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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 Resistance

Center of Resistance 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)


Center of Rotation

Center of Rotation & Center of Resistance • 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


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



Explanation Resultant moment = Fd1 + Fd2 F1



F1 x d1 = Fd1 d2

F2 x d2 = Fd2


d1 d2


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



dd 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.


• 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) x d(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)


• 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



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Controlled Tipping At the BRACKET



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Translation At the BRACKET




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Root Movement At the BRACKET



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Pure Rotation At the BRACKET



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