Force n Moment

7/31/2019 Force n Moment

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Understanding Forces and Moments 2 12

UNDERSTANDING

FORCES AND MOMENTS2

For some reason, the terms forces and moments do not always

seem to be thoroughly understood. It is true that the English

language seems to suffer over a period of time, but in the area of

mechanics it is important to understand exactly what each term

means and to use these terms properly. The terminology whichfollows will be used in a practical manner. There are exacting

definitions that may be confusing to many while there are

descriptions that may convey a practical meaning to most

clinicians.

Orthodontic clinicians know from

personal experience that a specific

force system does not necessarilyproduce the same response for

different patients. Nothing in life

happens without a reason. Force

magnitude can be very significant.

as stated in Figure 2-1.

Figure 2-1

With an intrusion arch molars might erupt and/or incisors may

intrude. Bicuspids are more likely to undergo an equal and

opposite rotational response with powerchain elastics. These

responses are illustrated in Figures 2-2 thru 2-4.

FORCE SYSTEMS

Thesame force system may produce avariable response.

Force magnitude is a significant factor.


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Molars may

erupt.

Forces may produce

variable response.

Forces may produce

variable response.

Incisors may

intrude

Teeth may rotate

Forces may produce

variable response.

Figure 2-2 Figure 2-3 Figure 2-4

The following illustrations may help to clarify some of the

misconceptions that are present in the orthodontic profession.

TRANSLATION

When a force acts through the Center of

Resistance or Center of Mass, only bodily

movement takes place.

FORCES (MxA)

Forces act in astraight line.

Forces consist of apush or pull.

Figure 2-5 Figure 2-6

In Figure 2-5, a force is applied through the center of mass, aterm used in reference to a free body such as a golf ball or

baseball. When the same force is applied through the center of

an attached body - such as a tooth - the term used is center of

resistance. This is nothing new to the orthodontist, but building

blocks will slowly be established so that confusion does not

arise later when discussing biomechanics.

The definition of a force could properly be defined as MxA

(Mass times Acceleration), but what meaning would this have

for the clinical orthodontist? If we describe rather than define a

force, it can be seen in Figure 2-6 that a force acts in a straight

line and may consist of a push or pull.


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Retracting cuspids with an open coil spring does not result in

forces acting in a curve. If wepush from the lingual surface of a

tooth with a lingual arch, or pull from the buccal surface of a

tooth with an archwire, the force acts in a straight line as itpasses through the tooth.

Figure 2-7 demonstrates this by using descriptions rather than

definitions which so often confuse the issue. Depending on

exactly where these forces act, moments may or may not be

produced. This will be discussed later during the subject of

forces and moments.

Push fromthe lingual

Pullfromthe buccal

Forces act in

astraight line

not a curve1

2 3

Figure 2-7


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MOMENTS (FxD)

Moments are produced as a

result of forces actingaway

from the Center of Resistanceor Center of Mass.

ROTATIONThe product offorce x distance produces

the moment on the body.

Therefore, 1/2 the force x twice thedistance produces the same moment as

1/2 the distance x twice the force.


When a force acts on a body, but away from the center of

resistance (or center of mass), there is a perpendicular distanceestablished between the applied force and the center of the

object as shown in Figure 2-8. It is the product of this distance

and the force that produces a moment. In other words, if either

the force or the distance doubles, the moment produced would

double. This is significant because in Figure 2-9 it can be seen

that different force magnitudes can produce the same moment.

If one force is half the magnitude of the other, but acting attwice the distance, the moments in each case will be equal. This

is important to recognize in orthodontic treatment as it affords

the opportunity to produce desirable moments without the

disadvantage of high force magnitudes, particularly in the

vertical plane of space where vertical dimension of the patient

might be compromised.

Personal experience in our lives can be of great help in

recognizing forces and moments produced in orthodontic tooth

movement. Most of us have probably played the game ofpool -

often referred to as billiards - sometime in our lives or at least

observed it being played by others. It is quite popular on TV.


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So, lets take a look at the game

ofpool and see how it may be

of help in learning. For those

who may not be aware, the ballin question is known as the cue-

ball and is the white one seen in

Figure 2-10. Keep this in mind

so as not to become confused

Figure 2-10 with conservation of momentum

which involves the other balls. The following examples are

those we have experienced or can experience in our daily lives.

Visualize thecrown of

a tooth as acue-ball

Cue Stick

This represents the Pointof Force Application

The Cue Stick represents the

force that will be applied to the

brackets and tubes of the teeth.


The first step involved is to visualize the crown of the tooth as a

cue-ball as seen in Figure 2-11. The next step will be to identify

the point of force application shown in Figure 2-12 . The cue

stick used in the game of pool will represent the source of the

applied force. The next question is: In what direction will the

cue-ball move and how will it rotate? Keep in mind that the

rotation will be clockwise or counterclockwise in pool this is

referred to as left or rightEnglish. Naturally, the ball will roll

down the table due to friction, but disregard this rotation.

For those

who are

unaware,

the cue-ball

is the white

ball.


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CUE-BALL CONCEPT

1. A force applied through thecenter of abody will cause the body to move in astraight line and in the same direction

as the applied force.

2. A force appliedaway from the center ofa body will cause the body to move insame previous direction, but rotation willalso occur as a result of the momentcreated by the line of force acting at aperpendicular distance to the center ofthe body.


There are three possible

movements that may occur, just

as in the real world oforthodontics. The first movement

we observe is pure translation as

seen in Figure 2-13. The force

has been applied through the

center of the bodies shown.

Figure 2-15

Translation and rotation may occur as shown in Figure 2-14where the force has been applied away from the center of the

body as illustrated. The moment in such a case is referred to as

the moment of a force.

Figure 2-15 shows equal and opposite forces (known as a

couple) being applied and producing pure rotation.. The moment

in such a case is referred to as the moment of a couple. A pure

moment always acts around the center of resistance. Regardlessof the where the equal and opposite forces are applied, the body

will undergo pure rotation around the center of resistance.

Lets see where this concept applies at the clinical level.

3. Equal and opposite forces applied on a

body in the same plane of space and

parallel to each other (Couple) will

produce a pure moment causing the body

to rotate only.


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Translation

The result of the

applied force is a

moment and a

force at the centerof resistance.

Center bend

producing equal

& opposite

moments to those

already present. This is anEquivalent Force System.

Figure 2-16

In Figure 2-16 upper left, forces have been applied at the crownlevel resulting in tipping moments. The force system is always

shown at the center of resistance. Remember that a force

applied away from the center of a body will cause the body to

move in the direction of the applied force and rotate because of

the perpendicular distance. With the addition of a center (gable)

bend shown in the lower part of the illustration, moments

opposite to the tipping moments are created thereby eliminating

tipping moments measured at the center of resistance.The resultis that only pure forces remain as seen on the right in Figure 2-

16. This is referred to as an equivalent force system. Remember

the so-called powerarms that were introduced to the profession

in order to create a translatory force through the center of

resistance? Where are they now? Does this tell you how

successful or unsuccessful the results have been?

A clinical example of the above application is seen in Figure 2-

17. Tipping moments are eliminated by equal and opposite

moments resulting from a center bend. As will be explained

later, all archwire bends are done intraorally and activated 45


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degrees. All adjustments for

increasing or decreasing

moments for the proper force

system are created byadjusting whatever closing

mechanism is in use, such as

coil springs or powerchain.

In Figure 2-18, tipping the

Figure 2-17 incisors together would not

be acceptable. The placement

of a center bend into the wireproduces moments which

then result in bodily

movement as a result of

eliminating the tipping

moments produced by the

closing mechanism which

could be coil springs orpowerchain elastics.

Figure 2-18

Translation and Rotation

Figures 2-19 and 2-20 demonstrate that a force applied away

from the center of a body will cause the body to translate and

rotate. Looking at a rotated bicuspid with space mesial to the

tooth, it can be seen that applying a mesial force at the bicuspid

bracket will produce the necessary force and moment. This

obviously simple approach is intended only to illustrate the cue-

ball concept regarding translation and rotation.

A closing force at the brackets

producestipping moments

eliminated by Center Bends.

Tipping Moments

Eliminating the

Tipping Moments


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C.C.

Translation & Rotation Required

Translation & Rotation Required


Figure 2-21 and Figure 2-22 demonstrate the same concept

beautifully as will be seen later when wire/bracket relationshipsare discussed. For now however, simply keep in mind that by

excluding the second bicuspid brackets from the archwire, an

off-center bend has been created without the need to remove the

wire. In a full appliance the toe-in bend at the molar would

actually be a center bend when related to the adjacent molar tube

and bicuspid bracket on each side. By not engaging the wire

into the second bicuspid bracket an off-center bend has beencreated. Do you remember the rules for off-center bends? An

off-center bend contains a long and a short section. The short

section points opposite to the forceproduced thereby indicating

a buccal force on the molar. The toe-in bend (short section) also


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produces a rotational moment. This approach allows both

correction of the molar rotations and crossbites simultaneously

without removal of the archwire or use of crossbite elastics.

This is only one of many similar approaches that can minimizechairside time for the orthodontist as well as providing a variety

of noncompliant and exciting approaches not taught in school.

This might be a good time to mention that in over 46 years of

practice - thus far - never has the author used a crossbite elastic,

transpalatal arch, lingual arch, or any other type of lingual

attachments. Why not? Because there are so many alternative

and noncompliant approaches that do not require this. Manyother types of laboratory appliances which are commonly used

today can also be avoided. This will be discussed in the

upcoming chapters.

Pure Rotation

The final cue-ball concept relating to pure rotation - moment of acouple - can now be illustrated. Remember that equal and

opposite forces produce a couple.

Surgical

Exposure

Moment of a couple(Pure Rotation)



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Following surgical exposure seen in Figure 2-23, elastics were

utilized to create equal and opposite forces (couple) once the

cuspid was brought into alignment (Figure 2-24). The lingual

bracket had been placed at the time of exposure as no othersurface of the tooth was available for bonding. Simply adding a

labial bracket later afforded the opportunity to provide a couple.

PURE

ROTATION

Applied

Couple

Couple

Required


Although there is no difficulty in treating the above rotation with

another approach, Figure 2-25 demonstrates the application of a

couple in providing the correction seen in Figure 2-26.

Figure 2-27 will provide the

final example for pure rotation.

Following space closure, center

bends have been placed to

provide for equal and opposite

moments at each bracket in

order to parallel the roots.

Figure 2-27

While discussing forces and moments, we should look at the

effect of vertical forces acting through the molar tubes.

Undesirable consequences often occur as a result. Figure 2-28

Remember to

visualize the crownas a Cue-Ball


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shows that intrusive forces may cause buccal displacement of

molars due to buccal crown moments produced.

Intrusive force

producesbuccal

crown moment.

Extrusive force

produces lingual

crown moment.

IMPORTANT!

Intrusive force

producesbuccal

crown moment.

As the upper molars are widened,the

curve of Monson increases and no longer

harmonizes with the curve of Wilson.


In the lower part of the same illustration, it is seen that an

eruptive force acting through the molar tube produces exactly

the opposite moment and therefore possible lingual

displacement of molars. These undesirable responses may or

may not occur. Steep cusps and brachycephalic individuals with

strong musculature are only some of the factors which may playa role. When such undesirable movements do occur, an easy

solution is provided by the utilization ofmolar control bends to

be discussed later.

In Figure 2-29, it can be seen that buccal displacement of the

molars may also result in an increase in the curve of Monson

an important functional curve involved in axial loading. It isthis type of occurrence that contributes so much to instability

and the increase in permanent retention seen today.

Since functional curves are an important part of orthodontic

treatment, this topic will be discussed now.


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Functional Curves


Three important functional curves are shown in Figure 2-30. In

Figure 2-31, it can be clearly seen that excellent axial loading is

achieved in #1, as the curves of Monson and Wilson nicely

coincide. However, in #2 there is an excessive curve of Monson

while in #3 there is a reverse curve of Wilson. In the latter two

cases there is a loss of axial loading which is apparent. These

discrepancies can very easily result from vertical forces acting

through the molars tubes as shown earlier. It has been shownthat eruptive forces through molar tubes create lingual crown

moments while intrusive forces acting through molar tubes

result in buccal crown moments.

The following illustrations will show the potential buccal and

lingual displacements that may occur as a result of vertical

forces acting through the molar tubes. If the second molars havenot yet erupted and the first molars are displaced without the

orthodontist being aware of such displacement, then upon

second molar eruption it may mistakenly be assumed that

second molars are at fault. As a result, treating to the first molar

width may then result in a faulty curve of Monson or Wilson.

The long axis should

lieparallel to the

Internal Pterygoidresulting inaxial

loading (stability).

Curve of Monson

2

1

Curve of Wilson

3

These curves

can be helpfulin determining

which arch is

involved and to

what degree.

Spee

Monson

Wilson


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In Figure 2-32 #1, the eruptiveforce has caused the first

molars to move lingually as

observed in #2. In #3, the

second molars have now

erupted. It remains important

to know which of the molars

are out of position. In Figure

2-33 the same series of eventsFigure 2-34 has occurred with first molars

moving buccally due to intrusive forces acting through the

molars. It can be observed that second molar eruption may

create the illusion that they have erupted too far to the lingual. In

Figure 2-34 it can be seen that casual observation could easily

lead one to believe the first molars are normal in width with

second molars being the problem.

The above movements make it important for the clinician to

include the functional curves of Monson and Wilson in

observing treatment progress. A failure to harmonize these

Buccal

Crown

Displacement

Original Molar Width

Change in Molar Width

2nd Molar

Width is

Normal

1

2 3

Lingual

Crown

Displacement

1

3

Original Molar Width

Change in Molar Width

2nd Molar

Width is

Normal

2

Second Molars are in normal transverse dimension.

Second Molars are in

normal position.


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curves may result in functional problems involving axial loading

and leading to later instability.

This concludes the chapter regardingforces and moments. Whatmay have appeared to be quite elementary at this point will

prove to be highly important in applying fundamental mechanics

in everyday treatment.

Most of what is contained in this book has not been taught as

part of an orthodontic curriculum. By understanding the

contents presented there will be many opportunities to treat

patients in a unique manner regarding the applied mechanics. Inaddition it will be discovered that there are many approaches

available that will lessen the need for patient cooperation

without the need for appliances that displace lower incisors

because of the undesirable reciprocal effects when treating

opposing arches with interarch appliances. You are about to

discover many ways of providing intra-arch solutions for many

malocclusions that will help to avoid placing appliances onopposing arches which may be normal and require no change.


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THE SHORT STORY

Forces and moments have been discussed in a manner somewhat

different than presented in the usual literature. Rather than

defining forces, they have been described. Description has

meaning to the practicing orthodontist whereas definitions

sometime seem to separate the academic nature of mechanics

from the reality of application to the patient.

It has been pointed out that force systems for the patient producevariable responses. Molars may erupt for one patient but not

another simply because of force magnitude. Other movements

such as reciprocal first and second bicuspid rotations tend to be

quite similar. It has been stressed that force systems must be

predicted and understood in order to effectively utilize them for

patient treatment. For many, biomechanics may seem like an

academic adventure because of unexpected responses. Differenttypes of responses have been demonstrated with the so-called

cue-ball concept and clinical examples illustrated. If the

orthodontist can begin to associate tooth movement with what

has been experienced in life, such association may gradually

lead to applications in orthodontic treatment.

Finally, the functional curves of occlusion have been presented.

It has been shown that the curves of Monson and Wilson should

be harmonized for axial loading during occlusion. Such

harmony contributes to stability. The forces causing a lack of

harmony have been presented and the clinician made aware of

their importance in observing functional curves.


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SUGGESTED READINGS

Smith RJ, Burstone CJ. Mechanics of tooth movement. Am J Orthod

1984;85:294-307.

Dawson PE. Evaluation, diagnosis, and treatment of occlusal problems.

St. Louis: CV Mosby, 1989;85-91.

Mulligan TF. Common sense mechnics. 2. Forces and moments. J Clin

Orthod 1979;13:676-683.

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