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Retraction mechanics in swa /certified fixed orthodontic courses by Indian dental academy
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Retraction mechanics in swa /certified fixed orthodontic courses by Indian dental academy

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The Indian Dental Academy is the Leader in continuing dental education , training dentists in all aspects of dentistry and offering a wide range of dental certified courses in different formats.

Indian dental academy provides dental crown & Bridge,rotary endodontics,fixed orthodontics,
Dental implants courses.for details pls visit www.indiandentalacademy.com ,or call
0091-9248678078

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    Retraction mechanics in swa /certified fixed orthodontic courses by Indian dental academy Retraction mechanics in swa /certified fixed orthodontic courses by Indian dental academy Presentation Transcript

    • INDIAN DENTAL ACADEMY Leader in continuing dental education www.indiandentalacademy.com www.indiandentalacademy.com
    • RETRACTION MECHANICS IN SWA www.indiandentalacademy.com
    • INTRODUCTION www.indiandentalacademy.com
    • Mechanics is the discipline that describes the effects of forces on bodies Biomechanics refers to the science of mechanics in relation to biologic system. www.indiandentalacademy.com
    • MECHANICAL PRINCIPLES IN ORTHODONTICS STRESS- internal distribution of the load defined as force per unit area STRAIN- internal distortion produced by the load deflection per unit length www.indiandentalacademy.com
    • STRENGTH- maximal load that the material can resist measured in stress units( gm/cm2) www.indiandentalacademy.com
    • STIFFNESS- inverse of springiness given by the slope of the stress strain curve RANGE- distance that the wire will bend elastically before permanent deformation occurs measured in mm www.indiandentalacademy.com
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    • STRENGTH = STIFFNESS X RANGE RESILIENCE- energy storage capacity area under the stress strain curve upto the proportional limit FORMABILITY- amt of permanent deformation that a wire can withstand without failing www.indiandentalacademy.com
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    • SOME BIOMECHANICAL TERMS FORCE- load applied to an object that will tend to move it to a different position in space F = ma units are newton,gms or ounces www.indiandentalacademy.com
    • 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. www.indiandentalacademy.com
    • 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” CENTER OF RESISTANCE- is the equivalent balance point of a restrained body. www.indiandentalacademy.com
    • Center of resistance of 2 teeth Center of resistance of maxilla Center of resistance of Maxillary molar www.indiandentalacademy.com AJO DO 90: 29-36, 1986
    • Center of resistance depending upon the level of alveolar bone. www.indiandentalacademy.com
    • Center of resistance during anterior teeth retraction BURSTONE et al in 1987 BURSTONE et al in 1991 TURK et al in 2005 www.indiandentalacademy.com
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    • Center of rotation defined as a point about which a body appears to have rotated, as determined from its initial and final positions. www.indiandentalacademy.com
    • 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 www.indiandentalacademy.com AJO DO 85(4):294-307,1984
    • 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) www.indiandentalacademy.com
    • The direction of moment of force can be determined by continuing the line of action around the Cres www.indiandentalacademy.com
    • Couple A couple consists of two forces of equal magnitude, with parallel but noncolinear lines of action and opposite senses. 1000gm.mm www.indiandentalacademy.com
    • Moment of a couple The tendency of a couple to produce pure rotation around the Cres The magnitude of a couple is calculated by multiplying the magnitude of forces by the distance between them Unit :- Newton . mm (Gm . mm) Cres www.indiandentalacademy.com
    • 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 www.indiandentalacademy.com
    • 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. www.indiandentalacademy.com
    • MC-MF F F MC MF www.indiandentalacademy.com
    • 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 www.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 JCO13:676-683,1979 www.indiandentalacademy.com 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 www.indiandentalacademy.com AJO 85(4):294-307,1984
    • 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. www.indiandentalacademy.com
    • Static Equilibrium 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 www.indiandentalacademy.com
    • 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. www.indiandentalacademy.com
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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. www.indiandentalacademy.com
    • h a ø b sin ø= a/h cos ø = b/h a = h sin ø b = h cos ø www.indiandentalacademy.com
    • Resultant of forces F1 F1 ø F2 F2 F1 cos ø + F2 cos ø The parallelogram method of determining the resultant of 2 forces having common point of application www.indiandentalacademy.com
    • Components of a force F sin ø F ø F cos ø www.indiandentalacademy.com
    • 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 www.indiandentalacademy.com
    • Centered „V‟ bend www.indiandentalacademy.com AJO DO 98(4):333-339 1990
    • Off Centered ‘V’ Bend www.indiandentalacademy.com AJO DO 98(4):333-339 1990
    • RETRACTION MECHANICS FRICTION CONTINUOUS FRICTIONLESS SEGMENTAL CONTINUOUS www.indiandentalacademy.com SEGMENTAL
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    • FRICTION MECHANICS www.indiandentalacademy.com
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    • ROLE OF FRICTION When one moving object contacts another tangentially friction at the interface resists the movement . Consequently , orthodontists have to apply more force to overcome the frictional force to achieve the desirable result, due to which there is more patient discomfort and pain and also increases anchorage demands. www.indiandentalacademy.com
    • Factors effecting frictional resistance during tooth movement. PHYSICAL 1. Arch wire Material cross section size and shape surface texture stiffness 2. ligation of arch wire and bracket ligture wire elastomerics method of ligation 3. Bracket material Manufacturing process Slot width and depth Design of bracket Second order angulation Third order bend www.indiandentalacademy.com
    • 4. Orthodontic appliance interbracket span level of bracket slots b/w adjacent teeth forces applied for retraction BIOLOGICAL saliva Plaque corrosion www.indiandentalacademy.com
    • Components of resistance to sliding (RS) 1 st component – classical friction (FR) is a product of co –efficient of friction (µ) and normal force. Co –eff of friction- it is the objects frictonal proportionality constant. i.e surface roughness of the material. Nis the amount of force acting perpendicular to the surface of the object such as ligation force.on the bracket. www.indiandentalacademy.com
    • 2 nd component – Binding SECOND ORDER ANGULATON – it is the angle b/w base Of The wire (vertical dimension of wire) and the bracket.{θ}. Critical contact angle – the level where the wire contacts both the ends of the bracket slot. .{θc}. When the second order angulation increases to critical angle binding occurs . www.indiandentalacademy.com
    •   Passive configuration- FR exsists has an only component when the arch wire and bracket have clearance, in this angulation b/w arch wire and bracket is less than critical angulation. Active configuration- when clearance is absent and interferance occurs (θ = θ c) binding occurs. Under these conditions two forces exsists i.e. N and binding force(BI). www.indiandentalacademy.com
    • Factors determining critical contact angle      Slot size Bracket width Arch wire size Engagement index – size/ slot Bracket index – WIDTH / SLOT www.indiandentalacademy.com
    • Bracket width Wire size Slot size www.indiandentalacademy.com
    • 3rd component - notching www.indiandentalacademy.com
    • Influence of arch wire and bracket dimensions on sliding mechanics : derivations and determinations of the critical contact angles for binding ( robert .p. kusy and whitley -1999) Derived an equation size/ slot = width/ slot(sin θc)+cos θc. In this equation size/slot defines the engagement index .This index defines the fraction of the bracket slot filled by the arch wire . width/ slot defines the bracket index – the number of times the bracket width is more than slot dimension. Together , these two dimensionless indices define all that is necessary to determine θc as the point at which the binding starts. This study derived the maximum and minimum engagement and bracket indices possible, www.indiandentalacademy.com
    • For maximum bracket index - large bkt width/ small bkt slot = size= 250 mil/18 = 13.9 For minimum bracket index - small bkt width/ large bkt slot size=125mil/22=5.7 The range bracket index is 5.7 to 13.9 For maxi engagement index – large wire size/ small bkt slot= 16/18=.86 For mini engagement index – small wire size/ large bkt slot= 14x22=.64 The range for engagement index is .5 to1 When the nominal parameters of arch wire and bracket used in sliding mechanics were estimated for critical contact angle three important conclusions were drawn www.indiandentalacademy.com
    • 1) Narrow bracket showed θc double the value when compared to the wider brackets. 2) Smaller bracket slot showed decreased θc value .Hence, more precise aligning and leveling is required before retraction. 3)Smallest wires used for retraction i.e. 16 size wire in 22 slot, 125mil width . θc =2.8 degrees. Same wire in 18 slot showed θc =0.9 degrees. Even in the best scenario the practitionar must align and level so that the angulation b/w wire and Bracket is within the range of 1-4 degrees or else binding increases and sliding ceases. To accomplish the best scenario most easily within the strength and stiffness requirements. The bracket width and wire size should be small and bracket slot should be larger. www.indiandentalacademy.com
    • INFUENCE OF BINDING OF THIRD ORDER TORQUE TO SECOND ORDER ANGULATION (ROBERT P. KUSY 2004) As base dimensions of arch wire increases, bracket width decreases, bracket slot size decreases the critical contact angle for binding decreases. But when torque is incorporated into the wire ,the height of the wire is also considered. ( depth of the wire). As the torque angle is increased, clearance b/w arch wire and bracket decreases reducing the critical contact angle. Thus, increasing the chances of binding. www.indiandentalacademy.com
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    • stainless steel brackets    These are the most popular brackets till today. Friction is minimum in these brackets due to smoother surface. Sintered stainless steel brackets had low friction then cast stainless steel brackets due to more smoother surface texture. www.indiandentalacademy.com
    • CERAMIC BRACKETS demonstrated significantly higher frictional forces than ss brackets.highly magnified views revealed numerous small indentations in ceramic brackets. monocrystalline alumina brackets had smoother surface than polycrytalline bracket,but their frictional characteristics are comparable. since ,greater forces are required to slide the teeth. Caution in preserving anchorage must be exerted in such situations. ceramic brackets with metal slots showed decreased friction as wire is contacting the www.indiandentalacademy.com smoother metal slot.
    • Zincornia brackets  Zincornia brackets has been offered as an alternative to the ceramic brackets since surface hardening treatments to increase fracture toughness are available for zincornium oxide . However, the frictional co-efficients for these brackets were found to be greater than or equal to polycrystalline brackets in both wet and dry states. Surface changes consisting of wire debris and surface damage in zincornia brackets after sliding of wires were observed. www.indiandentalacademy.com
    • Titanium brackets Introduced in response to reports of the corrosion of stainless steel brackets and increased sensitivity to nickel content of the alloy. It is proven to be biocompatible. It is very rough as the titanium content of the alloy is increased. More chance of cold weld formation with the titanium brackets at bracket wire interface which increases resistance to sliding. www.indiandentalacademy.com
    • Plastic brackets In an attempt to make a esthetic bracket with low frictional resistance and easier debonding features than ceramic ,a wide variety of new ceramic reinforced plastic brackets with or without metal slots were introduced. several studies showed that when these brackets were tightly ligated with steel ligatures deformed slightly to squeeze the bracket slot thereby increasing friction. www.indiandentalacademy.com
    • WIRES Specular reflectance studies have shown that stainless steel wire have smoothest surface followed by co –cr, beta–ti, niti in the order of inceasing surface roughness. Beta titanium wires may form micro-welds in dry states and further increase the frictional forces. frank and nicoli found that stainless steel wires had least friction at non binding sites ,but as angulation increased and binding was present , the reverse was true. www.indiandentalacademy.com
    • MECHANICAL AND SURFACE CHARACTERISTICS OF 3 ARCH WIRE ALLOYS. ( VINOD KRISHNAN AND JYOTHINDRA KUMAR 2002 ). SEM of STAINLESS STEEL SS IS STRONG , HAS SMOOTH SURFACE SEM of BETA TITANIUM BETTER LOAD DEFLECTON, LESS STIFFNESS THAN SS,ROUGH SURFACE SEM of TIMOLIUM IT IS A α AND BETA TITANIUM, HAS INTERMEDIATE PROPERTIES TO SS AND BETA TITANIUM. www.indiandentalacademy.com
    • Co-efficient of friction and surface roughness Kusy et al used laser spectroscopy to study surface roughness of orthodontic wires . Among the four wire alloy types that are commonly used in orthodontics , stainless steel appeared to be lowest followed by cobalt chromium, beta titanium and nickel titanium. kusy and whiteley were the first to look at the effect surface roughness on friction co-efficient . The results showed that low surface roughness was not sufficient condition for low friction co efficient. For ex: beta titanium has decreased roughness than niti wires but frictional force resistance is more for beta titanium. www.indiandentalacademy.com
    • Ion implantation Gas ions like nitrogen and oxygen are implanted into the wire surface, resulting in a surface that is hard and creates a considerable compressive force at atomic level. This improves the surface characteristics and reduce co=-efficient of friction. Burstone and farzin –nia demonstrated that ion implanted beta titanium wires produced the same level friction as stainless steel, www.indiandentalacademy.com
    • Round vs rectangular wires. Several studies have found that an increase in wire size increase bracket wire friction. Rectangular wires produce more friction than round wires. At non binding sites contact area between arch wire and bracket is an important factor in friction hence more friction with rectangular wires. At binding sites with rectangular wire the force is distributed over a large surface area resulting in less pressure and less resistance to movement. At binding sites with round wires the bracket slot can bite the wire causing indentations resulting in more friction. www.indiandentalacademy.com
    • Ligation techniques. Normal ligation force ranges from 50 to 300 grams. Edward et al in 1995 compared the frictional forces produced elastomeric modules applied conventionally or figure of eight , stainless steel ligatures and teflon coated stainless steel when used for arch ligation. Figure of 8 configuration appeared to create highest friction. No significant difference between normal conventional module and stainless steel ligature. Teflon coated stainsteel had lowest frictional force. Even the composition of the ligature is another variable in determining the co_efficient of friction. www.indiandentalacademy.com
    • As the elastomeric ligatures are polyurethane based polymers , studies have shown that when exposed to oral environment they undergo stress relaxation and hydrolytic decompensation over time which will effect the properties of the module. Frictional forces by ligation can be reduced by pre streching the module , or by using stainless steel ligatures or using self ligating brackets. Backing of one quarter turn after tying steel ligatures. www.indiandentalacademy.com
    • Conventional ties such as O-rings and stainless steel ligatures make using optimal forces impossible due to friction and binding. Elastomeric O-rings will lose half their elasticity within days of initial tie in, thus compromising tooth control. O-rings are extremely plaque retentive and greatly increase the number of microorganisms attached to appliances during treatment, increasing the incidence of decalcification during treatment. www.indiandentalacademy.com
    • Self ligating brackets The first self ligating bracket was the Russel lock.  Self ligating brackets are ligatureless bracket system that have mechanical device built into the bracket to close off the edgewise slot .  These brackets show low frictional resistance.  They are 2 types – 1) Active-spring clip which presses against archwire. 2) passive- slides which does not press against wire and produces less friction.  { This difference in friction is seen only when the bigger sized arch wire is used.}  www.indiandentalacademy.com
    • A new low force ligation system (jco 2005)    This article describes an alternative to self ligating systems a ligature that markedly reduces the friction b/w the arch wire and bracket. The slide ligature is made of special polyurethane ,is applied in the sameway as a conventional elastomeric ligature .Like a passive self ligating it forms a fourth wall and allows the archwires to slide freely in the slot while transmitting its full force to the teeth. www.indiandentalacademy.com
    • •This ligature also forms the buffer b/w the bracket and soft tissues considerably improving patient comfort. www.indiandentalacademy.com
    • Leveling & Aligning Wider bracket Narrower bracket More Mc Less Mc More contact angle Less 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 used if the angles of the bracket remained constant to www.indiandentalacademy.com the interbracket axis. AJO DO 1988 Jan (59 – 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) www.indiandentalacademy.com
    • MC MC MC Am J Orthod 1974;65:270-289 MC www.indiandentalacademy.com MC
    • 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 www.indiandentalacademy.com 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. www.indiandentalacademy.com 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 www.indiandentalacademy.com Semin Orthod 2001;7:16-25.
    • In the maxillary arch shown in Figure 5A, 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 . www.indiandentalacademy.com 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 www.indiandentalacademy.com 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. www.indiandentalacademy.com 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 Mc Mc www.indiandentalacademy.com
    • Headgear F F MF www.indiandentalacademy.com MF
    • U/L Molar Rotations: D M MF MF Mc Mc www.indiandentalacademy.com
    • Simultaneous Intrusion & Retraction: www.indiandentalacademy.com
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    • MF MF MF MF Cross bite elastics www.indiandentalacademy.com
    • Force vectors in Cl-III elastics Force Vectors in Cl-II elastics Favorable in low angle deep bite Favorable in low angle cases www.indiandentalacademy.com cases
    • Space Closure Group A Anchorage Group B Anchorage Group C Anchorage www.indiandentalacademy.com
    • Force system for Group B space closure M/F Ratio 10/1in anterior & posterior – Translation of anterior & posterior Mc www.indiandentalacademy.com Mc
    • 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 www.indiandentalacademy.com
    • Forces Differ www.indiandentalacademy.com
    • Moments Differ www.indiandentalacademy.com
    • 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. www.indiandentalacademy.com
    • TORQUING WITH THE MOMENT OF A COUPLE System equilibrium Incisor movements AJO DO1993 May (428 – 438) www.indiandentalacademy.com
    • TORQUING WITH THE MOMENT OF A FORCE System equilibrium Incisor movements AJO DO1993 May (428 – 438) www.indiandentalacademy.com
    • CONCLUSION 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 patient , with a beautiful smile leaving your clinic at the end of treatment. www.indiandentalacademy.com
    • 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: Equlibrium 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 www.indiandentalacademy.com 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. www.indiandentalacademy.com
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