Common Sense Mechanics Guide

PRESENTED BY –
DR. FIRDOSH ROZY
ORTHODONTICS AND DENTOFACIAL
ORTHOPAEDICS
COMMON SENSE MECHANICS

CONTENTS :
 Common Sense Mechanics Part 1
-Introduction
-Visual inspection
-Simple rule
-Forces and Moments
-Cue Ball concept
-Translation, Rotation
-Forces and moments on teeth
-Lingual root torque
-Static Equilibrium
-Requirements
-Cross Bites
-Expansion/contraction overlays

CONTENTS :
-Diving board concept
-Cantilever principle
-Constant load versus constant deflection
-Clinical application of the diving board concept
-Distalization with differential torque
-Class II correction without head gear or elastics
-Wire bracket relationships
 MOLAR CONTROL

COMMON SENSE MECHANICS
….THOMAS F. MULLIGAN
• A Series of articles presented by him in the Journal
of Clinical Orthodontics (JCO).
• Sep. 1979 – Dec. 1980
• The title “COMMON SENSE MECHANICS” is
based on the simple fact that no appliance exists
which will allow an orthodontist to treat orthodontic
problems without adding the necessary ingredient of
Common Sense to the mechanics instituted for
correcting the malocclusion.

 Appliances are being refined and will continue to improve with passage of time.
 Refinement in appliances may ↓ the physical effort, but will not eliminate the need
for the orthodontist to
- Think
- understand
- Apply basic principles of mechanics
in a common sense manner

This means that regardless of how well we understand mechanics
and regardless of how much the appliance is refined, we are dealing
with a biologic environment whose variation in response will
continue to challenge the orthodontist in many ways.
As an Orthodontist we face the Challenging Arena of biophysics
where we take many principles into account, mix them with
common sense, and proceed to treat the problem in more
predictable & efficient manner with a high level of confidence.

(JCO,Volume 13(9);588-594,Sep1979)
 VISUAL INSPECTION METHOD
• Often confuses the orthodontist in attempting to determine with reliability what
forces are present.
• The visual method seems to be so obvious, but faulty conclusions.
• Not to be misled by determining forces present through the visual inspection
method.
COMMON SENSE MECHANICS – PART 1

For example (Fig. 2), the orthodontist inserts an archwire into the molar tubes and observes that prior to placement of
the archwire into the incisor brackets, the wire lies in the mucolabial fold, it is often concluded that this means there
must be produced an anterior intrusive force upon engagement. This may very well be true, but likewise, it may be very
untrue. There not only may be no force present, but there might even be present an anterior extrusive component of
force. This visual method seems to be so obvious, but it is this method that so often leads us down the road to faulty
conclusions.

• ….So, not to be mislead by determining forces present through the visual inspection method, Thomas Mulligan
presented a number of “two teeth” illustrations to make a quick visual determination of the forces present.
Q. What force will produced on the…. a) molar and b) on the cuspid ?

Q. What force will produced on the…. a) lateral incisor and b) on the
central incisor ?

What force will be produced? A) on the cuspid? B) on the molar?

What force will be produced? A) on the central incisor? B) on the
lateral incisor?

A SIMPLE RULE
 First, if the bend is located off center, there will be a long segment and a short segment.
When the short segment is engaged into the bracket or tube, the long segment will point in
the direction of the force produced on the tooth that will receive the long segment.
 Another way to think of it is this: The short segment points in the opposite direction of the
force. This is certainly different than visual inspection might lead us to believe.
Different than visual inspection

 It can be seen that although the wires are bent
in the same direction, it is the different location
of each of the bends responsible for the
entirely different forces produced on the
molars and the cuspids.

 FORCES & MOMENT
 Force is nothing but a “push” or “pull” &
acts in a straight line
 Moment is the product of force times distance.
M = 𝐹 × 𝐷
(JCO,Volume 13(9);676-683,Oct1979)

 Each body has a point in its mass, which behaves as if the whole mass is concentrated at that single point,
which we call the center of mass in a gravity free environment.
 For any restrained bodies CENTER OF RESISTANCE (COR) analogues to the center of mass.

In case of understanding the magnitude and direction of tooth
movement, “point of application of force” is very important.

 When line of action of force passes through any point other than the COR, a moment is produced.
This turning effect of force is also known as “Moment of Force” .

M = 𝐹 × 𝐷
 A moment is the product of force times distance.
If the line of force does not pass through the
center of resistance of the tooth, then there is a
distance between this line of force and the
center. It is the perpendicular distance from this
line of force to the center that causes the moment
on the tooth, resulting in rotational tendencies
 When the line of force passes through the COR, No
Moment is produced, & therefore no rotational
tendencies.

 A larger force may produce no moment or a small moment,
while a small force might produce a large moment due to
the distance involved.
M = 𝐹 × 𝐷
 By doubling the force and cut the distance in half, or
double the distance and cut the force in half, and in
both cases we would produce the same moment or
rotational tendency.

CUE BALL CONCEPT
If we desired English (moment), we applied a force off center. We produced left or right English at will, simply by
deciding to apply the force to either the left or right side of center on the cue ball.
If we only wished to "translate" the cue ball— move it in a straight line with no left or right English— we applied
the force right through the middle of the cue ball

TRANSLATION
• Again, if we apply a force through the
center of the cue ball, it will move forward
in a straight line (Fig. 23). Whenever a
force passes through the center of such a
body, the body will translate.

PURE ROTATION / COUPLE
• Although when we play pool, we do not apply two
forces on a cue ball at the same time, we could do it to
prove a point. If we were to apply two forces on the
cue ball, equal and opposite, in the same plane of
space, the ball would not translate in any direction.
Instead, it would simply maintain its position and
"spin" (rotate) .

A pure moment always acts around the center of resistance. Regardless of the where the equal and
opposite forces are applied, the body will undergo pure rotation around the center of resistance.

FORCES & MOMENT ACTING ON TOOTH
.
When the wire is brought down from the mucolabial fold for insertion into the incisor brackets (Fig.B), the force
required acts at a perpendicular distance from the center of resistance in the molar (Fig.C), thus producing mesial root
torque or distal crown thrust on each of the molars involved.
If we use a tipback bend for overbite correction, we can recognize that when the short segments are placed into the
molar tubes, the long segments, prior to bracket engagement, lie in the muco-labial fold (Fig.A). From this we can
see that the long segment points apically in the incisor area and therefore indicates an incisor intrusive force while
the molars have an extrusive force present

When the wire is engaged into the incisor brackets, the intrusive force acts in a straight line and usually passes
labial to the center of resistance in the incisors. This produces a smaller moment that on the molar, because in
spite of the fact the forces are equal, the distances involved are radically different.

So, when the archwire is tied into place and tied back at the molar tubes, we have significantly different
(relatively) magnitudes of torque, which we can refer to as "differential torque".

But, again, that is not all that is taking place. Let us take a look at a distal view of the molar teeth and keep the cue
ball concept in mind.
If the wire is round, instead of rectangular, and permitted to "roll" inside the tubes, the extrusive force present on
the molar teeth then acts at the molar tubes which lie, usually, buccally to the center of resistance in these teeth.
This force times distance results in molar lingual crown torque.
If a wire were very rigidly attached to the tubes, the applied force would pass lingual to the center of resistance,
thereby inducing buccal crown torque instead

LINGUAL ROOT TORQUE
• If we place lingual root torque into the incisor section,
we produce a long segment and a short segment, just as
was the case with the tipback bend. The long segment
indicates a molar intrusive force and therefore an
extrusive force on the incisors. We can also see that the
torque produced on the incisors is a result of force times
distance, since the long segment has to be brought down
to the molar tube, and the force required to bring it down
acts at a perpendicular distance to the incisors.

If the long segments from the tipback bends
maintain the same angular relationship as the long
segments from the incisor torque bend, the vertical
forces cancel each other and only moments remain.
Therefore, no overbite correction may occur even
though we might expect it. (A)
If the long segments just discussed are unequal in
angular relationship, then the one producing the
greater angle relative to t he level of the archwire will
determine the net force present. For example, if
lingual root torque produces the greater angle as
shown in Fig B, the net forces will be intrusive on the
molar and extrusive on the incisor. Therefore, if we
are hoping for overbite correction, but increased our
lingual root torque to this point, we can expect our
overbite to increase instead of decreasing.

So, we might decide, if we know this beforehand, to either increase the molar tipback bend,
decrease the amount of lingual root torque on the incisor segment, or a combination of each,
in order to assure ourselves of a net intrusive force on the incisor segment for overbite
correction.
Recognition of the problems and intelligent decision making will only follow a thorough
understanding of the underlying principles.

(JCO,Volume 13(9);762-766,Nov1979)
The experiment consisted of a glass with a coin
sitting on the lip of the glass with two forks
suspended on the edge of the coin.
 When forces acting on an object which is at rest are balanced, then we say that the
object is in a state of static equilibrium. The resultant of these forces equals zero.
 Eg- Teeter-totter….When a large person sat at one end and a smaller person at the
other end, the board was not in balance until the heavier end struck the ground.

If we, desired to convert this "dynamic" state to a state of statics, either shift the
unequal weights or the fulcrum point on the board .

Requirements for Static Equilibrium
Sum of all the vertical forces present must equal
zero .
This is why we must deal with extrusive components of force during
overbite correction.
Sum of all horizontal forces present must equal
zero.
This is why we cannot correct a unilateral crossbite with a single
horizontal force
Sum of the moments acting around
ANY point must also equal zero .

With two equal moments at either end of the archwire, the system is in
balance. B. With two unequal moments at either end of the archwire,
the system reaches a balance, but seems to be unbalanced and with the
entire unit rotating counterclockwise. C. Actually, the unequal
moments create (in this case) an extrusive force on the incisor and an
extrusive force on the molar. The sum of these forces is zero, but the
configuration causes the entire unit to rotate clockwise.

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. We are acquainted with such
forces in a reverse curve of Spee, full strapup.

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 have not 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 vertical forces
are usually kept as light as reasonably possible.

(JCO,Volume 13(9);808-815,Dec1979)
CROSSBITES
 If an individual molar, or an entire buccal segment in crossbite.
 when we observe a buccal segment in crossbite, it may be a unilateral crossbite, or in most
of cases a bilateral crossbite with a lateral mandibular shift

The term "overlay" as used here will most often refer to a heavy wire overlaying the main
archwire. It can either be inserted into the headgear tube or be designed with terminal hooks to
engage the archwire
 OVERLAYS
0.36 mm over lays in 0.45 mm head gear tubes.

Upon insertion into both molar tubes, there exists a buccal force
on both the left and right sides. It will leads to correction of
crossbite in bilateral crossbite cases.
In unilateral crossbite cases sometimes the normal side
will become "worse", while the opposite side shows
improvement. By the time overcorrection of the side in
crossbite is obtained, the "normal" side is in
buccoversion, but readily "relapses" to its normal
position, while the side originally in crossbite relapses
to the point of improved function— and HOPEFULLY
this improved function will maintain the position.

Cosmetic Overlays
The overlay is referred to as "cosmetic" because it is designed not to show when the patient smiles.
It is, therefore, ideal for the adult patient who is concerned about the cosmetics of appliance
therapy. It can also be removed by the patient, if necessary for any reason such as illness or broken
appointments.
Reduction of Posterior Arch Width
The same overlays as used for expansion are utilized. Instead of the overlay being expanded, it is
constricted. All of these overlays are much easier to use in the maxillary arch due to the tendency for
occlusal interference in the lower arch, as well as the fact that the lower arch usually does not contain
a headgear tube for convenience.

(JCO,Volume 13(9);53-57,Jan1980)
THE DIVIDING BOARD CONCEPT
 It is not that we use the diving board in force control, but the mental image should permit us to recall more
vividly the advantages involved in utilizing the factor of "length" in our archwires.
 There is a formula that says that stiffness ( the amount of deflection we get from a given load)— or
load/deflection rate— is inversely proportional to the cube of the length. Formulas of this kind often seem
confusing and of little use to the orthodontist, as well as difficult to remember.
𝑆𝑇𝐼𝐹𝐹𝑁𝐸𝑆𝑆 ∝ 1/𝐿³

The formula tells us that if we are dealing with a cantilever (such as a diving board), by doubling the length
stiffness is reduced to one-eighth. By doubling the length, only one-eighth the force will be required to
produce the same deflection or the same force acting at double the length will produce eight times as much
deflection
A. 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

Load on diving board produces bending moments along the board, with the maximum
moment being located closest to the point of attachment .
In orthodontics, we often refer to this moment as the "Critical Moment", as it is the largest moment
involved and is often responsible for breakage in an archwire at that particular point .

A. Bending moments decreases as the distance from the load decreases.
B. As the load moved to the end of dividing board the distance double so does the
critical moment.

A cantilever is characterized by a pure force at one end and a single moment at the point of
attachment. a cantilever system will be introduced by locating a bend at a particular position
between the brackets.
when only cuspid intrusion is required, a continuous archwire can be placed under the cuspid bracket. It
will provide a cantilever force for cuspid intrusion .
Cantilever Principle

CONSTANT LOAD VERSUS CONSTANT DEFLECTION
To seek an exact force level requires varying
deflection of the archwire. when we place a given
bend, we must determine what angle is necessary
to produce the desired load (force). It also
requires that we must know the length of wire
between brackets and tubes. We can resort to
reference tables or we can go through "trial and
error“ until we arrive at the bend which gives us
the force we want.
If, instead, we choose to place a "constant" bend
(angle), we find that we create variable loads
(forces)

(JCO,Volume 13(9);98-103Feb1980)
CLINICAL APPLICATION OF THE DIVIDING BOARD CONCEPT
 From the "Diving Board Concept", we recognize that length affects the load (force).
 If we double the length of wire, we reduce the force per unit of deflection to one-eighth. Therefore, if we
bypass bicuspids and cuspids during overbite correction, and use a wire with tipback bends at the molars, we
have in effect created a "diving board“.
 If the tipback activation is constant, such as a 45° angle, then as the
distance doubles, so does the deflection (Fig. 69). Therefore, although the
load per unit of deflection is reduced to one-eighth, the unit of deflection
is doubled, resulting in a net force of one-fourth (2 × 1/8 = ¼). However, it
is quite evident that the length of wire is increasing much more than
"twice", and therefore the net intrusive force on the anterior segment is
dramatically reduced.

The name of this series involves "Common Sense", and it is good to know what is technically
correct, but at the same time what is practical and works. There is nothing that says we must
adhere to a certain method derived from a given principle. We are free to modify any method in
any way that gives us the end result we seek. Each orthodontist may choose his preferred method.
The underlying principles offer him an intelligent choice. In any case, the force magnitudes in the
non-cantilever system remain light, and this is our primary concern.
As we can see, there is a reason for all responses. Whenever we witness responses for "no apparent reason", we
have failed to recognize the cause, and as a result made our treatment somewhat more difficult. The recognition
of causes permits us to utilize as well as avoid various types of tooth movement.

COMMON
SENSE
MECHANICS –
PART 7
Distalization With Differential Torque
The tipback bend has been discussed and
demonstrated .
We know that the tipback bend is an off-center
bend and that the long segment and short segment
indicate the direction in which the forces act.
We also know that the moments involved are
unequal, thus resulting in "differential torque".
(JCO,Volume 13(9);180-189March1980)

ROWBOAT EFFECT
 “Rowboat effect", is the tendency for the maxillary teeth to move forward
during anterior lingual root torque.

We have all experienced this tendency for Class II relapse following headgear or Class II elastics when
such torque is applied. If we can simply understand WHY this occurs, then we can reverse the
conditions and create the opposite tendency, distalization. ( Opposite of Rowboat effect)

We already know that when we apply anterior
lingual root torque, crown movement tends to
precede root movement. When the archwire is tied
to the molar tubes, this "rowboat effect" is
transmitted to all of the teeth. Anterior lingual root
torque can be applied in many ways. It makes little
difference whether we use a rectangular wire, or
round wire with torquing loops, or whatever other
means one may choose. When a rectangular wire
with anterior lingual root torque is engaged into
the molar tubes, anterior lingual root torque is
produced (Fig.A). Therefore, we can produce the
opposite tendency for tooth movement by placing
mesial root torque on the molars using a tipback
bend in a round wire (FigB).

 Keep in mind that if the second bicuspid is engaged, the bend is no longer an off-center bend
and will result in, basically, equal and opposite torque on the molars and bicuspids. We are
looking for unequal or differential torque at the anterior and posterior ends of the archwire.
 If overbite interferes, at the time, with the distal crown movement (tendency), mesial root
movement of the molars will occur. These responses are highly variable, as are many other
responses such as headgear, etc. The most desirable responses occur where teeth need
uprighting, as these are tipping movements rather than bodily movements.

In general, the level of unerupted second
molars does not pose the threat of impaction
with the use of a tipback bend, except with
techniques that use excessively high vertical
force levels.
The most serious tipback ever placed
on molars by mulligan

Simply by starting treatment prior to loss of the
second deciduous molars, think of how many
more patients can be included in nonextraction
treatment if you could simply gain another 1½ to
2 millimeters of space in each quadrant (Fig. 81).
Since differential torque can do this, particularly
where molars require some uprighting, the
combination of "E" space with that gained
mechanically is significant.

 Mulligan credited his treatment
planning with additional arch length on
patients who are still growing vertically,
while he credited additional length with
a big ZERO on non growers, such as
adult patients.

Class II Correction Without Headgear or Elastics
He presented a few cases to show some of the variations in response that occurred with use of the
tipback bend during overbite correction.
This is not a means of eliminating headgear or elastics. The amount of headgear treatment
originally planned is either reduced, some times dramatically, or even eliminated.

 He used differential torque with a tipback bend.
 Tipback bends were used in both arches (Fig. 85). Movement was found usually
more responsive in the maxillary arch,

 This "distalization" tendency - easy to check simply by observing the unbanded cuspids
and their change in axial inclination.
 The cuspid crowns tip distally as they are forced back as a result of the thrust being
received at the crown level.

Another case presented by Mulligan with mild Class II with only moderate overbite and
upper anterior crowding.

There was decalcification present on
lower molars, but no appliance was ever
placed in the lower arch. The lower arch
was reasonably satisfactory, so only upper
incisors and molars were banded and the
case treated with an .016 archwire with a
tipback bend. Anterior alignment in itself
could be expected to result in overjet, but
with no headgear or elastics ever utilized,
and only a total of six bands placed,
treatment was concluded successfully.

The tipback is not a substitute for headgear or elastics. However, because of the characteristics of the
force system, variations in correction will take place. Common sense helps to predict which cases are
most likely to be involved. Since the system works "with" the headgear and elastics and not "against"
them, progress is often made even with lack of cooperation. Also, because Class II elastics tip an occlusal
plane downward, use of a tipback in an upper arch only, does just the opposite, and can permit the use of
Class II elastics in such cases without affecting the upper occlusal plane..
Summary

EXTRAORAL ELASTICS
• Extra oral elastics are used with
extra oral mechanic systems. They
can hook from the face bow to the
cervical strap (cervical head gear),
or from the face bow to the high
pull strap (high pull head
gear).These includes plastic chains
and heavy elastics.

ACCORDING TO FORCE :
a)High Pull Ranges from 1/8” (3.2mm) to 3/8” (9.53mm). It gives 71 gm force (2 ½
oz) .
b)Medium Pull Ranges from 1/8” (3.2mm) 3/8” (9.53 mm). it gives 128gm or 4 ½ oz
force.
c)Heavy pull Ranges from 1/8”(3.2mm) 3/8”(9.53 mm). It gives 184gm or 6 1/2oz
force.
The force depends on the diameter and thickness of the elastic .The elastic force is
measured in ounces( 1 ounce = 28.34 g)

According to availability
INTRAORAL ELASTICS

JCO,Volume 1980 Apr:(265-272)

WIRE – BRACKET RELATIONSHIP
 The relationship of the archwire to the brackets and
tubes, prior to engagement, offers valuable and
interesting information.
 If a straight wire is placed over angulated brackets, a
certain angular relationship develops between the wire
and the plane of the bracket slot.
 The same wire/bracket relationship can be created by a
bend in the wire or a straight wire in relation to a
malocclusion.

Basically, as an orthodontist we deal with various wire/bracket relationships created
by the malocclusion, archwire bends, or both. For practical reasons, Mulligan
prefered to attain bracket alignment regardless of the force systems produced in the
process. Once this is accomplished, desirable force systems can be attained by
placing bends at specific points along the archwire. In other words, we then
determine what we want by creating our own relationships.

So, to get a further insight as to the force systems created by wire/bracket relationships, let us consider the
variations. If we begin by using a constant interbracket width (any width) and a center bend, it can be seen that the
relationship can be created by the bend in the wire or by the malocclusion. In either case, the force system is the
same. As already said, Mulligan prefered aligning the brackets and then determined his own systems by placing the
bends where needed.

If we now look at Figure 97, we can see that the bend has been moved off center, but
still remains identical to the relationship created by the malocclusion.

Again, in either case the force system is the same. Finally, in Figure 98 we see that two off-center bends
have been placed, the second being inverted, but placed equidistant from the bracket. Yet the relationship
is no different than the one produced by the malocclusion and a straight wire, so the force systems are
identical.

Now, if we go back and look at all 3 figures and concentrate on the angulated brackets only, we can see
what caused the change in the wire/bracket relationships. The bracket on the left in each case remained
constant in angular relationship with the archwire, while the bracket on the right was slowly rotated
clockwise. Therefore, we can readily accomplish the same by placing bends instead, once the brackets
have been aligned.

Center Bend Force System
Let us begin to determine the forces and moments present in the two extremes of the wire/bracket
relationships— the center bend and the step bend by applying the requirements for static equilibrium.

 “Assume" that the four activational forces shown are equal. If
so, the sum of the vertical forces equals zero and the first
requirement for static equilibrium has been fulfilled. Next, the
horizontal forces equal zero because there are none, so the
second requirement is, likewise, fulfilled.
 Force A produces a clockwise moment (activational), equal
and opposite to the magnitude of the counterclockwise
moment produced by Force D. Now, Force B produces a
counterclockwise moment smaller in magnitude, because it
acts at a smaller distance from this point. Force C, acting at
the same distance, produces the same magnitude, but the
moment is clockwise. When we add the four moments
produced around this point, the sum is zero.

Since Forces A and B produce a couple (pure moment) which is clockwise, and since Forces C and D produce
a counterclockwise couple, we can say that the net activational force system— two moments, equal and
opposite in magnitude. ( If the forces are equal).

Step Bend Force System
Again "assume" that the four activational forces shown are equal. If so, the sum of
the vertical forces equals zero and the first requirement for static equilibrium has
been fulfilled. Next, the horizontal forces equal zero because there are none, so the
second requirement is, likewise, fulfilled.

Using the same center point, we can readily
see that Force A produces a clockwise
moment, the same as that produced by
Force D. Both are clockwise and both are
equal in magnitude. However, although the
moments produced by Forces B and C are
equal to each other and counterclockwise,
they are smaller in magnitude than Forces A
and D, because they are produced at
smaller distances. Therefore, the sum of the
moments does not equal zero. Since ALL
THREE requirements are not fulfilled, the
original assumption that all activational
forces were equal was incorrect. Or the
system is not in equilibrium.

Step bend force system where forces A & D are less than forces B & C are in static
equilibrium.
 Although Forces A and D (equal) are smaller than
Forces B and C (equal), the sum of the vertical forces
can be seen to equal zero. The horizontal sum
remains zero, as there are no horizontal forces.
 The third requirement is finally met, because Force A
and Force D each produce clockwise moments equal in
magnitude and opposite in direction to the
counterclockwise moments produced by Forces B and
C.
 In spite of the fact that Forces B and C act
at smaller distances, balance is
maintained due to their greater
magnitudes of force.

VARIOUS STEP BENDS RELATIONSHIPS PRODUCED BY MALOCCLUSION

JCO,Volume 1980 May:(336-342)

Extraction Mechanics
Earlier, in the "Fallacy of Visual Inspection in Force Analysis", it was shown that a wire with a bend off
center is clearly different than one with a bend in the center, since one produces net forces at the bracket,
while the other does not. A center bend involves no net forces, but only equal and opposite moments with
full wire/bracket engagement in any plane of space.
The tipback bend is an off-center bend. The long segment indicates the direction of the force produced,
while the short segment points in the opposite direction to the force it produce. In the tipback, two
moments are also produced, but they are unequal. The larger moment lies at the bracket or tube containing
the short segment. The smaller moment lies at the bracket or tube containing the long segment. This
smaller moment may, at times, be clockwise; and at other times counterclockwise; and even disappear,
producing the cantilever effect, because only a pure force would exist at that bracket. These various results
are dependent on the angle at which the wire crosses the bracket.

This series was concentrated on a practical clinical approach in which principles of mechanics was
used to predict and interpret tooth movement. Complete orthodontic records, including cephs were
taken and studied for all full treatment procedures, but focus was attempting to discuss only the
mechanics following treatment decision and statement of objectives.
The typical extraction strapup involves the banding/bonding of cuspids, second bicuspids, and first
molars. Many prefer to band second molars for anchorage purposes as well as for gnathological
considerations. Others band second molars for alignment and control.
Obviously, there are situations when they MUST be banded but As far as intraoral anchorage is
concerned, mulligan discussed about the effectiveness of differential torque as a means of control by
Keep in mind, there is no such thing as PERFECT intraoral anchorage, his focus was seeking a method
which offers the optimum for anchorage control.

Since the forces during retraction are equal and opposite on the two units — anchor unit and non-anchor
unit — the multibanded unit actually receives the lesser amount of force per unit area (stress) along the
periodontal membrane while the non-anchor unit (cuspid) receives the greater.
Anti-rotational ties are placed next to the extraction sites, unless such rotations are indicated
Also, anytime teeth are being retracted, there is a mesial force at the molar tubes. Toe-in bends should be
placed early, so as to initiate a counterrotation, so that we do not produce a mesiolingual rotation of the
molars when retraction is begun. Remember the "Cue Ball Concept". Of course, many will offset this
rotational tendency with lingual elastics.

Bends were given intraorally using a tweed loop forming plier , to create differential torque.
Power chain or cuspid were tied up directly to the molar , while the 2nd bicuspid was tied up
individually with ‘O’ ring. This allowed a greater range of force.

The anchor unit should remain relatively upright, while the non-anchor unit will undergo tipping until archwire binding
occurs. Once binding occurs, the roots will respond to the moments produced by the archwire, until binding stops and
crown movement is resumed. Remember, the anchor side is located closest to the bend while the non-anchor side is
furthest from the bend. As cuspids continue to move distally, the bend automatically "approaches" the center of the wire,
until finally, when the extraction sites are closed, the bend is centered. So you can see that as the off-center bend moves
toward the center during space closure, the differential torque begins to gradually disappear, and becomes equal and
opposite torque when the bend is finally centered. Root parallelism begins to take effect as the bend approaches center.

COMMON SENSE MECHANICS –
EXTRACTION MECHANISM &
MOLAR CONTROL
JCO,Volume 1980 May:(336-342)

During the discussion on cuspid retraction, it was pointed out that : there are various
anchorage concepts, including multiple banding/bonding on the anchorage side of the
extraction site. Obviously, there are different types of extraoral anchorage, but we are
discussing intraoral anchorage, with the orthodontist choosing a method of control. In
addition to the method of multiple banding to form large resisting units, it was shown
that anchorage can be instituted by banding a lesser number of teeth and locating
archwire bends in such a manner as to produce "differential torque". When the bend
is placed off center, the tooth (bracket or tube) located closest to the bend contains the
largest moment and, therefore, indicates the anchor side.

 It was also shown earlier, that these unequal moments are important in terms of their
"net difference". The smaller moment can sometimes be in the same direction
depending on the angular relationships of the wire to the bracket.
 if the unequal moments are in the same direction, their additive effect increases the
effectiveness of the anchorage (Fig. 117).

In those cases where the smaller moment is opposite in direction to the larger moment
(Fig. 118), there is still a "net difference" in favor of the anchorage side.
However, as the interbracket distance becomes smaller, the bend is closer to center and,
therefore, the two moments are more nearly equal, which reduces the effectiveness of the
anchorage. By recognizing these factors, we can keep treatment simple and practical.

Since differential torque considers the effectiveness of a net moment, total root area
in the anchor unit is not the primary consideration.
As a result, bicuspid retraction can be considered in the same way as cuspid retraction.
Bicuspid retraction with severe anchorage requirements can be performed on one side,
while the same wire can be utilized to perform molar protraction on the opposite side of
the same arch. In fact, protraction is accomplished in the same manner— by locating the
bend off center. However, protraction will simply utilize the non-anchor side of the
bend. In other words, the bend is moved "away" from the teeth to be protracted

Bicuspid Retraction
 The malocclusion includes a deep overbite with a Class I molar relationship,
 a missing lower left second bicuspid with the second deciduous molars still in place. The lower left
first bicuspid is almost in contact with the mandibular lateral incisor.
 And tissue blanching can be seen as a result of the unerupted permanent cuspid lying labial to the
lateral incisor and first bicuspid.

Treatment was instituted with the removal of the lower second deciduous molar, 45,
and 14.
Only a minimum appliance was placed and treatment began with an .016 archwire in
the lower arch. Because the molar was to serve as the anchor unit, a bend was placed
mesial to the tube, thus producing the largest moment on this tooth. An elastic was
used to retract the first bicuspid (Fig. 120).

• Clinically, the non-anchor tooth (first bicuspid) is observed tipping,
while the molar remains relatively upright. This verifies the anchorage
and non-anchorage sides due to the unequal moments present. As the
bicuspid continues to move distally, it gradually approaches the off-
center bend lying mesial to the molar tube. As this happens, the two
moments gradually become more and more equal (decreasing
differential), but opposite in direction. This gradual equalization
provides the root paralleling that is necessary due to the initial tipping.

Molar Protraction
• The lower right cuspid and bicuspid are banded to begin
molar protraction on the right side (Fig. 121).
In this case, since the molar is to be protracted, it belongs on the
non-anchor side, and therefore, furthest from the bend. The opposite
side becomes the anchor side, so the bend is placed immediately
distal to the first bicuspid bracket. Differential torque is again
produced, just as occurred on the left side, except the directions of
movement are reversed because the locations of the bends are
reversed

On the lower right side, there is no tieback loop mesial to the molar as this tooth is to be protracted into the second
bicuspid extraction site. The wire is usually an .018 followed by an .020 on occasion, as the tipping tendency for
molars is too great with a lighter wire in an .022 ´ .028 tube.
If mesiolingual molar rotation is desired— and most often it is not— no bend need be
placed, as a mesial force acting at the molar tube during protraction produces the rotation
as a result of the "Cue Ball" effect. If the opposite rotation is indicated, a sharp toe-in
bend must not be placed, as it will interfere with protraction by binding at the molar tube.
A gentle curve can be placed instead. It will produce the same required moment, as it still
produces the same wire/tube relationship (Fig. 122).

• Now that cuspid retraction, bicuspid retraction, and molar protraction have been
discussed, all involving the application of differential torque applied by the simple
location of a bend, it will be shown that the same relatively simple concept can be
applied to the simultaneous retraction of bicuspids and cuspids using only single
molars as anchorage units. Again, there is no such thing as perfect intraoral
anchorage, but there is such a thing as providing maximal intraoral anchorage with
mechanical principles that provide greater reliability and consistency.

Applying Principles to Total Treatment
Class I Nonextraction
Case 1.
Class I malocclusion
with considerable crowding in the
mandibular arch
and moderate overbite with linguoversion
of the lower right bicuspids (Fig. 140).
Based on profile requirements, it was decided to treat this boy on a nonextraction basis, in spite of
the amount of crowding in the mandibular arch.

Only a minimal appliance need was anticipated. Upper and lower 2×4 (incisors and
molars) were placed, with initial .016 archwires (Fig. 141), and tipback bends in
the lower arch.
The tipback produced light intrusive forces on the incisors, while the eruptive forces
were shared by the molars resulting in each molar receiving only one-half of an
already light force.

Lower right bicuspids, which were in linguoversion
and required only a buccal force at the crown level,
have been ligated to the archwire.
The temporary buccoversion of the upper molars is
increasing, particularly on the right side, as the lower right
first molar responds to both the tipback bend and reciprocal
movement resulting from the buccal forces on the bicuspids.
the case does not look pretty at this stage, but presents no
problem if one remains aware of what is happening

Tip back bend
created space in
lower arch…that is
utilised for slight
anterior crowding.

• A heavier wire has been placed in the lower arch, usually an .020. and molar
uprighting was done.

As discussed earlier that .036 overlay can be used for either expansion or constriction of
arch width. In this case, the upper first molars are now ready for an .036 overlay
constriction arch, designed with an anterior vertical loop and then constricted (Fig. 146).

The archwire bend labial to the cuspids produces a "long arm" indicating lingual
forces on the molars. These bends are not necessary, as the forces produced from the
overlay will easily overcome the archwire resiliency.
When the maxillary molars have been constricted, all wires are removed (Fig. 148),
to allow function to perform its role. Wires are reinserted, when indicated, to control
or produce additional rotations (Fig. 149).

Class II, Dlvision 2 Malocclusion
• The patient is a young female
with a serious Class II, division 2
malocclusion (Fig. 153).
• It is very important that you
take notice of the buccoversion
of the maxillary second
molars. The lingual cusps
contact the buccal surfaces of
the mandibular molars.

Upper first bicuspids have been extracted and treatment initiated with an .016 spiral
arch and no extractions in the lower arch (Fig. 155).
Case was treated to a Class II molar relationship, and

maxillary labial crown torque will be
required to produce the necessary
overjet to permit alignment of the
mandibular incisors.
Intrusion in the upper arch only is
accomplished, until such time as the
lower incisor bands/brackets can be
placed (Fig. 156).

The off-center bend located mesial to the bicuspid brackets. This bend provides the
intrusive force to the incisors, while the distal crown thrust on the bicuspids
enhances the anchorage during space closure. The eruptive force acting on the
bicuspids provides, in addition, an "interlocking" tendency with the unbanded lower
bicuspids.

The lower incisors are purposely being expanded, due to the facial profile and
cephalometric data. Cuspid bands were placed and the cue ball concept applied (Fig.
159).

The lower archwire was segmented and the molars "set free" (Fig. 161).
Additional anterior intrusion was gained with an .018 cantilever overlay
(Fig. 163).

see the upper second molars, which will require some lingual crown torque.

An .018 archwire, with distal extensions, was prepared for lingual crown movement of the maxillary
second molars (Fig. 164). The archwire was inserted (Fig. 165) with the extensions in contact with the
second molars.

Intraoral activation was obtained with a Tweed loop pliers (Fig. 166). A center (gable) bend
was placed intraorally in the extraction sites (Fig. 167). Because of the full strapup in the upper
arch— excluding second molars — this center bend caused the archwire to behave as a reverse
curve of Spee and, therefore, intrusion occurred at both ends of the archwire, unlike the tipback
bend. Figure 168 shows the amount of overbite correction at this point in treatment.

• The distal extensions were cut off after sufficient lingual
crown movement of the maxillary second molars occurred (Fig.
169)

A rectangular arch, .019 × .025, was fabricated (Fig. 170) for the anterior lingual root torque and placed (Fig.
171).

 Appliances were removed prematurely at the request of the patient
 Everything was satisfactory at this point, except for the needed lingual root torque.

Class II Open Bite, Extraction
This case presented with the right side in Class I and the left side in Class II
with open bite and midline discrapancy (Fig. 175).

Due to the midline discrepancy, asymmetrical extractions were done. 14, 44, and 35 were extracted.
Asymmetries have already been demonstrated and corrected with asymmetrical mechanics, such as
retraction on one side of an arch with protraction occurring on the opposite side of the same arch at the
same time.
The same mechanics as described in the section on cuspid and bicuspid retraction was used, except that in
this case, the cuspid and bicuspid on the lower left side were retracted only part way and the molar
protracted the remainder of the distance. This is accomplished by use of a center bend in which neither
side becomes the anchor side. The other three cuspids were retracted individually.

The occlusal views (Fig. 177), again, point out the importance of placing toe-in bends early.
Toe –in bend placed in early stage to correct the mesiolingual rotation of molar.

In Figure 179, the anterior teeth have been banded and the spaces closed. In this case, up-and-down
anterior elastics were used to close the bite. They were used in a rectangular fashion. For a short period
of time, rectangular up-and-down elastics were used on the right side, but triangular Class II elastics
were used on the left side for some additional Class II correction, in addition to the maxillary and
mandibular teeth being brought together.

Class III (Atypical), Mandibular Displacement
Class III malocclusion (atypical) involving a slight forward displacement of the
mandible during closure and a severe midline discrepancy
Case was started
with all 4
extraction.

Maxillary cuspids were retracted until sufficient space was gained to align the six
anterior teeth (Fig. 184). An off-center bend is used to assure sufficient anchorage,
but once the space has been gained, the mechanics are reversed so as to produce
buccal protraction of the maxillary molars.
It was intended, as part of the treatment plan, to maintain the anterior/posterior position
of the maxillary incisors and to retract the lower anterior segment sufficiently to
eliminate the mandibular shift and establish a Class I occlusion. Lower retraction is
accomplished with an off-center bend to maintain anchorage on the molar side of the
extraction site.

Class III, Dental/Skeletal
This girl presented with a difficult Class III malocclusion. There was no displacement on closure of the
mandible, meaning the entire dental relationship would require correction purely by tooth movement (Fig.
189).
Ideal correction in a case such as this would require surgery because of the skeletal contributions to the
malocclusion. But this case was treated by orthodontics alone, meaning that compromise must be part of the end
result.

• Notice the crossbite in the buccal
segments in addition to the anterior
crossbite. Merely correcting the
crossbite in the buccal segments will
worsen the Class III anterior relationship.
There is also lower anterior collapse
present, meaning that correction in this
area will worsen the anterior
relationship.

Note the facial profile
and the typical "dished
in" middle third (Fig.
190).

By considering the profile of the patient Nonextraction treatment was instituted, with the clear intent to expand
the maxillary teeth and to correct the molar relationship as much as possible with Class III elastics.
Only 2×4 appliances in each arch. Nothing more than an .036 overlay was used to correct the buccal segment crossbite.

After placing 2´4 appliances, a maxillary archwire was placed using coil springs
to advance the incisors (Fig. 191). Note that aligning the mandibular incisors at
this time would make the problem even worse. They are aligned later. There is no
"shift" present in this case, so all changes shown are due to tooth movement.

Six and one-half months later, a mild overbite has been established and space opened for the
upper left cuspid (Fig. 192). The molars have moved distally as a result of the prolonged
distal forces at the molar tubes. This seems to occur readily in a dental/skeletal Class III
malocclusion. The lower anterior segment is being aligned at this time.

An .036 overlay to correct the crossbite was used in the manner described earlier (Fig. 193). Class III
elastics are worn throughout this period to prevent Class III reoccurrence in the anterior segment during
expansion of the buccal segments.
The .036 overlay is certainly a heavy force and should never be activated for any type of vertical movement

Molar Control
When using loop-free archwires, bends can be placed between tubes and/or
brackets in such a location that certain wire-bracket angles are created at the
adjacent brackets. This affords the choice of various force systems and the
opportunity to produce a direct response.
This series will offer an easier approach to the control of molar position without
requiring an in-depth knowledge of various wire-bracket relationships, which
may result in difficult-to recognize force systems for many clinicians.

three wire-bracket relationships are shown. To a certain degree, all of these wire-bracket relationships
represent some form of off-center bend.

 simple rule regarding off-center bends…..LONG & SHORT segment
 The bracket located closest to the bend will contain the larger moment, while the bracket located farthest
from the bend might contain a clockwise moment, a counterclockwise moment, or no moment at all. It
simply depends on the precise location of the bend.

The step bend is a combination of two
off-center bends, with the short
sections bent in opposite directions and
parallel to each other (Fig. 1-5), while
the center bend is the equivalent of two
off-center bends, with the short
sections bent in the same direction
(Fig. 1-6).

 It will be seen that the bends that are used in molar control will allow
the clinician to maintain molar position and to restore correct position if
it is lost. These same bends will allow crossbite corrections without the
use of interarch elastics and will therefore require no patient
cooperation.

Causes of Molar Displacemen
Extrusive forces create the potential for lingual crown tipping (Fig. 1-8), whereas intrusive forces result
in the potential for buccal crown tipping (Fig. 1-9). The word potential is emphasized because the
forces of occlusion may or may not permit the effect to take place. But the forces and resulting
moments are present and
must be recognized.

Any type of tooth movement that creates these extrusive forces
in the posterior area results in the potential for lingual crown
displacement (ex- Incisor intrusion in a partial strap-up…so
lingual root torque act as a balancing system). Vice versa Any
type of tooth movement that produces intrusive balancing forces in
the posterior area has the potential for molar crown displacement to
the buccal.

Recognizing Molar
Displacement
 If the second molars are
present and unbanded, first
molar displacement is rather
obvious. If the first and second
molars are banded, displacement
may occur laterally, but the
central grooves will remain
aligned with each other. If the
first molars are banded, but the
second molars have not yet
erupted, lateral displacement of
the first molars may go
unrecognized.
If the forces of occlusion are such that crowns are able to respond, the molars will tip.

Differential Diagnosis
The changes that may take place in the functional curves of occlusion afford an opportunity to determine
which arch is involved in the molar displacement. If buccal overjet is present in the molar area, it must be
determined whether the upper molars have been displaced to the buccal, the lower molars to the lingual, or a
combination of the two.
From a frontal view, any change in the curves of Monson or Wilson will offer the answer .

Creating
Horizontal Forces
• Horizontal forces
generally produce
greater moments
than will vertical
forces acting
through the same
molar tubes.

The forces shown are those that will purposely be introduced by the orthodontist
to produce the moments necessary for molar control. A lingual force through the
molar tube results in a lingual crown moment, whereas a buccal force applied
through the same tube will produce a buccal crown moment (Fig. 1 - 20).

Keep in mind that buccal and lingual displacements may occur due to the vertical forces already
discussed, but
bracket and tube alignment are not necessarily affected. Molar rotations may occur following original
bracket alignment or may exist from the onset. To be more specific, it should be said that brackets should
be leveled and aligned, while molar tubes need to be leveled, but not necessarily aligned. In short, level
and align all brackets,
and level the molar tubes.
Archwires in Use
A “step” archwire is used whenever it is desirable to increase the arch length (Fig. 2-1). A “wraparound”
archwire is
used any time arch length is to be reduced (Fig. 2-2). Either wire may be used if the existing arch
length is to remain unchanged.

Partial Appliance or Equivalent
Brackets are not bonded for the purpose of placing molar-control bends. The
molar-control bends are placed for a specific purpose, regardless of whether the
appliance happens to be a 2 * 4 or 2 * 6. Whatever the situation may be, brackets
are not added or removed to enable the orthodontist to apply the molar control
concept.
If all teeth were ligated during the use of molar-control bends, the desired force
systems would not be created, as each bend placed would become almost centered in
relation to the adjacent brackets. The primary force system will take effect at the
brackets or tubes adjacent to the bend. Ultimately, other teeth will be affected by the

Sequence of Bend Placement
To apply the molar-control bends in a manner that will maximize the use of forces and
moments produced, the sequence of bend placement will be critically important.
This sequence cannot be violated at any time, as the desired force systems would
be change.
Each time by seeing from the occlusal view, two questions need to be asked:
First, “Do the molars need to be rotated?” (Either Toe-in or Toe-out )
Second, “Are buccolingual displacements present?” ( In- bend or Out-bend)
Each answer will be dealt with in that exact order.

Toe- in and Toe- out bends are the short segment of the off-center
bend. In & Out bends are the long segment of the off-center bend.
(SIMPLE RULE APPLIED)

Locating the Bends
The in-bends or out-bends are always placed in the embrasures between
the first bicuspids and the cuspids, regardless of whether the appliance is
a 2 × 4 or 2 × 6.
Toe-in & Toe-out bends are located just mesial to the molar tubes.

Case 1
 The first patient shows bilateral
mesiolingual rotations of the maxillary
molars, which are also lingually
displaced on each side (Fig. 2-8).
Toe –in bends ( Short section at each end)
Therefore buccal forces at each molar tube
EXCLUDE THE 2ND PM ….SO THAT THE BEND REMAIN OFF-CENTER.

 Toe-in bends have been placed to provide the necessary moments for
rotational correction.
 the second question pertaining to molar displacement requires no action.
The necessary buccal forces are already present.

Case 2
ML Rotation only one side ( Right) Toe –in bends (Right side only)
Therefore buccal
forces at one
molar tube.
EXCLUDE THE 2ND PM ….SO THAT THE BEND REMAIN OFF-CENTER.

Case 3 • This patient was seen by several
orthodontists who recommended palate-
splitting appliances.
• Having bilateral constriction of maxillary
arch.
• Lingually displaced as well as inclined
lingually inclined buccal teeth.
Toe –in bends for max 16,26
Therefore buccal forces at each molar tu
Bicuspids tied to archwire with ligature wire.
Effective tooth movement using ligature ties.

Case 4
Patient came with palate- splitting appliance in place for planned surgical procedure.
Crossbite in posterior
segment
Buccally tipped 36,46
(Reverse curve of spee)
Rotated 25
Slight central groove
discrepancy between 1st
& 2nd molar
Lower anterior crowding

The first step in treatment was to remove the palate-splitting appliance and all brackets in the
bicuspid areas (Fig. 3-4) . In bend in combination with Toe-out bends was used for molar correction.
Elastomeric tie to rotate second bicuspid.
IPR was done following appliance removal.

The Step Bend
Whenever two bends are involved and each bend produces a force in the same direction.
Significance lies in the increases in force magnitude.

Case 10
 Pt only concern was dental cosmetics.
 Constriction of maxillary arch is evident
 Slight ML rotation of molar.
 Buccally placed canine.
 Toe-in + Out bends ( Having combined buccal force on
molar)
 Step bend (Lingual displacement of canine)
7th was not bonded …if banded buccal force on 6th would
produce lingual force on 7th .

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