oppositelaw: every action has an equal and opposite
reaction.reaction.

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

On a sub clinical level:On a sub clinical level:

Control the centre of rotation of the toothControl the centre of rotation of the tooth

To maintain a desirable stress level in the pdlTo maintain a desirable stress level in the pdl

To maintain a relatively constant stress levelTo maintain a relatively constant stress level
On a clinical level:On a clinical level:

The M:F ratioThe M:F ratio

The load deflection rateThe load deflection rate

The maximal forces or moment of anyThe maximal forces or moment of any
component of an appliancecomponent of an appliance

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

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

Smith and Burstone (1984)

Resultants form a single point

Resultant form two point of application

R2
= a2
+ b2
– 2ab

Tan theta = p/q
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 beForces in general can be

Active and reactive (Newton)Active and reactive (Newton)

Concentrated or distributedConcentrated or distributed

External or internalExternal or internal

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

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

Types of tooth movementTypes of tooth movement
Pure translationPure translation
Pure rotationPure rotation
CombinationCombination ofof bothboth

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

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

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

C res. Of aC res. Of a
Single rooted tooth---on the long axisSingle rooted tooth---on the long axis
between 1/3between 1/3rdrd
andand
½ of the root½ of the root
apical to alveolarapical to alveolar
crest.crest.
Multirooted tooth--- between the roots,Multirooted tooth--- between the roots,
1 to 2 mm apical to1 to 2 mm apical to
the furcation.the furcation.

Effect of forcesEffect of forces
Translation: If the line of action of an appliedTranslation: If the line of action of an applied
force passes through the center offorce passes through the center of
resistance of a tooth, the tooth willresistance of a tooth, the tooth will
respond with pure bodily movementrespond with pure bodily movement
(translation) in the direction of the line of(translation) in the direction of the line of
action of the applied force.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 :Couple :

Is a system consisting ofIs a system consisting of twotwo forces that areforces that are equal inequal in
magnitudemagnitude, with, with parallelparallel butbut nonnon collinearcollinear lines oflines of
action and opposite senses.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

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

Centre of rotation can also be defined asCentre of rotation can also be defined as
that point that has the least magnitude ofthat point that has the least magnitude of
moment (m = 0) ormoment (m = 0) or
Can also be defined as the point that hasCan also be defined as the point that has
moved the least during tooth movementmoved 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 systemsEquivalent systems

Criteria for systems to be equivalent :Criteria for systems to be equivalent :

(1) the sums of forces in the x direction are(1) the sums of forces in the x direction are
identical,identical,

(2) the sums of forces in the y direction are(2) the sums of forces in the y direction are
identical,identical,

(3) the sums of moments about any point are(3) the sums of moments about any point are
identical.identical.
Smith and Burstone(1984)

What would the force system at the bracket in B be so that
It would be equivalent to the system in A
1200gmm
150gm

Moment to Force ratioMoment to Force ratio
The type of tooth movement would beThe type of tooth movement would be
determined by the ratio of the moment ofdetermined by the ratio of the moment of
the couple and the force applied at thethe couple and the force applied at the
bracket.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)

Burstone and Pryputniewicz
A = uncontrolled tipping
B = controlled tipping
C = bodily movement
D = bodily movement
E = root movement
F = pure rotation
0
7/1
10/1
12 or 13/1
20/1

F1d = F3dc F3dc > F1d
F3dc >> F1d
F1d>f3dc

Statically determinate systems (oneStatically determinate systems (one
couple system)couple system)

This means that the magnitudes and theThis means that the magnitudes and the
direction of the forces and moments exerteddirection of the forces and moments exerted
by the wire can be determined clinically onceby the wire can be determined clinically once
the appliance is inserted into the bracketthe appliance is inserted into the bracket

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

Statically indeterminate systems (twoStatically indeterminate systems (two
couple systems)couple systems)

The ,magnitude of the force systemsThe ,magnitude of the force systems
produced cannot be determined clinically butproduced cannot be determined clinically but
the direction can be.the direction can be.

The force systems produced depend both onThe force systems produced depend both on
the wire geometry and the bracketthe wire geometry and the bracket
angulationsangulations

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

referencesreferences
Graber and Swain :Orhtodontics: CurrentGraber and Swain :Orhtodontics: Current
principles and practiceprinciples and practice
Smith and Burstone: mechanics of toothSmith and Burstone: mechanics of tooth
movement, AJO 1984; 85: 295 – 300.movement, AJO 1984; 85: 295 – 300.
Hocevar: understanding, planning and managingHocevar: understanding, planning and managing
tooth movement, AJO 1981; 457 -477tooth movement, AJO 1981; 457 -477
Mulligan: Common sense mechanics JCO – 13;Mulligan: Common sense mechanics JCO – 13;
676 – 683 1979.676 – 683 1979.
Hurd and Nikolai: centers for rotation ofHurd and Nikolai: centers for rotation of
combined vertical and transverse toothcombined vertical and transverse tooth
movements, AJO 1976; 70 : 551movements, AJO 1976; 70 : 551

Nikolai : bioengineering analysis ofNikolai : bioengineering analysis of
orthodontic mechanicsorthodontic mechanics
Burstone and Koening, Forces in an idealBurstone and Koening, Forces in an ideal
arch. AJO; 1974: 65, 2670 – 289.arch. AJO; 1974: 65, 2670 – 289.
Demange C: Equilibirium situations inDemange C: Equilibirium situations in
bend force systems. AJO – DO; 1990: 98,bend force systems. AJO – DO; 1990: 98,
333 – 339333 – 339
Marcotte MR: AJO: 1969, 511 – 523,Marcotte MR: AJO: 1969, 511 – 523,
1976.1976.

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