Definitions Properties of force Center of mass, gravity and resistance Moment Natural- mechanical force interaction Description of mechanical forces Force magnitude Duration of force Classification of therapeutically induced force Orthodontic force system (law and mechanics) Two couple system Symmetric and a symmetric bends Lingual arch as two couple system

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Dr. Mohammed Alruby
Mechanics in orthodontics
Prepared by:
Dr. Mohammed Alruby

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Dr. Mohammed Alruby
Definitions
Properties of force
Center of mass, gravity and resistance
Moment
Natural- mechanical force interaction
Description of mechanical forces
Force magnitude
Duration of force
Classification of therapeutically induced force
Orthodontic force system (law and mechanics)
Two couple system
Symmetric and a symmetric bends
Lingual arch as two couple system
= Mechanics; branch of physics concerned with the mechanical aspect of any system

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Dr. Mohammed Alruby
Divisions: statics: study of factors associated with non-moving (rigid) system
Dynamics: study of factors associated with moving system
= Biology: biomechanics: when mechanics applied on structure and function of living system
= Quantitative biomechanical approach: describe movement of teeth or associated skeletal structure, 3mm
canine retraction and 15 degrees in incisors flaring
= Qualitative biomechanical approach: describe tooth movement in non-numerical terms (without
measuring or counting anything) as yipping and translation
= Force: something that cause or tends to cause a change in motion or shape of an object or body
Or: cause an object to accelerate or decelerate
Properties of force:
1- Magnitude: amount of force being applied (1n, 2n)
2- Direction: the way the force being applied on its orientation to the object (forward, upward,
backward)
3- Point of application: where the force is applied on the body (in the center, at the bottom)
4- Line of action of force: straight line constructed in the same plane of direction of force extending
through the point of application.
N: B: force measured in newton (N) but in orthodontics measured in gm
To move a tooth predictably, a force must be applied with optimal magnitude, in desired direction
and at the correct point on the tooth.
Vector addition:
Law of vector addition:
F R: thought as retractive force in incisors
F E: force from Class II elastics
R: net effect of two forces

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Dr. Mohammed Alruby
N: B: the amount of intrusion of incisors can be measured by two methods:
Vector resolution:
Method used to determine two component vectors that form one vector given initially.
Single vector given is divided into two component horizontal and vertical, the direction of these component
is relative to some reference frame such as occlusal plane or Frankfort horizontal
F H= F cos ϴ: horizontal component
F V = F sin ϴ: vertical component
Center of Mass, center of gravity and center of resistance:
= center of mass of body may be thought as, the point at which all of body seems to be concentrated
= if a force is applied through this point, the system or body will move in a straight line without any rotation
= if the force of gravity is concentrated at a single point called center of gravity
= the position of center of resistance is directly depend on clinical root of the tooth (distance between
alveolar crest and root apex) incrementing this value by root thickness
= the position of center of resistance C Res is also function in nature and depend on:
1- Periodontal structure
2- Density of alveolar bone
3- Elasticity of dento-alveolar ligament
So we called C Res associated with the tooth rather than C Res of the tooth

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Dr. Mohammed Alruby
=The center of resistance of the tooth is located
slightly apical to the center of gravity
=The periodontal structures surrounding the tooth
root cause this apical migration
moment: torque:
force acting to static system, potential of rotation
= when an external force acts on the body at its C Res it will cause
that body to move in linear path
= when other forces act away from this center called eccentric force
which cause the body to torque (moment)
moment = force X force arm distance (⊥) (moment arm, leaver arm)
M = F X d⊥
M: amount of moment or torque degree
F: amount of force applied
d⊥: force arm distance: line perpendicular from C Res to line of force application
= moment in orthodontics measured by newton millimeter (N mm) or (gm mm)
The amount of force is equal to the magnitude of the force multiplied
by the perpendicular distance from its line of action to the center of
distance
the direction of the moment of a force can be determined by
continuing the line of action around the center of resistance
N: B: pure translation is particularly impossible in living organism
because it will require to apply force perpendicular to the center of
resistance which lies on the root, however if the force is applied near

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Dr. Mohammed Alruby
the center of resistance, translation will occur but also moment is created due to distance between point of
application and C Res. (increase distance ---- increase moment)
The equivalent force system:
= Introduced by Smith and Burston to control and standardized the moment
= The force is applied to the tooth by means of bracket not located at the same level in all teeth, thus the
distance between point of application and center of resistance will be vary creating various moment for
each tooth. So the Smith and Burston produce an equivalent moment by varying the magnitude of force
= Examples:::
- if the distance between point of application was 8mm and the force applied was 50gm so the
moment = 8 X50= 400gm
- If the bracket is placed more gingivally to make the distance 4mm so to obtain the same moment
the force doubled: 100gm so moment = 4 X 100 = 400gm
The equilibrium
State of rest: object or system is not experiencing any acceleration, and according to Newton law, the sum
of all forces should be zero
Newton’s laws of motion:
Law I: an object continuous in its state of rest or motion unless an external force is applied to it
Law II: the greater the mass of an object, the greater the amount of force is needed to accelerate it
F = m a (F: force, a: acceleration m/s, m: mass kg)
Law III: for every action, there is an equal and opposite reaction
Equilibrium theory:
= although a variety of forces acting upon the teeth from many direction, the tooth position is remains
relatively stable under the forces
= all forces acting upon teeth should be in a state of equilibrium at these areas to maintain balance of the
teeth
= the area occupied by the teeth in the system in which the teeth are relatively stable and balanced is called
the natural zone or area of functional tolerance.
= the dento-facial complex is in constant state of charging dynamic balance between the forces and
dentition, the highly adaptive ability of dentofacial structure is the most important properly in maintaining
dynamic balance under the present condition and help obtaining equilibrium under new condition as that
obtained by orthodontic treatment
= equilibrium theory is very important clinical concept;however it is difficult to be understood because of:
1- Difficult to identify single abnormal forces in each individual
2- Difficult instrumentation necessary to measure all forces at any time
3- Large sample size required for this research
= Proffit concluded that, the most important factors in the equilibrium of teeth are:
a- Resting position of the lips, tongue, cheeks, and mandible
b- Metabolic force produced in periodontium
These two factors are of low intensity and longer duration
Quasi- static system:
= when orthodontic appliances are activated and inserted, the tooth displacement that occurs is very small
and takes over a relatively long period of time, and at any point of time if you look in patient’s mouth you
do not see any movement however, after waiting for sufficient period of time the movement will occur
N: B:
Force: it is an external influence which tend to move a body or change its position
Orthodontic force: it is a mechanical force that applied to the teeth to change their position
Natural forces: force of oro-facial musculature to which the dentofacial structure are constantly subjected
during function as; mastication, swallowing, respiration, speech, growth,……….

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Dr. Mohammed Alruby
Natural force – mechanical force interaction
During orthodontic treatment the teeth are subjected to both natural and mechanical forces, that
may modify or interfere with action of each other
If natural forces modify the action of mechanical forces, the tooth movement;
- Will be more easy, less anchorage demand
- More stable results, more successful treatment
- If natural forces interfere with the action of mechanical forces, the teeth movement:
will be more difficult more anchorage demands
more prolonged treatment time. Less stable results
therefore, the orthodontist must have a well knowledge about the native and direction of natural forces if
more success is needed
Description of mechanical forces:
1- Force vector;
it is the relationship among direction, magnitude, point application of force and center of
resistance (as discussed previously)
2- Center of resistance: means center of mass:
In single tooth root: lies in the middle of root between cervical and middle third
In multi rooted tooth: lies apical to the furcation
3- Center of rotation:
it the point around which the body seemed to be rotated, it was a changeable point during treatment
according to type of movement
= in body movement; the center of rotation is at infinity
= in controlled tipping; at root apex
= in uncontrolled tipping: near to center of resistance
= in torque movement: at incisal edge
= in intrusion and extrusion: outside the tooth
N: B: Nanda suggestions for center of rotation:
= center of rotation is fixed point around it two dimensional figure appear
to be rotated from its initial and final position
Or = in rotation the only point that does not moved is called center of rotation
and the rest of the plane is rotated around this fixed point
During movement: changing in center of rotation is the rule rather than the
exception
Estimation of C Rot:
A point and A point represent the cusp tip before and after treatment

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At midpoint of this line a perpendicular constructed which intersect with other perpendicular that
constructed between the apex of the roots, this point is center of rotation
4- Rotation:
Occurs when the force applied away the center of resistance and the potential of rotation is called moment
5- Resistance:
The resistance to an applied force is called anchorage, the anchor point is subjected to force equal in
amount and opposite to the applied force (3rd
law of newton)
As; when canine is retracted on 1st
molar using 200gm of force, the canine is subjected to 200gm and at
the same time the 1st
molar is subjected to 200gm but this force is enough only to move canine
6- Stress:
It is internal resistance of the body to the deforming action of external force
It is equal in magnitude and opposite in direction of an applied forces.
In rigid bodies it is equal to the strength of the body ( stress = Force / area kgm / cm)
Types of stress:
a- Tensile stress: result when a couple of force are directed away from each other on the same straight
line. It is always accompanied by tensile strain
b- Compressive stress: result when a couple of force are directed toward each other in the same
straight line tending to compress or shorten a body. It is always accompanied by compressive
strain.
Both compressive and tensile stress, the force applied at right angle
c- Shear stress; occurs when a body is subjected to a couple of forces directed toward each other but
not in the same line tending to twist the body. It is always accompanied by shear strain
d- Complex stress; it is being difficult to induce stress of single type, but usually the applied force
induces a combination of tension, compression and shear stress.
7- Strain:
it is the change in the form or size of the body as it responds to external forces. It represents the ratio
of deformation occurring in size or length of body per unit to the original length or size
(strain = L1 – L2 / L1)
Types:
a- Compressive: shortening deformation
b- Tensile: elongation deformation
c- Shear: twisting or rotation deformation
Or: a- elastic strain: occurs in elastic material and is reversible
b-plastic stain: occurs in plastic material and is irreversible
c-combined strain: combination of both in which the strain is elastic until the elastic limit of the
material then plastic
** stress – strain relationship curve:

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within the elastic limit of the material, the stress is directly proportional to strain, if stress exceed the elastic
or proportional limit, this relationship will be altered.
** Hook’s law; law of proportionality:
Within limit, the stress is directly proportional to the strain
The strain below the proportional limit is elastic and reversible while the strain above the proportional
limit is and irreversible
** proportional limit:
The greatest stress that material can withstand without deviation from law of proportionality (Hook’s law)
** elastic limit:
The maximum stress that the material can withstand without permanent deformation. Thus the proportional
limit and elastic limit are synomonas but proportional limit used to describe Hook’s law while the elastic
limit used to describe behavior of material
** yield strength:
Stress at which the material begins to function in plastic manner or the stress required to produce limit
value of permanent deformation
Yield strength is greater than elastic and proportional limit
** modulus of elasticity: young modulus: E:
It is the ratio of stress and strain below the elastic limit of the material, the low modulus of elasticity, the
more the elasticity of the materials
E = stress / strain
** flexibility:
Larger value of strain can produce by slight value of stress
** maximum flexibility:
Strain occurs when material stressed to its proportional limit
Proportional limit P / modulus of elasticity E
Directly proportion to the proportional limit and inversely proportion to modulus of elasticity
** Resilience:
Amount of energy absorbed by structure when stressed below the proportional limit.
Resilient material is that can absorb a greater amount of stress without permanent deformation
** toughness:
Amount of energy required to fracture the material
Tough material: the material can absorb greater amount of stress without fracture. Usually tough material
is strong
** plasticity:
The ability of material to withstand permanent deformation without fracture
** Malleability:
It is ability of material to withstand permanent deformation without fracture under compressive force
(hammered or rolled into sheets), malleability increase as temperature increase
** Ductility:
It is ability of material to withstand permanent deformation without fracture under tensile force (when
drum into wires), ductility increase as temperature decrease and vice versa
8- Force:
It is an external influence which tend to move or change its position
Types:
a- Compressive: squeezing together force or forces that tends to compress or squeeze a body
As: use of coil spring for space opening
b- Tensile force: force tend to stretch body; it is result when a couple of force directed a way from
each other on straight line tend to stretch or elongate the body
As: use elastic force to space closure

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c- Shearing: a couple of force directed toward each other, but not in the same straight line tending to
twist the body.
As: torque movement: rotation
d- Weight of the body: also represent a type of force application where, there is gravitational force
between the body and earth. Force is measured in pounds or kgm
All forces and its effect are governed by newton’s laws motions
e- Torsion: two opposite forces applied on one or both sides of center of rotation of an object
producing rotation around the center
f- Bending force: force applied between two point of resistance will producing bending of an elastic
material
Force magnitude:
Various according to each other, the lighter the force the more rapid tooth movement and less
damaged to supporting structure
Ideal force: the force that can initiate maximum tissue response with:
- Minimum pain
- Minimum damaged of supporting structure
- Minimum root resorption
- Maintain the health of periodontium throughout tooth movement
According to Schwarz, the ideal force should not exceed capillary blood pressure (32mm/Hg) or that
force that can move the tooth 1mm / month.
Optimum force:
1- Basically maintain the vitality of the tissue
2- Initiate a maximum cellular response (resorption and deposition)
= According to Sassoni: 50 to 75 gm/ cm
= According to Moyers 26gm /cm
= Schwarz 1832 proved experimentally that; ideal orthodontic force should be equal capillary blood
pressure (32mm/Hg) = 20 –26 gm/cm.
If the force exceeds this limit ------- shunt of capillaries ------- necrosis ------ bone and cementum resorption
= Rutan 1957 reported that the more favorable force is between 70gm to 100gm, he proved experimentally,
the force between 100 -200 gm is needed to moves maxillary canine bodily, 100 –200 gm for mandibular
one and only 25 gm for extrusion of incisors
= Storey and Smith 1952, studied the optimum force for canine retraction on a sample of 5 patients ranged
between 12 and 15 years requiring an orthodontic treatment. Extraction
of 1st
premolars and retract canines using the 2nd
premolars and 1st
molars
as an anchorage.
They using coil spring dispense light force (157 –300 gm) for retraction
of canine on one side, and other coil spring dispense a heavy force (400 –
600 gm) to retract canines on the other side.
They observe:
1- The 1st
canine does not move until the force reach the B level on
the curve (sufficient limit for minimum movement)
The force is more rapid until the force reach the level C
After level C the rate of movement decrease as the force is increase
until D level
After the D level, the force is heavy and the tooth does not move
but hyalinization and permanent damaged of periodontium may occur
** Storey and Smith describe the C level as the optimum force for
canine retraction
2- The 2nd
canine on the other side:
It was found that by application of heavy force (400 – 600 gm) the canine does not move but the
anchor unit moves forward until the force reach 200 –300 gm as in light spring, then the anchor

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unit stop to move and the canine begins to move distally in a behavior similar to that described in
the first case
They found that the optimum force for canine retraction is 150 – 200 gm, if the force increase above 200
gm the movement will decrease until 400 – 600 gm the molars will move forward.
Light force induced uniform movement while heavy force causes undermining resorption, followed by rapid
movement and looseness of the teeth.
Differential light force:
Is that force value which causes minimum discomfort, minimum looseness of the teeth, minimum damaged
to the investing tissue and at the same time moves the teeth more rapidly and more controlled
The initial tooth movement occur 6 –7 days after force application and continuous 10 –12 days after
removal of the force.
Types of tooth movements:
A: uncontrolled tipping: CRot near to C Res
B: controlled tipping: CRot at the apex
C: root movement: torqueing: CRot at incisal edge
D: bodily movement: translation: CRot at infinity
Application of power arm to create different type of tooth movement

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Force constant through all from A to D
A: uncontrolled tipping, with no power arm (CRot near to CRes)
B: controlled tipping produced by power arm below CRes ( CRot at apex)
C: translation produced by power arm at same level of CRes (increase the length of power arm) ( CRot at
infinity)
D: root movement with minimal crown movement (torque): (CRot at crown): power arm beyond CRes