biomechanical principles in orthodontics / prosthodontic courses

The biologic cascade of events that ultimately results in bone
remodeling and orthodontic tooth movement begins with the mechanical
activation of an orthodontic appliance. The force systems produced by
orthodontic appliances, consisting of both forces and moments, displace
teeth in a manner that is both predictable and controllable. By varying the
ratio of moment to force applied to teeth, the type of tooth movement
experienced can be regulated by the orthodontist. Orthodontic appliances
obey the laws of physics and can be activated to generate the desired force
systems to achieve predetermined treatment goals for individual patients.
Likewise, any orthodontic appliance can be analyzed to define the
mechanical force systems it produces. Understanding the biomechanical
principles underlying orthodontic appliance activations is essential for
executing efficient and successful orthodontic treatment.
INTRODUCTION
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Biomechanics Terminologies &
Laws
Forces
Moments
Couples
Moment-to-Force Ratio

FORCE
The two broad classes of mechanical forces are:
Static: which deals with bodies at rest
Dynamic: which deals with moving bodies.
At any moment the oral structures can be considered to be in a state of
static balance.
Force is defined as an act upon a body that changes or tends to change
the state of rest or the motion of that body.
Though defined in units of Newtons it is usually measured in units of
grams or ounces.
Forces are vectors, having both direction & magnitude. Point of
application of force is also important in the understanding of tooth
movement.

Force (contd.,)
Direction
Pull and push
Magnitude
Light and Heavy
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 a biologically
controlled phenomenon

Force (contd.,)
Point of application
Center of Mass
Center of Gravity
Center of Resistance

Center of Mass:
Each body has a point in its mass, which behaves as if the wholemass is
concentrated at the single point, which we call the center of mass in a
gravity-free environment. The same called center of gravity in an
environment where gravity is present.
Point of application of force in relation to center of Mass:
Tipping – When a force is applied on this pencil below its center of mass,
it tips and moves forward. When another force is applied above the center
of mass, the pencil will again tip are move forward.
Translation – If the force is passing through the center of mass, the whole
body moves in a straight line, in a parallel fashion. Here all the points of
the body get displaced equally from the initial position. This is called
bodily movement or translation
Therefore, same laws of mechanics apply to a tooth; for example, a force
applied below the center of gravity of the tooth will cause the tooth to tip.

Center of Resistance:
Since the tooth is partially restrained, as its root is
embedded in bone, its center of gravity shifts
apically and is then referred to as the Center of
resistance
The center of resistance is a point at which the
resistance to tooth movement is concentrated. It is
determined by the nature of the external
constraints.

Moment
A moment is defined as a tendency to rotate.
Moment of the force:
When a force is applied at any point other than through the
center of resistance, in addition to moving the center of
resistance in the direction of the force, a moment is
created. Since the tooth is embedded in the alveolar bone,
we can never apply a force directly on the center of
resistance. We can only apply a force 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, invariably create a moment, which is
called as moment of force.
A moment may be referred as “Rotation”, “Torquing”

Factors controlling the moment:
it is the product of the force(F) times the
perpendicular distance from the point of force
application to the center of resistance (d).
measured in hybrid units such as grams-millimeters
(gm-mm).
Since the value of a moment is the product of a
force value (Such as grams) multiplied by linear
value (Such as millimeters) -therefore either
increasing the magnitude of the force or applying the
same force even further from the center of resistance
will increase the tendency for rotation .

Center of Rotation:
if we draw the long axis of the tooth in its initial and final
positions, we will find that both these lines intersect at a point.
This is the point around which the tooth rotates and is called
the center of rotation .
Center of Rotation and Center of Resistance:
The center of rotation can be at the center of resistance,
apical to the center of resistance, at the root or at infinity.
Their position will determine the type of tooth movement.
Uncontrolled tipping:
Controlled tipping:
Translation or bodily movement:
Generally speaking, the center of resistance of a tooth does not
change, only the center of rotation changes.

Couple
The moment of couple
instead of single force, we apply two forces equal in magnitude and opposite in
direction at a distance, the movement thus created is called the moment of a
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. Either way, no net force is felt by
the pencil, only a tendency to rotate.
A couple applies a pure moment to a teeth.
Moment of force
The concept of couple actually encompasses all situations involving rotation.
In other words any rotational tendency is related to couple. But a moment
(rotational tendency) can be achieved with a single force. The moment thus
created is called the moment of the force

Axis: An axis is any point about which rotation takes place; it is dependent
only on the influence of outside forces any may be located anywhere
within or outside the rotating object.
Fulcrum: A fulcrum is a physical support such as an axle or the pivot under a
lever. A fulcrum is an actual point of application of force, either applied or
reactive, so it is an element of input into the total force picture.
Because of its structural function, a fulcrum may frequently be the
location of an axis as well.
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. Using this
couple mechanism we can achieve various tooth alignment procedures,
irrespective of the center of the resistance of the tooth.
Depending on the place in which the couple is acting, this rotational
tendency (moment) has been called “rotation” (first order), “tipping”
(second order), or “torque” (third order)

Moment – to – Force Ratio
If a bracket is 10 mm from the center of
resistance, a force applied at the bracket causes the
tooth to tip because of a moment that is 10 times
the magnitude of the force. To counter-act this
tendency to tip, a couple is applied in the
magnitude of the force. This would be an applied
moment-to-force ratio of 10:1, resulting in
displacement of the tooth as if the force alone had
been placed through the center of resistance.

Tooth Movement
A comprehensive way of describing tooth movement is to
express the components experienced by the tooth at the center
of resistance, which includes both translation and rotation.
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.
Whenever a force is applied at the crown of a tooth, a
tendency for the tooth to rotate, tip or torque is also created
(moment of force). In addition to the force applied, a couple
may also be engaged intentionally to partially correct,
completely correct, or over-correct this tendency. By
changing the ratio of the moment from the applied couple
(counterbalancing moment) to the force applied, the center
of rotation of tooth movement can be varied to produce the
type of tooth movement desired

Uncontrolled tipping:
When only a force is applied at the bracket to move a
tooth, the equivalent force system at the center of
resistance is the force plus a moment that will tip the
crown in the direction of force. Without a moment to
counteract the tendency of the tooth to tip in the direction
of the force, the center of resistance of tooth moves in the
direction of the force, the crown moves further than the
center of resistance, and the apex actually moves in a
direction opposite to the force. Therefore the center of
rotation when the moment –to –force ratio is zero is just
apical to the center of resistance.

Controlled tipping:
To counteract the tendency for tipping, a couple can
be applied intentionally at the bracket to produce a
moment of less magnitude in the opposite direction
(counterbalancing-moment). When a moment to force
ratio of 7:1 is applied at the bracket, the equivalent force
system at the center of resistances is a force to move the
tooth plus a small net tendency for the crown to tip in the
direction of the force. Therefore the center of rotation
when the moment-to-force ratio is 7:1 is at the apex of the
tooth, and only crown movement occurs.

Translation:
To counteract the tendency for tipping, a
couple can be applied intentionally to produce a
moment of equal magnitude in the opposite
direction (counterbalancing-moment). When a
moment to force ration of 10:1 is applied at the
bracket, the equivalent force system at the center
of resistance is a single force with no net moment.
In the pure translation, the center of rotation is
considered to be at infinity because no rotation
occurs.

Root movement:
When the counter-moment applied intentionally at a
bracket is more than the moment of force, the tooth
moves in the direction of the force but the crown tips in the
opposite direction. When a moment to force ratio of 12:1
is applied at the bracket, the equivalent force system at the
center of resistance is a force to move the tooth plus a
small net tendency for the tooth to tip in the direction of
the force. The center of rotation when the moment to
force ratio is 13:1 is at the crown of the tooth and only root
movement occurs.

Pure rotation:
If only a couple, and no force is applied to a tooth, the
tooth will rotate around its center of resistance and the
tooth will not translate. Because the action of a couple
does not depend on its point of application, a pure
moment always acts at the center of resistance.
The forces of couples cancel out any tendency for the
center of resistance of the tooth to move, but the moment
produced by the couple causes the tooth to rotate. The
moment to force ratio is infinite and the center of rotation
is coincident with the center of resistance.

Predicting the force systems:
Understanding the physics that determine the force system
generated by activating orthodontic appliances discloses the force and
moment that are applied to teeth at their point of attachment, usually at
the brackets.
To deduce how each tooth will be displaced as a result of activation, the
equivalent force systems acting at the centers of resistances must be
accessed subsequently.
Visual inspection method:
In determining what forces are present, the arch wire is fully
engaged into a bracket or tube and possible force system is evaluated
by the eyeballing. This method is based on laws of static equilibrium
and if not understood correctly can confuse further.

Static equilibrium:
According to Newton’s third law, every action has an
equal and opposite reaction.
Requirement for static equilibrium:
Three requirements are accomplished automatically
whenever static equilibrium is established. They are:
The sum of all forces present must equal zero.
The sum of all moments present must equal zero
The sum of all forces and moments present must equal
zero.

When an arch wire is fully engaged, we are generating
unequal moments. Forces are also generated to keep the
system balanced. Therefore, all the moments and forces
will sum up to zero (i.e. always results in static
equilibrium).
This application is the for every appliance, but not
necessarily for every tooth to which it is attached, the sum
of the forces and the sum of the moments must equal to
zero. That is because the orthodontic appliance itself does
not move instantaneously once it is placed (e.g. an arch
wire fully engaged will not move the teeth
instantaneously).

Conclusion
the choice of appliances and technique used by
practitioners varies radically among individuals,
but the fundamental forces and moments they
produce are universal.
Appliance will always act according to the laws of
physics
Understanding the basic force systems helps
achieving controlled tooth movement in a
predictable manner

REFERENCES
• Michael Marcotte; Biomechanics in Orthodontics, Decker Publishers, 1990, 1-22.
• R.Nanda; Biomechanics in Clinical Orthodontics, Saunders, 1996, 1-22.
• Graber Vanarsdall Vig, Orthodontics current principals and technique, Elsevier
publications, 4th
ed. Pg no. 293- 299.
• Proffit , contemporary orthodontics, Mosby publications , ed.3rd
,pg no. 340- 360.
• Steven J. Lindauer, Principles of biomechanics; Seminars in orthodontics,Vol 7
,No.2,March 2001.

THANK YOU

biomechanical principles in orthodontics / prosthodontic courses

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