Biomech 01

INTRODUCTIONINTRODUCTION
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INTRODUCTIONINTRODUCTION
• Orthodontic problemsOrthodontic problems are the result ofare the result of
mechanical forces, andmechanical forces, and their correctiontheir correction
depends ondepends on mechanical forces.mechanical forces.
• The force systemsThe force systems in the face can form orin the face can form or
deform, and their conscious control is adeform, and their conscious control is a
continuing challenge in orthodontics.continuing challenge in orthodontics.

• AlteringAltering the balance of forcesthe balance of forces can arrest orcan arrest or
reverse progressive deformities duringreverse progressive deformities during
growth, and it can correct many of theirgrowth, and it can correct many of their
effects even in the adult.effects even in the adult.

• Thus understanding ofThus understanding of the fundamentalsthe fundamentals
of mechanicsof mechanics must be the starting point formust be the starting point for
understanding orthodontics.understanding orthodontics.

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

• In applying them to oral environment, oneIn applying them to oral environment, one
combinescombines engineeringengineering withwith dentistry,dentistry,
which requires a mixed terminology that iswhich requires a mixed terminology that is
partly foreign to each discipline:partly foreign to each discipline:
BIOBIOLOGYLOGY
++
MECHANICSMECHANICS
______________________________
BIO-MECHANICSBIO-MECHANICS

BIOMECHANICSBIOMECHANICS
LawsLaws
&&
TerminologiesTerminologies

Laws & TerminologiesLaws & Terminologies
This chapter is divided into following parts:This chapter is divided into following parts:
• ForceForce
– DirectionDirection
– MagnitudeMagnitude
– Point of applicationPoint of application
(Center of Resistance)(Center of Resistance)
• MomentMoment
– Moment of forceMoment of force
– Factors controlling theFactors controlling the
moment of forcemoment of force
– Center of rotationCenter of rotation
– Center of rotation and typeCenter of rotation and type
of tooth movementof tooth movement
• CoupleCouple
– Moment of coupleMoment of couple
– Factors controlling theFactors controlling the
moment of couplemoment of couple
• Moment to Force ratioMoment to Force ratio

Mechanical ForcesMechanical Forces
• The two broad classes of mechanicalThe two broad classes of mechanical
force are:force are:
– StaticStatic
– DynamicDynamic
• At any moment the oral structures can beAt any moment the oral structures can be
considered to be in a state ofconsidered to be in a state of staticstatic
balance.balance.

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

Magnitude of forceMagnitude of force
• Increasing theIncreasing the amount of forceamount of force willwill
increase the amount of a free bodyincrease the amount of a free body
displacement.displacement.
• However, it is unclear how forceHowever, it is unclear how force
magnitude is related to themagnitude is related to the rate of toothrate of tooth
movementmovement, which is biologically controlled, which is biologically controlled
phenomenon.phenomenon.

Point of ApplicationPoint of Application
• Center of MassCenter of Mass
• Center of GravityCenter of Gravity
• Center of ResistanceCenter of Resistance

Center of Mass:Center of Mass:
• Each body has a point in its mass, whichEach body has a point in its mass, which
behaves as if the whole mass isbehaves as if the whole mass is
concentrated at that single point, which weconcentrated at that single point, which we
call it thecall it the center of Masscenter of Mass in a gravity-freein a gravity-free
environment.environment.
Flash Player Movie

Back to EarthBack to Earth

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

• The center of gravity of the tooth is locatedThe center of gravity of the tooth is located
more towards the crownmore towards the crown of the tooth asof the tooth as
the mass of the tooth is concentratedthe mass of the tooth is concentrated
more coronallymore coronally

Center of ResistanceCenter of Resistance
• It is a point at whichIt is a point at which resistance to toothresistance to tooth
movementmovement is concentrated.is concentrated.
• It is at theIt is at the approximate midpoint of theapproximate midpoint of the
embedded portion of the root.embedded portion of the root.

Center of Gravity
Center of Resistance

Where is the Center of resistanceWhere is the Center of resistance
of…of…
• Single Tooth ?Single Tooth ?
• Anterior Segment ?Anterior Segment ?
• Full Upper Dentition ?Full Upper Dentition ?
Flash Player Movie
Center of Resistance

MomentMoment
Is defined as a tendency to rotateIs defined as a tendency to rotate

Moment of forceMoment of force
• We can apply a force only on the exposedWe can apply a force only on the exposed
part of the tooth, which is at apart of the tooth, which is at a distancedistance
from the center of resistance.from the center of resistance.
• Therefore with a single force in a typicalTherefore with a single force in a typical
clinical situation we invariably create aclinical situation we invariably create a
moment, called asmoment, called as moment of force.moment of force.

• In orthodontic terminology we refer toIn orthodontic terminology we refer to
moment asmoment as
– RotationRotation
– TippingTipping
– TorquingTorquing
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Factors controlling the Moment:Factors controlling the Moment:
• Moment (M)Moment (M)
• Force (F)Force (F)
• Perpendicular Distance (d)Perpendicular Distance (d)
M = F x dM = F x d

Center of RotationCenter of Rotation

Center of Rotation &Center of Rotation &
• Changing theChanging the point of force applicationpoint of force application
and its relation toand its relation to the center of resistancethe center of resistance
of the tooth will create:of the tooth will create:
Uncontrolled tippingUncontrolled tipping Controlled tippingControlled tipping Root MovementRoot Movement Bodily MovementBodily Movement
Center of
Rotation
at infinitywww.indiandentalacademy.com

CoupleCouple
Two equal and opposite, non-collinearTwo equal and opposite, non-collinear
forcesforces

CoupleCouple
• TheThe two forcestwo forces cancel outcancel out any tendencyany tendency
for the center of resistance of the pencil tofor the center of resistance of the pencil to
move, butmove, but the momentthe moment created by the twocreated by the two
forcesforces does not cancel each other.does not cancel each other.
• The pencil therefore, rotates about itsThe pencil therefore, rotates about its
center of resistancecenter of resistance regardless of theregardless of the
point of applicationpoint of application of the couple.of the couple.

• If the two forces of the couple act onIf the two forces of the couple act on
opposite sides of the center of resistanceopposite sides of the center of resistance,,
their effect istheir effect is additive.additive.
• However, if they are on theHowever, if they are on the same side ofsame side of
the center of resistancethe center of resistance, their effect is, their effect is
subtractive.subtractive.

A clinical exampleA clinical example
AdditiveAdditive SubtractiveSubtractive

ExplanationExplanation
Resultant moment = FdResultant moment = Fd11 + Fd+ Fd22
F1 x d1 = Fd1
F1
F2
d1
F1 F2
d1
F2 x d2 = Fd2
d2
d2

Factors controlling the MomentFactors controlling the Moment
of a Coupleof a Couple
• Moment (M)Moment (M)
• One of the forces (F1 or F2)One of the forces (F1 or F2)
• Moment arm of the couple (d)Moment arm of the couple (d)
M= F1 x dM= F1 x d
OROR
M= F2 x dM= F2 x d
F1
F2
d
F1
F2
d

Couple – Clinical pointCouple – Clinical point
• When the tooth is embeddedWhen the tooth is embedded within thewithin the
alveolar bonealveolar bone we cannot apply a couplewe cannot apply a couple
with one force on the crown and the otherwith one force on the crown and the other
force on the root.force on the root.
• We can apply a couple only on theWe can apply a couple only on the
exposed partexposed part of the tooth.of the tooth.

• Irrespective of point of applicationIrrespective of point of application ofof aa
couple on a body or a tooth, the body willcouple on a body or a tooth, the body will
experience a moment & it will rotateexperience a moment & it will rotate
around it’s center of resistance.around it’s center of resistance.
Stick.swfwww.indiandentalacademy.com

• Depending on the plane in which theDepending on the plane in which the
couple is actingcouple is acting, this rotation has been, this rotation has been
calledcalled “rotation”“rotation” (first order),(first order), “tipping”“tipping”
(second order), or(second order), or “torque”“torque” (third order) in(third order) in
orthodontics.orthodontics.

• I am sure all of you already familiar with theI am sure all of you already familiar with the
above mentioned points.above mentioned points.
• I will assume that from now onwards you areI will assume that from now onwards you are
familiar with terminologies such as,familiar with terminologies such as,
– ForceForce
– Moment of a forceMoment of a force
– CoupleCouple
– Moment of a coupleMoment of a couple

• Next we will cover-Next we will cover-
– Moment to Force RatioMoment to Force Ratio
• And I am sure many have this question:And I am sure many have this question:
– Which moment?Which moment?
– WhetherWhether moment of forcemoment of force oror
moment of couple?moment of couple?

Moment-to-Force ratioMoment-to-Force ratio
The ratio ofThe ratio of counter-balancing momentcounter-balancing moment
produced toproduced to net forcenet force that is applied tothat is applied to
a tooth.a tooth.

An example:An example:
• In order to retract an incisor tooth weIn order to retract an incisor tooth we
apply aapply a forceforce on the crown of the tooth.on the crown of the tooth.
• This force tends to move the center ofThis force tends to move the center of
resistance of the tooth, however it alsoresistance of the tooth, however it also
creates acreates a moment of force (clockwise).moment of force (clockwise).
F = Force
d = distance (X) F x d(X) = M(X)
F
M(X)

• AnAn counter-clockwise momentcounter-clockwise moment can becan be
generated easily by applying agenerated easily by applying a couple.couple.
Note couple generates a momentNote couple generates a moment
irrespective of center of resistance of theirrespective of center of resistance of the
tooth.tooth.
F(X) x d = M(X) M(X)
F = Force (X)
d = distance www.indiandentalacademy.com

• The two moments (i.e.The two moments (i.e. the moment ofthe moment of
forceforce andand the moment of couplethe moment of couple) cancel) cancel
out any tendency for the rotation of theout any tendency for the rotation of the
tooth, thereby allowing the force to movetooth, thereby allowing the force to move
the center of resistance of the tooth.the center of resistance of the tooth.

Bodily movement of a tooth requires a moment-to-Bodily movement of a tooth requires a moment-to-
force ratio offorce ratio of 8:18:1 oror 10:110:1, depending on the length of, depending on the length of
the root,the root, BUT WHY?BUT WHY?
10 mm
20 mm
M : F
10 : 1
M :
F
20 :
1www.indiandentalacademy.com

Tooth MovementTooth Movement
Orthodontic ApplicationOrthodontic Application
ofof
Moment to Force RatioMoment to Force Ratio

• As we have seen whenever a force isAs we have seen whenever a force is
applied at the crown of a tooth, a tendencyapplied at the crown of a tooth, a tendency
for the tooth tofor the tooth to rotaterotate,, tiptip oror torquetorque (a(a
moment) is also created.moment) is also created.

• TheThe forceforce at theat the
bracketbracket is equivalentis equivalent
to ato a forceforce at theat the
center of resistancecenter of resistance
plus aplus a momentmoment thatthat
will cause the toothwill cause the tooth
to tip.to tip.

• In addition to theIn addition to the
force applied, aforce applied, a
couplecouple may also bemay also be
engaged intentionallyengaged intentionally
to partially correct,to partially correct,
completely correct, orcompletely correct, or
over-correct thisover-correct this
tendency.tendency.

• By varying theBy varying the ratio of moment to forceratio of moment to force
applied to teeth, the quality of toothapplied to teeth, the quality of tooth
movement can be changed amongmovement can be changed among
uncontrolled tipping, controlled tipping,uncontrolled tipping, controlled tipping,
translation and root movement.translation and root movement.

Uncontrolled TippingUncontrolled Tipping
At the
CENTER OF
RESISTANCE
At the
BRACKET
NET
MOMENT
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Controlled TippingControlled Tipping
At the
CENTER OF
RESISTANCE
At the
BRACKET
NET
MOMENT
Flash Player Movie

TranslationTranslation
At the
CENTER OF
RESISTANCE
At the
BRACKET
NET
MOMENT ZER
Flash Player Movie

Root MovementRoot Movement
At the
CENTER OF
RESISTANCE
At the
BRACKET
NET
MOMENT
Flash Player Movie

Pure RotationPure Rotation
At the
CENTER OF
RESISTANCE
At the
BRACKET
NET
MOMENT
Flash Player Movie

CONTINUECONTINUE

Biomech 01

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Biomech 01