Moment to Force Ratio Final Presentation / orthodontic courses by Indian dental academy

INDIAN DENTAL ACADEMY

Leader in continuing dental education www.indiandentalacademy.com

www.indiandentalacademy.com

MOMENT TO

FORCE RATIO


INTRODUCTION

Understanding the biomechanics is essential to determine the working of

an appliance system and more importantly the undesirable changes

associated with it.

This seminar tells about the basic concepts of biomechanics and their importance in clinical application


FLOW CHART OF THE PRESENTATION

DEFINITION OF THE BASIC CONCEPTS

PAE

Various stages

EXTRA ORAL

Head gears

BEGG

Various stages

COMMON SENSE MECHANICS

MOLAR CONTROL


. Forces may be treated as vectors and are conveniently represented as arrows. A force vector is characterized by

four features: magnitude, point of application, line of action, and sense.

F

O

R

C

E

DEFINED as a load applied to an object that will tend to move it to a different position in space


The parallelogram method for resolving a force into vertical and horizontal components.


. The parallelogram method of determining the resultant of two forces with a common point of application.

F

O

R

C

E


A, Two equal and opposite, parallel, forces form a couple. B, The translational effects of the forces cancel each other out, but the

moments of each force combine. The result is a moment with no net force.

Couple force


CENTER OF RESISTANCE

Center of mass is a point through which an applied force must pass for a free object to

move linearly without any rotation.

The center of a mass is for a generic free body.

Tooth – not generic free- periodontal support.

The analogus to center of mass for a restrained body is CENTER OF RESISTANCE


CENTER OF ROTATION

The point around which rotation actually occurs when an object is

being moved


M

O

M

E

N

T

Defined as the rotational tendency when force is applied away from the center of resistance

A force acting at a distance

Mathematically given as M = f x d

Where M is the moment

f is the force

And d is the perpendicular distance of the line of action to the center of resistance


The direction of the moment of a force can be determined by continuing the line of action around the center of resistance

towards the point of origin.

F

O

R

C

E

Direction of a moment


The force in A, passing through the center of

resistance, will result in translation of the tooth. The

force in B, at the bracket, will also translate the tooth but, in addition, will cause a

rotation because of the moment created at the center of resistance.

Teeth move according to the forces and moments acting at the center of resistance. Most orthodontic forces are applied to the tooth at the bracket. Understanding the relationship between force systems at the

bracket and the center of resistance requires using the rules for equivalent force systems.


Force applied on a tooth

Crown moves more than root

To maintain the inclinationOf the tooth

Overcome the moment Created by the force applied

to the crown

Counter moment


To maintain axial inclination

Apply the force close to the center of resisitance

Create a 2nd moment In the direction opposite

to the first

Practical difficulty

Power arm

Counter moment

Tooth remain uprightAnd move bodily


Various tooth movements

Uncontrolled tipping

Controlled tipping

Translation

Root uprighting

M/F (moment to force ratio) is the relationship between the force and the counter balancing

couple that determines the type of tooth movement .


Consider the moment created when force is applied Mf and the counter balancing moment generated by the couple within the

bracket Mc

Mc/Mf = 0 –Pure tipping Crot and cres same,thus the tooth rotates around the Cres

0 < Mc/Mf >1- Controlled tipping – Crot displaced away from Cres – crown and root move in the same direction

Mc/Mf = 0 – Bodily movement – equal movement of crown and root

Mc/Mf > 1 Torque – root apex moves further than the crown www.indiandentalacademy.com

M/F 5 : 1 Uncontrolled tipping

M/F 8 : 1 Controlled tipping

M/F 10 : 1 Translation

M/F >10 : 1 Root movement

MOMENT TO FORCE RATIO FOR VARIOUS TOOTH MOVEMENTS


P

A

E

TORQUE

A rectangular wire ina rectangular slot

Generate the momentof a couple necessary

to control rootposition

Torque acting as the counter moment

Bracket system


TIP In the PAE bracket system, the tip incorporated into the bracket acts as the counter moment in the mesio distal

direction

This prevents the tipping of the tooth in the mesio

distal direction

P

A

E

Bracket system


P

A

E

Bracket system

Bracket width and interbracket span

The width of the bracket on a tooth determines the length of the moment arm

for the control of the mesiodistal root position

Inter bracket span increases

Increase in the length of the wire

Increased flexibility

Decreased forceswww.indiandentalacademy.com

The line of action of the force passes through the center of resistance. This tooth will translate, even though the point of attachment to the tooth is at the bracket.

Principle of power arm


A

L

I

N

G

I

N

G

Lingually malposed premolar

Aligning wire engaged

Bucally directed simple tipping

First order angular displacementsOf the adjacent teeth

Decrease the magnitude of the force

To counteract

Broad distribution of Responsive force


Canine tip

When increased - during aligning there is a tendency for the canine to be thrown forward

- tends to deepen to the bite

To counter act

Reduce the canine tip (MBT)

Placement of canine lace back

A

L

I

N

G

I

N

Gwww.indiandentalacademy.com

Reverse curve of Spee. The vertical forces cancel out in the manner shown, but moments produced at either end of the

archwire result in torques on the incisors and molars (anterior

lingual root torque or labial crown torque; posterior mesial root torque

or distal crown torque).

Arch leveling

Since intrusion is placed on the incisor segment, and because the molars then become the reciprocal teeth, they

incur eruptive forces. Since extrusive forces acting through the molar tubes usually result in lingual crown torque on the molars, we have the potential for lingual crown movement

(lingual "dumping").

L

E

V

E

L

I

N

Gwww.indiandentalacademy.com

L

E

V

E

L

I

N

G

Highly placed canine

Continuous arch wire

Intrusive force on lateral greater than the extrusive force

on canine

Lateral intrusion rather than canine extrusion due

to the increased root length of canine

Engage a continuous wire only after

reasonable aligning of the anterior segment

excluding canine www.indiandentalacademy.com

BITE

OPENING

Round wire with reverse curve of Spee

Forward tipping of the lower incisors

Tipping of the lower molar

Cinched back

Lower premolars extruded

Roots of the lower incisor thrown forward

Forward mvt of lower molarForward mvt.of lower In.

Class III ElasticsTo counteract

To counteract

Eruptive forces on lower In. and upper molarsTo counteract

High pull head gear or extractionswww.indiandentalacademy.com

COUNTERACTING EFFECTS OF

LEVELING WITH ROUND WIRE


Banding of the second molars

BITE

OPENING

Extrusion of the first molars

Opening of the bite

Second molars being at a higher level


Bioprogressive Therapy

Typical variations of the mandibular utility arch.


UTILITY ARCHES

DISTAL UPRIGHTING

DISTO LINGUAL ROTATON

BUCCAL EXPANSION

BUCCAL ROOT TORQUE

450 TIP BEND

300 ROTATION

2MM BUCCAL EXPANSION

450 BUCCAL ROOT TORQUE

50 LABIAL ROOT TORQUE ON LOWER INCISORS


Segmented approach to simultaneous intrusion and space closure

. Comparison of force system developed on molar with identical 30 gm intrusive forces. A, Perpendicular to the occlusal plane. B, Parallel to the incisor long axis and lingual to CR. Note reduction of the moment on the molar in B.

BURSTONE INTRUSION www.indiandentalacademy.com

Forces acting on the teeth from an intrusive arch. The effect on the molar is extrusion and a negative rotation (crown-distal-root-mesial). The moment (M) is equal to the intrusive force (FA) times the distance (L) from the incisor to the center of resistance of the molar.

As the intrusive force is applied more anteriorly to the center of resistance of the incisors, a positive moment is created which tends to move the root lingually, provided the incisor is restrained from flaring labially.


Basic mechanism for intrusion; posterior anchorage unit, anterior segment in the four incisors, and an intrusive arch. The intrusion arch is placed in the auxiliary tube on the first molar attachment.


.

. Intrusive arch has been placed at the level of the incisors. A double rope tie prevents arch from being displaced into the mucobuccal fold if a tie is accidentally lost.


Force system of appliance.Note that the posterior extension allows force to be directed through the center of

resistance of the incisor. No incisor tipping will occur.

A long posterior extension is used to protrusive lower incisors to prevent flaring. The hook at the intrusive section

is shown.


The extrusive force on the molar during incisor intrusion tends to tip the crown lingually. This can be prevented by using a lingual arch.


A, Intrusive force through CR will intrude incisor along line of action of this force. B, An intrusive force perpendicular to the distal extension and through CR will have the same effect as in A.

THREE

PIECE

ARCH


Intrusive force can be directed along long axis of anterior teeth and applied lingual to CR. The farther lingual the force, the larger will be the moment acting to tip the incisors lingually.

THREE

PIECE

ARCH

Direction of net intrusive force through CR may be changed by application of a small distal force. The resulting intrusive force has a direction parallel to the long axis of the incisor and is distal to CR. .


Diagrammatic representation of three-piece base arch. The anterior segment extends 2 to 3 mm distal to the center of resistance (CR) of the anterior teeth. Force acts through center of resistance.

THREE

PIECE

ARCH


Diagram of three-piece base arch and Class I elastic stretched from maxillary first permanent molar to distal extension of anterior segment. Class I elastics are needed to redirect force parallel to the long axis of the incisor.

THREE

PIECE

ARCH


CONNECTICUT

ARCH 16 x 22 or 17 x 25 nickel titanium wire


Intrusion force system consists of anterior intrusive force, posterior extrusive force,and posterior tip back moment

CONNECTICUT

ARCH


Force system created by CTA and high-pull headgear. CTA force system (red) consists of intrusive force on incisors, extrusive force on molars, and moment tipping molar crowns distally. Headgear (blue) produces intrusive force on molars and moment allowing distal root movement. Purple arrow represents combined distal force of CTA and headgear on molars.

CONNECTICUT

ARCH


Force system for incisor flaring. CTA is not cinched back, and can be ligated directly into incisor brackets for maximum flaring.

CONNECTICUT

ARCH


A. Force system for incisor extrusion, with CTA is inserted into molar brackets upside down. Vertical forces shown are ideal for correction of minor open bites. B. Open-bite patient before treatment. C. Mechanics shown in A used to close bite, with high-pull headgear added to prevent forward tipping of molars and augment intrusive force of CTA on molars.

CONNECTICUT

ARCH


19 x 25 TMA with closed U loop 7mm long and 2mm wide

K

S

I

R

A

R

C

H 90 degree bend placed in the arch wire at the level of the U loop.centered V bend creates equal and opposite moment(red) that counter tipping moment(green) produced by activation forces


Off center v bend 60 degree placed 2mm distal to the loopThis bend creates an increased moment increased molar anchorage and intrusion of the anterior teeth.

K

S

I

R

A

R

C

H

20 degree anti rotation bends distal to the U loop


SPACE

CLOSURE

INDIVIDUAL CANINERETRACTION

ENMASSE RETRACTION

FRICTION

FRICTIONLESS


CANINE

RETRACTION

Individual canine retraction – friction mechanics

Do not change the power chain for 5 weeks ,let to comlplete the root uprighting

Initial controlled tipping of the tooth (m/f 8:1)

Force decay with time

Force level on the tooth decreases

M/f ratio is increased

Root uprighting

Walking of the canine


Source: 1993 JCO: Modified Lingual Lever Arm Technique - GERHARD KUCHER, MD, DDS, FRANK J. WEILAND, DDS,

HANS-PETER BANTLEON, MD, DDS, P.

Lever arm adapted to palatal vault and bonded to lingual surface of cuspid.

Extension soldered to palatal bar, and

activation achieved with buccal and

lingual Superelastic coil springs.

CANINE

RETRACTION


Schematic of force system: moments at lever arm and bracket cancel each other out, resulting in net translation

force.


Undesirable side effects from distal canine slide along continuous arch: tipping, binding, lack of vertical control and risk of anchorage loss, incisor extrusion


Effect of pure horizontal force at the canine bracket.

CANINE

RETRACTION


Antitip and antirotation moment-to-force conditions necessary for translation of canines with average dimensions.

CANINE

RETRACTION


CANINE

RETRACTION

PG retraction spring

Anti tip bend – 150 in the mesial leg

Beta bend - 300 in the distal leg

Anti rotation bend – 350


CANINE

RETRACTION

T LOOP The preactivated spring with the anti tip and anti rotation is placed

Activation on insertion is 6mm

The m/f is 8:1 – controlled tipping

Now as the tooth moves the activation reduced to 4mm – the force is reduced

M/f ratio is increased - bodily movement further

The activation is reduced to 2mm – force is further reduced

M/f ratio increased – 12:1

Root uprighting


CANINE

RETRACTION

T LOOP

Mesial leg angulated by150

Distal leg angulated by 300

Preactivation of 400

Increasing the gingival length of the wire increases the m/f ratio and

reduces the deflection rate


Space closure using a retraction appliance.

Source: AJO-DO 1997 : Three-dimensional effects in retraction appliance design D. W. Raboud, MSc, M. G. Faulkner, MSc, PhD, A. W. Lipsett,..,.

ENMASSE FRICTIONLESS www.indiandentalacademy.com

ENMASSE FRICTIONLESS

GROUP A ANCHORAGE

Distal force on anteriors Mesial forces on posteriors

Maximum potential for tooth mvt. Miminised or counteracted

Decrease moment Increase moment

Horizontal force acting on both segments are same

Moment to force ratio

Reactive unit Anchor unitwww.indiandentalacademy.com

Alpha moment Beta moment

Anteriors posteriors

Vertical forces created

Extrusion

When unequal or unbalanced

Intrusion

alpha

beta

alpha

beta

Intrusion Extrusion


A. Vertical force anterior to center of resistance, producing clockwise moment. B. Vertical force posterior to center of rotation,

producing counterclockwise moment.

Source: JCO 1990 : Vertical Force Considerations in Differential Space Closure - BIRTE MELSEN, DO, VASSILI FOTIS, DDS,

MSD, CHARLES J. BURSTONE,


Beta moment greater than alpha moment, producing net intrusive force on anterior teeth and extrusive force on posterior teeth. B. Alpha moment greater than beta moment, producing net intrusive force on posterior teeth and extrusive force on anterior teeth. C. Equal alpha and beta moments, producing no vertical component of force.

Source: JCO 1991 JULIE ANN STAGGERS, DDS, MS, NICHOLAS

GERMANE, DMD


With retraction spring, alpha moment produces distal root movement of anterior teeth; beta moment produces mesial

root movement of posterior teeth.


GROUP B ANCHORAGE


Equal potential for tooth mvt.

Alpha moment Beta moment



EQUAL

EQUAL

RETRACTION OF ANTERIOR

PROTRACTION OF POSTERIOR


GROUP C ANCHORAGE


Maximum potential for tooth mvt.Minimized or counteracted

Decrease momentIncrease moment



Reactive unitAnchor unit


Burstone and koenig 1976 AJOThree primary characteristics of retraction loops

1.moment to force ratio

2.the force at yield

3.the force to deflection rate

Factors that influence m/f

Height of the loop

Horizontal loop length

Apical length of the wire

Placement of the loop

Helix incoporation

Angulation of loop legs


Gradual sweep versus an acute bend

Acute bend

Force concentrated on the premolar

Mesial tipping of the premolar

Undesirable

Gradual sweep

Uniform distribution of the force and no concentration of the force on a particular

tooth

Force being distributed molar and premolar

No undesirable tipping


SLIDING MECHANICS

ENMASSE

FRICTION

The hook is soldered at the center of resistance of the anterior segment and active tie backs are placed from the molar hook to

the soldered hook. www.indiandentalacademy.com

B

E

G

G

Conventional Begg – type of tooth movement is uncontrolled or free tipping of the tooth

Amount of force required for this is less and the moment to force ratio is also decreased

Uncontrolled tipping is not desirable as it hastens root resorption and control of the tooth movement is also difficult (source: Biomechanical principles and reacions,

Reitan1985)

Refined Begg – controlled tipping


B

E

G

G

Stage 1 Intrusion and tipping of the incisors simultaneously

Intrusive force – crown labial root

lingualRetractive force – crown lingual

Root labial

Moment of the intrusive force acts to counter moment the moment of the elastic force

Moment of the intrusive force to the elastic force ratio determine the type of tooth movement


B

E

G

G

If the intrusive force is decreased

If the elastic force is increased

Moment to force ratioInadequate for

Controlled tipping

Thus, for controlled tipping

Keep the class II elastic force very light

Use adequate amount of intrusive force


B

E

G

G

Anchor bend and the class II elastic force

Distal crown tipping of

molars

Upright the lower molars

Retract the anterior teeth

Move the lower molar forward bodily

Class II elastics

Anchor bend

Intrusionof anteriors


Torquing auxillary with spurB

E

G

G

When spread along the wider curvatureLingual torquing

Vertical plane in which the aux orients when fitted into the incisor is changed to the horizontal plane of the arch

wire when tied to it

The larger arc of the anterior portion of the

wire roll inwards

The tip of spur to press in a lingual direction against the

gingival portion of the crown

Inter spur span – lift in a labial direction

Bracket slot Base arch wireCounter act


Light couple force acting on each tooth

Lingual crown torque with the intrusive

couple force

Opposite to the elastic force

M/F 8:1

Controlled tipping

II stage Intrusive force reduced

Additional moment created

by the MAA

Prevents labial tipping of the lower incisors

Shortens the third stage

B

E

G

G

MAA


Common sense mechanics Thomas F mulligan JCO 1979

Off center bend

Points in the direction of the force produced on the tooth

Center bend

Short segment Long segment

Points in the direction opposite of the force produced on tooth

No short or long segment

No force produced

COMMON

SENSE


COMMON

SENSE


Differential torque - the molar tip back bend produces a large distal moment on the molar and a small labial moment on the anterior segment in spite of the force being equal as the distances involved are radically different.

COMMON

SENSE


Round wire

Line of actionBuccal to center ofresistance

Lingual crown torque

Begg stage l expansion given toprevent lingualrolling of molars

Rectangular wire

Line of actionlingual to center ofResistance

Buccal crown torque

Beta bend to Produce buccal Root torque

COMMON

SENSE


A force off center causes the cue ball to rotate as well

as move forward in a straight line.

No left or right rotation is

produced when the force is

applied through the center of the

cue ball.

When the line of force acts through the

center of resistance,

only translation

results.

CUE BALL CONCEPT

Equal and opposite forces

(couple) produce

pure rotation.

COMMON

SENSE


If the tipback and torque bends produce equal angular relationships (A), the net forces are zero. If unequal (B), net forces occur.

This explains why there is extrusion with the increase in the alpha bend.

Thus the length of the segment and the angulation determine the tooth movement

ROW BOAT EFFECT

COMMON

SENSE


With a constant tipback angle, the deflection doubles as the wire length doubles, the force is reduced to one

fourth

When the length of the diving board is doubled, only one-eighth

the force is required to produce the same amount of deflection. B. The

same force acting at twice the length will produce eight times as

much deflection.

DIVING BOARD CONCEPT

COMMON

SENSE


MOLAR

CONTROL

Source : Thomas Mulligan JCO 2001

Bends placed in the arch wire

Variety of force systems to produce a direct response

Off set bend

Step bend

Center bend


MOLAR

CONTROL

Short section of the wire points in the direction of the long arm

OFFSET BEND

Vertical forces acting through the molar tube

Extrusive Intrusive

Lingual crown torque Buccal crown torque

Narrowing of the postArch width

Widening of the postArch width

Reduction in the curve of monson

Increase in the curve of monson


MOLAR

CONTROL

Rotations first displacement second

Rotation correction requiredToe in

Toe out

Represent the short section of the wire of the off center bend

Bends located just mesial to the molars


MOLAR

CONTROL

Toe out corrects the distal in and/ mesial out rotation with horizontal lingual force


MOLAR

CONTROL

Toe in corrects the mesial in or distal out with horizontal buccal force


MOLAR

CONTROL

In bend for the lingual displacement


MOLAR

CONTROL

Out bend for the buccal displacements


MOLAR

CONTROL

Step bend for the mesio lingulal rotation with a lingual displacement

When 2 bends are involved and each bend produces a force in the same

direction

Increases the force

magnitude


MOLAR

CONTROL

Center bend


HEAD

GEARS

CERVICAL PULL HEAD GEAR

LOW OUTER BOW Head gear force line of action mesial to the center

of resisitance

Extrusive component

Distal component

Large moment that Tends to steepen the

Occlusal plane

Clockwise Moment


HEAD

GEARS


OUTER BOW Head gear force line of action passing through the

center of resisitance

Extrusive component

Distal component

No moment that Tends to alter the

Occlusal plane

At the level of the inner bow


HEAD

GEARS


High OUTER BOW Head gear force line of action distal to the center

of resisitance

Extrusive component

Distal component

Large moment that Tends to flatten the

Occlusal plane

Anticlockwise Moment


HEAD

GEARS

HIGH PULL HEAD GEAR

SHORT OUTER BOWAngulated high to create head gear force line of action anterior to the center of resisitance

Intrusive component

Distal component

Large moment that Tends to flatten the

Occlusal plane

Anticlockwise Moment


HEAD

GEARS

HIGH PULL HEAD GEAR

OUTER BOWAngulated such that head gear force line of action

passes through the center of resisitance

Intrusive component

Distal component

No moment that Tends to alter the

Occlusal plane

Equal to the inner bow


HEAD

GEARS

HIGH PULL HEAD GEAR

LONG OUTER BOWAngulated to create head gear force line of action

posterior to the center of resisitance

Intrusive component

Distal component

Large moment that Tends to steepen the

Occlusal plane

Clockwise Moment


Conclusion Newton’s third law states that every action has a

equal and opposite reaction.

Its important to keep this concept in mind working with any appliance system and give adequate

importance to take steps to prevent the adverse effects.

In orthodontic terms, the understanding of the moment and the application of the necessary

counter moment to bring about the optimal tooth movement is the key to successful treatment results


Thank you

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Moment to Force Ratio Final Presentation / orthodontic courses by Indian dental academy

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Transcript of Moment to Force Ratio Final Presentation / orthodontic courses by Indian dental academy