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INTRODUCTION 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.

Mechanics is the discipline that describes the effects of forces on bodies Biomechanics refers to the science of mechanics in relation to biologic system.


An understanding of several fundamental mechanical concept is necessary to understand clinical relevance of biomechanics in orthodontics.


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)


Force is equal to mass times acceleration

F= ma Forces are actions applied to bodies

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.

h a ø b sin ø= a/h cos ø = b/h

a = h sin ø b = h cos ø

Resultant of forces


F1 ø




F1 cos ø + F2 cos ø

The parallelogram method of determining the resultant of 2 forces having common point of application

Components of a force F sin ø F


F cos ø

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

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.

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

Center of resistance of 2 teeth

Center of resistance of maxilla

Center of resistance of Maxillary molar

AJO DO 90: 29-36, 1986

Center of resistance depending upon the level of alveolar bone.

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):375-384,1987

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):211-220,1986

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.

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)

AJO DO 99(4):337-



Center of rotation 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.

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.

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

AJO DO 85(4):294-307,1984

Burstone stated in his simple formula: y Ă— (M/F) = 0.068 h2 where y = 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.

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):337-345,1991

More is the value of Ďƒ2 & Îł more is the resistance to tipping or rotation

AJO DO 99(4):337-345,1991

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.

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)

The direction of moment of force can be determined by continuing the line of action around the Cres

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)

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.


Irrespective of where on a rigid object a couple is applied; the external effect is the same. 50g

50gm 50gm 50gm

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.

In orthodontics depending up on the plane in which the couple is acting they are called as

Rotation-1st order

Tipping- 2nd order

Torque- 3rd order

Torque Torque is the common synonym of moments

Moments of forces moments of couples

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.






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 85(4):294-307,1984

AJO DO 90: 127-131, 1986

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 â&#x20AC;&#x201C; Between Cres and apex -Mc/F ratio 0:1 to 5:1 -0<Mc/MF<1

Controlled tipping: -Movement of the crown only - Crot â&#x20AC;&#x201C; At the root apex -Mc/F ratio 7:1 -0<Mc/MF<1


AJO 85(4):294-307,1984

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>1 JCO13:676-683,1979

AJO 85(4):294-307,1984

Newtonâ&#x20AC;&#x2122;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.

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

Intrusion arch

Centered ‘V’ bend

AJO DO 98(4):333-339 1990

Off Centered ‘V’ Bend

AJO DO 98(4):333-339 1990

Step bend

It is easy to understand that the forces generated in this type of situation are stronger than those generated in an offcenter 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

No Couple System


d F



One Couple System (Determinate force system)

Two Couple System (Indeterminate force system)

Leveling & Aligning

Wider bracket

Narrower bracket

More Mc

Less Mc

Less contact angle

More contact angle

More the play more is the Mc It was found that a predictable ratio of the moments produced between two adjacent brackets remained constant regardless of interbracket distance or the cross section of the wire if the angles of the bracket remained constant to the interbracket axis. AJO DO 1988 Jan (59 â&#x20AC;&#x201C; 67)

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)




Am J Orthod 1974;65:270-289



The 2 central incisors are rotated mesial in creating a symmetric V geometry. The desired corrective force system involves 2 equal and opposite moments as illustrated

Semin Orthod 2001;7:16-25.

The force system developed by inserting a straight wire into the brackets of the 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.

shows a lingually placed right lateral incisor. In this case, the geometric relationship between the right lateral and central incisors is a step geometry and 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.

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 as a 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.

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.

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.

During extrusion of a high canine unilaterally. Figure A shows the force 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.

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







U/L Molar Rotations:






Simultaneous Intrusion & Retraction:





Cross bite elastics


Force vectors in Cl-III elastics

Force Vectors in Cl-II elastics

Favorable in low angle deep bite Favorable in low angle cases cases

Space Closure

Group A Anchorage

Group B Anchorage

Group C Anchorage

Force system for Group B space closure M/F Ratio 10/1in anterior & posterior â&#x20AC;&#x201C; Translation of anterior & posterior



Force System for Group A space closure M/F ratio 12/1 or more in posterior & 7/1 or 10/1in anteriors â&#x20AC;&#x201C; Root moment of posteriors & tipping or bodily moment of anteriors


Forces Differ

Moments Differ

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.


Torquing arch Incisor movements

AJO DO1993 May (428 â&#x20AC;&#x201C; 438)


Base arch Incisor movements

AJO DO1993 May (428 â&#x20AC;&#x201C; 438)


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.

REFFERENCES 1. Smith RJ, Burstone CJ: Mechanics of tooth movement. AJO 85:294307,1984. 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):270289,1974. 4. Demange C: Equilibrium situations in bend force system. AJO DO98(4):333339,1990. 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.

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 94:426431,1989 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, 1 st Edition 17. Biomechanics in Orthodontics. Michael R. Marcotte, 1st Edition

18. Modern Edgewise Mechanics & Segmented Arch Technique, Dr C J Burstone, 1st Edition 19. Contemporary Orthodontics. W R Proffit 3 rd Edition 20. Orthodontics Current Principles & Techniques. T M Graber, R l Vanersdal. 3rd Edition 21. Systemized Orthodontic Treatment Mechanics. R P McLaughlin, J C Bennet, H J Trevisi

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