biomechancal principles in orthodontics / orthodontic courses by indian dental academy
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INDIAN DENTAL ACADEMY
Leader in continuing dental education www.indiandentalacademy.com
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INTRODUCTIONMECHANICAL CONCEPTS IN ORTHODONTICS -SCALAR -VECTOR -FORCE -RESULTANTS & COMPONENTS OF ORTHODONTIC FORCE SYSTEM -CENTER OF MASS -CENTER OF GRAVITY -CENTER OF RESISTANCE -CENTER OF ROTATIONS -SIGN CONVENTIONS -MOMENT OF THE FORCE -COUPLE -MOMENT OF COUPLE -
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-TORQUE -SYSTEMS EQUIVALENT FORCE -MOMENT TO FORCE RATIO & TYPES OF TOOTH MOVEMENT -NEWTON’S LAWS -STATIC EQUILIBRIUM -INTRUSION ARCH -CENTERED ‘V’ BEND -OFFCENTERED ‘V’ BEND -STEP BEND -NO COUPLE SYSTEM -ONE COUPLE SYSTEM(DETERMINATE FORCE) -TWO COUPLE SYSTEM(INDETERMINATE FORCE) LEVELLING & ALLIGNING -MOLAR ROTATIONS -UNILATERAL -BILATERAL -SIMULTANEOUS INTRUSION & RETRACTION -CLASS II & III ELASTICS SPACE CLOSURE -FORCE SYSTEMS FOR -GROUP B SPACE CLOSURE
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-GROUP A SPACE CLOSURE -GROUP C SPACE CLOSURE TORQUING -WITH THE MOMENT OF A COUPLE -WITH THE MOMENT OF A FORCE CONCLUSION REFERENCES
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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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Mechanics is the discipline that describes the effects of forces on bodies
Biomechanics refers to the science of mechanics in relation to biologic system.
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MECHANICAL CONCEPTS IN ORTHODONTICS
An understanding of several fundamental mechanical concept is necessary to understand clinical relevance of biomechanics in orthodontics.
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Scalar: When a physical property ( Weight, temperature ,force) has only magnitude , its called a scalar quantity.
( E.g.. A force of different magnitude such as 20gm,50gm etc)
Vector: When a physical property has both magnitude and direction its called a vector quantity.
(E.g.. A force vector characterized by magnitude, line of action, point of origin and sense)
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Force
Force is equal to mass times acceleration
F= maForces are actions applied to bodies
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RESULTANTS AND COMPONENTS OF ORTHODONTIC FORCE SYSTEMS
Teeth are often acted upon by more than one force. Since the movement of a tooth (or any object) is determined by the net effect of all forces on it, it is necessary to combine applied forces to determine a single net force, or resultant. At other times there may be a force on a tooth that we wish to break up into components. For example, a cervical headgear to maxillary molars will move the molars in both the occlusal and distal directions. It may be useful to resolve the headgear force into the components that are parallel and perpendicular to the occlusal plane, in order to determine the magnitude of force in each of these directions.
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ø
ah
b
sin ø= a/h a = h sin ø
cos ø = b/h b = h cos ø
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Resultant of forces
The parallelogram method of determining the resultant of 2 forces having common point of application
F1
F2
F1 cos ø + F2 cos ø
øF1
F2
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Components of a force
F
F cos ø
F sin ø
ø
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The resultant of 2 force with different point of application can be determined by extending the line of action to construct a common point of application
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Center of mass Each body has a point on its mass , which behaves as if the whole mass is concentrated at that single point. We call it the center of mass in a gravity free environment.
Center of gravity The same is called the centre of gravity in an environment when gravity is present.
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Center of resistance
Center of mass of a free body is the point through which an applied force must pass to move it linearly without any rotation. This center of mass is the free objects “Balance Point”
The center of resistance is the equivalent balance point of a
restrained body. Center of resistance varies depending up on the - Root length & morphology - Number of roots - Level of alveolar bone support
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Center of resistance of 2 teeth
Center of resistance of maxilla
Center of resistance of Maxillary molar
AJO DO 90: 29-36, 1986www.indiandentalacademy.com
Center of resistance depending upon the level of alveolar bone.
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Center of resistance during anterior teeth retraction
Center of resistance of 6 anterior teeth- ± 7mm apical to the interproximal bone
Center of resistance of 4 anterior teeth- ±5mm apical to the interproximal bone
Center of resistance of 2 anterior teeth- ±3.5mm apical to the interproximal bone The location of the instantaneous center of resistance shifted apically as the number of dental units consolidated (2, 4, and 6) increased.
Clinical implication: They suggest that little difference in the moment/force ratio (M/F) is required to translate a two- or four-teeth unit. However, for the retraction of a six-teeth segment, the M/F ratio of a retraction spring should be calibrated for a higher value to facilitate translation.
AJO DO 91(5):375-384,1987www.indiandentalacademy.com
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Center of resistance during anterior teeth intrusion
For an anterior segment comprising two central incisors, the center of resistance was located on a projection line parallel to the midsagittal plane on a point situated at the distal half of the canines
For an anterior segment that included the four incisors, the center of resistance was situated on a projection line perpendicular to the occlusal plane between the canines and first premolars.
For a rigid anterior segment that included the six anterior teeth, the center of resistance was situated on a projection line perpendicular to the occlusal plane distal to the first premolar.
AJO DO 90(3):211-220,1986www.indiandentalacademy.com
The center of resistance was found in different occlusoapical positions, depending on the direction of the force. Thus the location of the center of resistance cannot be considered to be constant, independent of the direction of loading, for a tooth with a given support.
AJO DO 99(4):337-345,1991
A force always acts to displace the center of resistance in the direction the force is acting (support being the same).
AJO DO 1993 May (428 - 438)www.indiandentalacademy.com
JCO28(9):539-546,1994www.indiandentalacademy.com
JCO28(9):539-546,1994www.indiandentalacademy.com
If a model of a tooth is attached to a piece of paper by a pin, the point with the pin in it cannot move, and this point becomes the center of rotation about which the tooth can spin. If the pin is placed at the incisal edge, only movement of the root is possible if it is placed at the root apex, movement is limited to crown tipping. In each case, the center of rotation is determined by the position of the pin. Thus, in two dimensional figures, the center of rotation may be defined as a point about which a body appears to have rotated, as determined from its initial and final positions.
Center of rotation
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The more nearly translational the movement, the farther apically the center of rotation would be located. In the extreme case, with perfect translation, the center of rotation can be defined as being an infinite distance away.
AJO DO 85(4):294-307,1984
A simple method for determining a center of rotation is to take any two points on the tooth and connect the before and after positions of each point with a line. The intersection of the perpendicular bisectors of these lines is the center of rotation
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Burstone stated in his simple formula:
y × (M/F) = 0.068 h2 wherey = Distance from center of resistance to center of rotation
M/F = Distance from center of resistance to point of force application
h = Root length
Thus, in this special case of a two-dimensional parabolic root, 0.068 is a constant for a given root length.
AM J ORTHOD 1969;55:351-69.www.indiandentalacademy.com
Two important parameters σ2 and γ, which measure the resistance of the tooth to tipping, were found to be constants for loading in one plane of space, independent of the position of occlusoapical force. Using experimental σ2 or γ values, one can calculate the location of the center of rotation of the tooth for a given force position or, conversely, when a center of rotation is desired, the position of the force (or the equivalent moment/force ratio at the bracket) can be calculated. Because the γ values differed as the load was changed from one plane to another through the long axis of the tooth, it was shown that different centers of rotation would be produced for a given force location if the direction of loading was changed. The center of rotation located more apically to the center of resistance with forces directed labiopalatally than mesiodistally.
AJO DO 99(4):337-345,1991www.indiandentalacademy.com
AJO DO 99(4):337-345,1991
More is the value of σ2 & γ more is the resistance to tipping or rotation
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Sign Conventions
A universal sign convention is available for forces & moments in dentistry & orthodontics.
Forces are positive when they are in :
-Anterior direction
-Lateral direction
-Mesial direction
-Buccal direction
-Extrusive forces
Moments are positive when they move the crown in a mesial, buccal or labial direction.
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Moment of the force :-It is the tendency of a force to produce rotation.
The force is not acting through the Cres
It is determined by multiplying the magnitude of force by the perpendicular distance of the line of action to the center of resistance.
Unit– Newton . mm ( Gm. mm)
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The direction of moment of force can be determined by continuing the line of action around the Cres
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Couple
A couple consists of two forces of equal magnitude, with parallel but noncolinear lines of action and opposite senses.
The magnitude of a couple is calculated by multiplying the magnitude of forces by the distance between them
Unit :- Newton . mm (Gm . mm)
1000gm.mm
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Moment of a couple The tendency of a couple to produce pure rotation around the Cres
Direction of rotation is determined by following the direction of either force around the Cres to the origin of opposite force.
Cres
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Irrespective of where on a rigid object a couple is applied; the external effect is the same.
50gm50gm
-500gm.mm
1500gm.mm
50gm
50g
1000gm.mm www.indiandentalacademy.com
The moment of force is always relative to a point of reference. The moment of a force will be low relative to a point close to the line of action and high for a point with a large perpendicular distance to the line of action.
A couple is no more than a particular configuration of forces which have an inherent moment. This moment of couple is not relative to any point.
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In orthodontics depending up on the plane in which the couple is acting they are called as
Torque- 3rd order
Rotation-1st order
Tipping- 2nd order
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Torque
Torque is the common synonym of moments
Moments of forces moments of couples
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Systems Equivalent force A useful method for predicting the type of tooth movement that will occur with the appliance activation is to determine the “ equivalent force system at tooth’s center of resistance.
It’s done in three steps
First- Forces are replaced at the Cres maintaining its magnitude and direction
Second- The moment of force is also placed at the Cres.
Third- Applied moment ( moment of couple in bracket wire combination) is also placed at Cres.
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MF
F
MC
FMC-MF
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Moment to force ratio & types of tooth movement The type of movement exhibited by a tooth is determined by the ratio between the magnitude of the couple (M) and the force (F) applied at the bracket. The ratio of the two has units of millimeters (this represents the distance away from the bracket that a single force will produce the same effect).
AJO DO 90: 127-131, 1986AJO 85(4):294-307,1984www.indiandentalacademy.com
Tipping-Greater movement of crown of the tooth than of the root
Uncontrolled tipping: -Movement of the root apex and crown in opposite direction
-Crot – Between Cres and apex
-Mc/F ratio 0:1 to 5:1
-0<Mc/MF<1
Controlled tipping:-Movement of the crown only
- Crot – At the root apex
-Mc/F ratio 7:1
-0<Mc/MF<1
AJO 85(4):294-307,1984JCO13:676-683,1979www.indiandentalacademy.com
Translation-Bodily moment occurs
-Crot – At infinity
-Mc/F ratio 10:1
-Mc/MF=1
-Root movement-Root movement occurs with the crown being stationary
-Crot – at the incisal edge or the bracket
-Mc/F ratio 12:1 - Mc/MF>1
Pure rotational movement-Root & crown move equally in opposite direction
- Crot – Just incisal to Cres
- Mc/F ratio 20:1 - Mc/MF>1AJO 85(4):294-307,1984JCO13:676-683,1979
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Newton’s Laws :First Law: The Law Of Inertia
Every body continues in its state of rest or uniform motion in a straight line unless it is compelled to change by the forces impressed on it.
Second Law :The Law Of Acceleration
The change in motion is proportional to the motive force impressed & is made in the direction of straight line in which the force is impressed.
Third Law :The Law Of Action & Reaction
To every action there is always opposing & equal reaction.
When a wire is deflected or activated in order to insert it into poorly aligned brackets the 1st & 3rd laws are apparent.
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Static Equilibrium It is a valuable application of Newton’s Laws of motion to the analysis of the force system delivered by an orthodontic appliance.
Static Equilibrium implies that, at any point within a body , the sum of forces & moments acting on a body is zero; i.e., if no net force or moments are acting on the body the body remains at rest (static).
The analysis of equilibrium can be stated in equation form
Σ Horizontal forces = 0
Σ Vertical forces = 0
Σ Transverse forces = 0
AND
Σ Moments ( Horizontal axis ) = 0
Σ Moments ( Vertical axis )= 0
Σ Moments ( Transverse axis ) = 0
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Intrusion arch
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Centered ‘V’ bend
AJO DO 98(4):333-339 1990www.indiandentalacademy.com
AJO DO 98(4):333-339 1990
Off Centered ‘V’ Bend
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It is easy to understand that the forces generated in this type of situation are stronger than those generated in an off-center V bend. Indeed, for a given angle between the wire and the brackets, the two moments, C1 and C2, add up in the step bend, yielding a stronger reactional moment, as well as stronger vertical forces.
AJO DO 98(4):333-339 1990
Step bend
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MF
No Couple System
d d
F F
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One Couple System (Determinate force system)
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Two Couple System (Indeterminate force system)
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Wider bracket
More Mc
Less contact angle
Narrower bracket
Less Mc
More contact angle
More the play more is the Mc
Leveling & Aligning
It was found that a predictable ratio of the moments produced between twoadjacent brackets remained constant regardless of interbracket distance or the cross section of the wire used if the angles of the bracket remained constant tothe interbracket axis. AJO DO 1988 Jan (59 – 67)
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We put thinner wires at the beginning of alignment i.e. more play - less applied couple - less M:F - no root moment only crown moment (tipping)
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Am J Orthod1974;65:270-289
MC
MC
MC MC
MC
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The 2 central incisors are rotatedmesial in creating a symmetric V geometry. Thedesired corrective force system involves 2 equaland opposite moments as illustrated
Semin Orthod 2001;7:16-25.www.indiandentalacademy.com
The force system developed by inserting a straight wire into the brackets ofthe 4 anterior teeth will create counterclockwise moments on the 2 central incisors as well as lingual movement of the left central incisor and labial movement of the right central incisor. The initial geometry is not favorable for alignment.
Semin Orthod 2001;7:16-25.www.indiandentalacademy.com
shows a lingually placed right lateral incisor. In this case, the geometric relationship between the right lateral and central incisors is a step geometryand the placement of a straight wire into the brackets of the 4 anterior teeth will align the teeth and also shift the midline to the right side
Semin Orthod 2001;7:16-25.www.indiandentalacademy.com
In the maxillary arch shown in Figure, the relationship between the central incisors is a step geometry and an asymmetric V geometry is observed between the central and lateral incisors on the right side. Analysis of the force system shows that, although correction of the 2 central incisors will occur asa result of straight wire placement, the right lateral incisor will be displaced labially, which is an undesirable side effect . Semin Orthod 2001;7:16-25.
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The relationship between the right lateral and central incisors is recognized as an asymmetric V geometry. Analysis of the force system shows that, although the left lateral incisor will be corrected by rotating mesial out and moving labially, the right lateral incisor will move further lingually
Semin Orthod 2001;7:16-25.www.indiandentalacademy.com
The relationship between the right lateral and central incisors is recognized as an asymmetric V geometry. Analysis of the force system shows that, although the left lateral incisor will be corrected by rotating mesial out and moving labially, the right lateral incisor will move further lingually
Semin Orthod 2001;7:16-25.www.indiandentalacademy.com
During extrusion of a high canine unilaterally. Figure A shows theforce system generated by the placement of a straight wire through a high maxillary right canine. The canine will extrude as desired, but the lateral incisor and first premolar on that side will intrude and tip toward the canine space. An open bite may result on that side of the arch, and the anterior occlusal plane will be canted up on the right side.
Semin Orthod 2001;7:16-25.www.indiandentalacademy.com
Molar Rotations- absence of maxillary molar rotation is highly desirable in obtaining class-I occlusion of the molars, premolars, & canines.
B/L Molar rotations:
Palatal Arch
Mc Mc
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Headgear
MF MF
FF
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U/L Molar Rotations:
D M
Mc
Mc
MF MF
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Simultaneous Intrusion & Retraction:
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Cross bite elastics
MF
MF
MF
MF
Cres
Creswww.indiandentalacademy.com
Force vectors in Cl-III elastics
Favorable in low angle deep bite cases
Force Vectors in Cl-II elastics
Favorable in low angle caseswww.indiandentalacademy.com
Space Closure
Group A Anchorage
Group B Anchorage
Group C Anchorage
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Force system for Group B space closureM/F Ratio 10/1in anterior & posterior – Translation of anterior & posterior
McMc
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Force System for Group A space closure M/F ratio 12/1 or more in posterior & 7/1 or 10/1in anteriors – Root moment of posteriors & tipping or bodily moment of anteriors
IDEAL
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Forces Differ
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Moments Differ
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Force system for Group C space closure mirrors that of group A.
The anterior teeth becomes the effective anchor teeth.
The anterior moment is of greater magnitude & the vertical force side effect is an extrusive force on the anterior teeth.
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TORQUING WITH THE MOMENT OF A COUPLE
System equilibrium
Incisor movements
AJO DO1993 May (428 – 438)
Torquing arch
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TORQUING WITH THE MOMENT OF A FORCE
System equilibrium
Incisor movements
AJO DO1993 May (428 – 438)
Base arch
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Various mechanics can often be used to achieve the tooth movements desired for orthodontic treatments. It is important however to understand the mechanics involved and to recognize when the appliance will not achieve adequate results or may result in undesirable side effects. This can help us to prevent prolonged overall treatment time and/or compromise in the final orthodontic outcome. The ultimate result will be a happy post treatment patient , with a beautiful smile leaving your clinic.
CONCLUSION
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REFFERENCES
1. Smith RJ, Burstone CJ: Mechanics of tooth movement. AJO 85:294-307,1984.
2. Burstone CJ, Koenig HA: Creative wire bending- The force system from step & V bends. AJO DO 93(1):59-67,1988.
3. Burstone CJ, Koenig HA: Force system from the ideal arch. AJO 65(3):270-289,1974.
4. Demange C: Equilibrium situations in bend force system. AJO DO98(4):333-339,1990.
5. Issacson RJ, Lindauer SJ, Rubenstein LK: Moments with edgewise appliance e: Incisor torque control. AJO DO 103(5):428-438,1993.
6. Koing HA, Vanderby R, Solonche DJ, Burstone CJ: Force system for orthodontic appliances: An analytical & experimental comparison. J Biomechanical Eng102(4):294-300,1980.
7. Kusy RP, Tulloch JFC: Analysis of moment/force ratio in the mechanics of tooth movement. AJO DO 90; 127-131,1986.
8. Nanda R, Goldin B: Biomechanical approaches to the study of alteration of facial morphology. AJO 78(2):213-226,1980.
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9. Vanden Bulcke MM, Burstone CJ, Sachdeva RC , Dermaut LR: Location of center of resistance for anterior teeth during retraction using the laser reflection technique. AJO DO 91(5):375-384,1987.
10. Vanden Bulcke MM, Dermaut LR, Sachdeva RC, Burstone CJ: The center of resistance of anterior teeth during intrusion using the laser reflection technique & holographic interferometry. AJO DO 90(3): 211-220,1986.
11. Mulligan TF: Common sense mechanics 2 . Forces & moments. JCO 13:676-683,1979.
12. Siatkowski RE: force system analysis of V-bend sliding mechanics. JCO 28(9):539-546,1994.
13. Tanne K, et al: Moment to force ratios & the center of rotation. AJO 94:426-431,1989
14. The basics of orthodontic mechanics. Semin Orthod 2001;7:2-15
15. Leveling & aligning: Challenges & Solutions Semin Orthod 2001;7:16-25.
16. Biomechanics in clinical Orthodontics. Ravindra Nanda, 1st Edition
17. Biomechanics in Orthodontics. Michael R. Marcotte, 1st Editionwww.indiandentalacademy.com
18. Modern Edgewise Mechanics & Segmented Arch Technique, Dr C J Burstone, 1st Edition19. Contemporary Orthodontics. W R Proffit 3 rd Edition20. Orthodontics Current Principles & Techniques. T M Graber, R l Vanersdal. 3rd Edition21. Systemized Orthodontic Treatment Mechanics. R P McLaughlin, J C Bennet, H J Trevisi
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