2. The title "Common Sense g 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.
3. we must gather as much information as
possible that will allow us to treat the patient
in a practical or realistic manner, rather than
treating in a textbook fashion. The textbook,
for example, may help us to determine how
equal and opposite forces are produced, but
such forces do not necessarily produce equal
and opposite response.
4. A. Vertical Plane of Space. Equal and opposite forces usually produce unequal response.
B. Horizontal Plane of Space. Equal and opposite forces tend to produce equal and opposite
response.
5. Perhaps it is a lack of a combination of the
two— knowledge of mechanics and common
sense application— that has led to the desire
on the part of many orthodontists to seek an
appliance which does the thinking. If such is
the case, there will be many frustrations which
will persist. orthodontists cannot escape the
need to understand the appliance of choice
and the various force systems which will enter
the treatment picture, either as our "friends"
or as our "enemies".
6. " Visual inspection method"
Wire inserted into molar tubes prior to insertion into incisor brackets.
7. 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. The visual method seems
to be so obvious, but it is this method that so
often leads us down the road to faulty
conclusions.
8. The followings are a number of "two teeth"
illustrations and permit you to make a quick visual
determination of the forces present. you will only
be attempting to determine forces, not moments.
Disregard the moments altogether and ask only
whether there will be an intrusive or extrusive force
present— or no force at all.
9. • Although we would normally insert the wire
into the molar tube first, it makes no
difference, since we are concerned only with
the total force system that exists when the
archwire is fully engaged in all brackets and
tubes.
10. What force will be produced? A. On the molar? (Extrusive Intrusive None).B.
On the cuspid ? (Extrusive Intrusive None).
What force will be produced? A. On the lateral incisor? (Extrusive Intrusive
None). B. On the central incisor?
(Extrusive intrusive none)
11. What force will be produced? A. On the cuspid? (Extrusive Intrusive None). B. On
the molar? (Extrusive Intrusive None).
What force will be produced? A. On the central incisor? (Extrusive Intrusive
None). B. On the lateral incisor? (Extrusive Intrusive None).
12. Actually, all we have done is to look at two
archwire bends. One bend was centrally
located while the other bend was located off
center. It was located either against the
bracket or the tube. Each time the bend was
located in the center, the answer was
constant, and each time the bend was located
off center, the answer was constant.
13. There is only one force system that can exist
for each of the two problems presented.
Actually, the centered bend produced only
equal and opposite moments, but no forces—
not a bad situation when we wish to parallel
roots following space closure, or rotate teeth
equally and oppositely. How about the off-
centered bend?
14. Well, the off-centered bend produced equal
and opposite forces, but the moments were no
longer equal. They became unequal when the
bend moved away from center.
What does all of this mean? Well, it means
that in a given plane of space, WE can determine
or recognize the forces present by noting the
location of the bend. Once we have attained
bracket alignment, further force systems can be
determined by the orthodontist instead of by
the malocclusion.
15. 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.
16. Another way to think of it is this: The short
segment points in the opposite direction of
the force that will be produced on the tooth
that receives the short segment. meaning that
the cuspid will receive an intrusive force. This
is certainly different than visual inspection
might lead us to believe.
17. Next, if the bend is in the center, there no
longer exists a long or short segment.
Therefore, no force is produced. these forces
cancel each other upon archwire engagement,
leaving pure moments.
18. • let us move from the buccal and anterior
planes of space and proceed to ask questions
similar to those before.
What force will be produced? A. On the molar? (Buccal Lingual None) B. On the
cuspid? (Buccal Lingual None)
19. What force will be produced? A. On the molar? (Buccal Lingual None) B. On the
cuspid? (Buccal Lingual None)
20. An approach has been presented to aid
the orthodontist in recognizing why these
forces seem somewhat difficult to recognize.
Archwire resilience and archwire shape can be
very misleading in the prediction of force
systems. Because the typical orthodontist
has been taught to read force systems by
visualizing the relationship of the archwire to
the bracket slot prior to insertion, incorrect
force systems are often anticipated.
21. Forces and Moments
• We all know what a force is, but sometimes
we tend to confuse the relationship between
force and moment. Simply stated,
• a force is nothing more than a "push" or
"pull," and acts in a straight line
Forces act in a straight line, producing a line of force.
22. • Whenever this line of force passes through the
center of a body— in orthodontics we refer to
the Center of Resistance— there is no moment
produced and therefore no rotational tendency
When a force acts away from the center, a
moment is produced and a rotational tendency
occurs.
A. When the line of force passes through the center of resistance no moment is produced and, therefore,
no rotational tendency. B. When the line of force does not pass through the center of resistance, a
moment is produced and rotation occurs.
23. • A moment is the product of force times
distance. It is the perpendicular distance from
this line of force to the center that causes the
moment on the tooth, resulting in rotational
tendencies .
24. We could double 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.
A moment is the product of force times distance. Doubling the force and halving
the distance maintains the same moment, and vice versa.
25. You can "sense" a force when you bend a wire,
but you cannot "sense" torque. Because the
latter is simply a product of force times distance,
as previously discussed, the distance (length) is
just as effective as the force. >>>> it is important
to get used to treating the two as separate
entities. One is a product of the other.
When the force passes through the center of resistance, no moment is produced. When
the force does not pass through the center of resistance, a moment is produced.
26. A large force (indicated by the longer horizontal line) might produce no moment, while a
smaller force might produce a large moment because of the distance from the center of
resistance.
27. Cue Ball Concept
If we desired English, 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 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. By
the way, with a tooth we use the term Center of
Resistance, whereas, in a free body we use the term
Center of Mass.
28. 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.
29. Translation
> From the cue ball rule: Whenever a force passes
through the center of such a body, the body will
translate. There will be no rotation— other than the
forward roll due to the friction of the table itself. The
reason there is no rotation > No moment produced
When the line of force acts through the center of resistance, only translation results.
30. Rotation and Translation
apply it off center, then we create a situation where
the line of force has a perpendicular distance from the
"Center of Mass" (a free body expression). This means
that we now produce not only translation, but also
rotation, as a result of the moment produced.
31. Pure Rotation (Couple)
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) . The reason for
this is that the two forces cancel each other
out, but leave a net moment (rotation) due to
the fact that each of these "Lines of Force"
acts at a perpendicular distance from the
center of the ball.
33. Forces and Moments Acting on Teeth
In the previous material, it was shown how
the force and direction can be determined by
whether the bend is in the center or off center.
A. Archwire with tipback bend Inserted in molar
tube. B. A force is required to bring the archwire
from the mucolabial fold to the incisor bracket. C.
A moment is produced on the molar as a product
of force times distance.
34. But, there is more to it than just these forces. What
about the moments?
When the wire is brought down from the
mucolabial fold for insertion into the incisor brackets ,
the force required acts at a perpendicular distance
from the center of resistance in the molar, thus
producing mesial root torque or distal crown thrust on
each of the molars involved. 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.
35. The intrusive force acting through the incisor
bracket usually lies labial to the center of resistance,
thus producing a moment, but smaller than the one
on the molar.
Differential torque.
36. 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.
37. • If lingual crown torque is desired, it should be
permitted to act. If undesirable, it can be prevented
with a lingual arch, a rectangular wire, or whatever
means the operator chooses.
An eruptive force at the molar tubes passing buccally to the center of resistance
produces lingual crown torque on molars.
38. vertical forces can well be the contributing cause molar
crowns due to the moments produced. Because vertical
forces usually act buccal to the center of resistance, the
perpendicular distance between the vertical force and the
center of resistance results in a moment. Eruptive forces
will result in lingual crown moments while intrusive forces
will create buccal crown moments. It can be seen that
horizontal forces acting through the molar tubes will
produce larger moments than those produced by the
vertical forces, because the perpendicular distance to the
center of resistance is larger than the previous.
39. 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.
40. Lingual root torque. A long segment and a
short segment are produced by torque bend.
Lingual root torque is produced
as a result of the force necessary
for molar tube engagement times
the perpendicular distance to the
center of resistance in the incisor.
41. 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. The anterior lingual root torque
introduces a vertical component of force that
must be considered .
42. 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 , 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
43. If the tipback and torque bends produce equal angular relationships
(A), the net forces are zero. If unequal (B), net forces occur
44.
45. Static Equilibrium
every action has an equal and opposite
reaction, Newton's Third Law has not really
been understood in such a way as to permit
the orthodontist to apply the principles in his
daily orthodontic mechanics in a simple and
practical manner. We do not, therefore, have to
concern ourselves with how to create static
equilibrium, but rather with how to recognize
the forces and moments (torques) that come
into existence to establish the static state.
46. Relating to our own lifetime experiences — as
we did with the "cue ball concept" — we can
recall the teeter-totter, familiar to us as
youngsters. When a large person sat at one end
and a smaller person at the other end (Fig. ), the
board was not in balance until the heavier end
struck the ground. If we, as youngsters, desired to
convert this "dynamic" state to a state of statics,
we simply shifted either the unequal weights or
the fulcrum point on the board (Fig. ). Then, we
encountered a state of balance. The question,
therefore, is why?
47. Unequal weights unbalance beam. Shifting fulcrum point (shown) or shifting
unequal weights establishes state of
balance.
48.
49. • Requirements for Static Equilibrium:
1- the sum of all the vertical forces present must equal
zero. This is why we must deal with extrusive
components of force during overbite correction (Fig. ).
Since we cannot eliminate these forces, we must learn
to control them.
First requirement for static equilibrium. Sum
of all vertical forces must equal zero.
Intrusive force on incisor
balanced by extrusive force on
molar.
50. 2- The second requirement for static equilibrium
is that the sum of all horizontal forces present
must equal zero (Fig. ). This is why we cannot
correct a unilateral crossbite with a single
horizontal force (Fig. ). We must apply common
sense when treating these problems.
Second requirement for static
equilibrium. Sum of all horizontal forces
must equal zero.
Buccal force on second molar balanced by
lingual force on first molar.
51. 3- The third requirement for static equilibrium is
that the sum of the moments acting around ANY
point must also equal zero (Fig.). We may choose
any point we wish— it does not matter. We may
produce heavy torques in a given area and little or
no torque elsewhere, but when added around any
given point, they will equal zero.
Third requirement for static
equilibrium. Sum of the moments
acting around any point must
equal zero.
52. If we have two moments, one acting at each end
of the archwire, and their magnitudes are equal
(Fig. A), it seems quite apparent that the system
is "balanced". But, if we have the same situation
with unequal magnitudes, it seems that the
system is no longer in balance (Fig. B).
A. 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.
53. • However, we KNOW that an archwire, when
fully engaged, always results in static
equilibrium. Therefore, regardless of the fact
that Figure B seems to be unbalanced, forces
are introduced to keep the systems balanced .
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.
54. Looking at the two unequal moments in Figure B, it
appears that the entire unit would rotate
counterclockwise. But, looking at Figure C, we see that
forces are automatically created which by themselves
would cause the unit to rotate clockwise. Actually, these
are equal and opposite forces—their sum must equal
zero — producing what earlier was referred to as a
couple or pure rotation. It was shown that with anterior
lingual root torque applied, a large moment was
produced in the anterior with a resultant eruptive force.
55. Figure below illustrates a full strapup with a
reverse curve of Spee. Note that the vertical
forces add up to zero along the archwire,
producing moments at each end resulting in
anterior lingual root torque (labial crown torque)
and posterior mesial root torque (distal crown
torque).
56. We are acquainted with such forces in a reverse
curve of Spee, full strapup. In spite of the fact
that we are usually attempting anterior intrusion,
we produce anterior and posterior forces with
equal and opposite extrusive forces occurring
through the bicuspid areas.
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).
57. • Arch Leveling:
When leveling an arch, it has already been
shown that in a full strapup, intrusive forces
act through the molar tubes, producing buccal
crown torque on the molars. Do you
sometimes observe the posterior teeth
moving buccally for no "apparent" reason
during arch leveling?
58. When a 2×4 (incisors and molars) strapup is
utilized for overbite correction, such as is
often done during late mixed dentition
treatment, the force system is not the same as
the one just described. 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").
59. During arch leveling procedures, we
frequently observe responses that may be
undesirable. They often occur unexpectedly
and in various forms. Too often, we tend to
look at all of this as variation occurring in the
individuals we treat, when in fact many of
these occurrences are predictable beforehand
and therefore avoidable from the onset.
60. The net force on a tooth during the
application of forces to teeth in orthodontic
treatment is always zero. An intrusive force on
an incisor tooth will be opposed by the forces
in the periodontium and its surroundings.
61. Crossbites
The vertical forces are usually kept as light as
reasonably possible, whereas no such attempt
is made at the horizontal level. In fact, the
forces used at the horizontal level are often
quite high. High magnitudes of force threaten
the vertical dimension, while posing little or
not threat to the horizontal dimension.
62. Expansion
Common sense must enter the picture. First
of all, when we observe a buccal segment in
crossbite, are we really observing a unilateral
crossbite, or are we witnessing a bilateral
crossbite with a lateral mandibular shift? In
my opinion, the latter is almost always the
case. Therefore, we need not fear the fact
that there will be equal and opposite
horizontal forces present (whose sum equals
zero), as both sides will require the force.
63. Overlays
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 (Fig.).
Overlays with and without terminal hooks. Midline loop Iies lingual to the
archwire and prevents the overlays from sliding forward.
64. With the use an .045 headgear tube, he
prefer the use of an .036 overlay for
expansion, as it provides sufficient binding in
the headgear tube when activated, to provide
the desired stability. If a segment of the dental
arch has collapsed for any reason, the point of
attachment can very well be that specific area,
since the heavy overlay can overcome the
resilience of the lighter archwire
65. Overlay arch with one side
inserted in buccal tube.
Overlay arch with terminal hooks
engaging the archwire.
66. • Figures below illustrates a patient with a
bilateral crossbite, but a lateral mandibular
shift which gives the clinical impression of a
unilateral crossbite and the insertion of the
.036 overlay, following activation by
expansion. Note the midline discrepancy as a
result of the lateral mandibular shift.
Case with bilateral crossbite which appears to be unilateral, due to mandibular shift.
67. Expanded overlay, before and after insertion.
Overcorrection of "worse" side resulted in buccoversion of "normal" molar.
68. Relapse to normal followed removal of overlay.
Case shown following treatment and retention.
69. HOPEFULLY this improved function will maintain
the position. If not, the overlay is reinserted.
The next case was treated in the same
manner, but involved a unilateral Class II
malocclusion and a unilateral tongue thrust .
The Class II molar relationship on the right
side was corrected with cervical headgear and
overlay treatment (Figures below).
70. Second case with crossbite, and unilateral tongue thrust.
Case following overcorrection with headgear and overlay.
71. Molars relapse to normal following removal of overlay.
Case at debanding and retention.
72. Cosmetic Overlays
Now, let us take a look at a late mixed
dentition case where only a single tooth is in
crossbite(Fig. ). The overbite is mild, as is the
lower anterior crowding, but this is pretty
normal at this stage of development. The
crossbite could be treated simply in a number
of ways. Use of an .036 overlay and two molar
bands provides a simple solution.
73. 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.
Case with only one molar in crossbite.
74. The overall movement is very rapid— usually
about three to six weeks . The normal side readily
"relapses" to its original position, while we are
hoping that the corrected side will maintain
normal position through improved function.
Since it is overtreated, relapse to the point of
normal function is desired. But common sense
and experience tell us that not all crossbites
maintain normal position when corrected. So,
never discard the expander— keep it in the
patient's model box. If the tooth (or teeth)
relapses, the expander may be reinserted and the
case expanded even further than the first time.
75. Overlay inserted in buccal tubes.
Overcorrected molar relapses rapidly. Corrected side held with removable retainer.
76. Overcorrected molar relapses rapidly. Corrected side held with removable retainer.
Case shown following settling.
77. Bodily Movement
All of the movements thus far described have
been tipping movements only. The force is heavy
and applied at the crown level. If bodily
movement is desired, a rectangular wire may be
placed to provide the necessary torque at the root
level. Normally, when we attempt to "bodily
expand", we find that buccal root torque in the
archwire causes the crowns to initially move in
the opposite direction we intend— that is, they
move lingually. This gets back to the old saying,
"Crown movement tends to precede root
movement". The overlay overcomes this initial
reaction by providing the necessary force at the
crown level.
78. 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.
79. Controlling Vertical Forces Intraorally
Much has been said and written about vertical
dimension and the problems involved with steep
mandibular plane angles and extrusive forces,
particularly on the molar teeth. Likewise, a
number of solutions have been offered, including
the use of various types of high pull headgear.
But little has been said in terms of controlling
vertical dimension problems by controlling
magnitudes of force intraorally in the vertical
plane of space.
80. • Whether the latter should be done may be
argued, but in my practice no high pull
headgear is used to intrude posterior teeth.
The force MAGNITUDES are controlled so that
posterior teeth are only allowed to erupt to
the extent of vertical growth within a given
patient, in which case the teeth would erupt
anyway, even without orthodontic treatment
(We are not talking about additional vertical
resulting from the overeruption of teeth due
to the forces of mechanics).
81. The Diving 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— or load/deflection
rate— is inversely proportional to the cube of
the length. Formulas of this kind often seem
confusing.
82. To make all of this useful and a little easier,
let us analyze the situation more closely. First
of all, stiffness is the amount of deflection we
get from a given load (force). 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 (fig)
83. 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.
84. If a person were to walk out only halfway on the
diving board, the board would bend or deflect a
given distance. Also, the weight (force) of the
individual standing at this halfway point times the
perpendicular distance to the point of
attachment of the board produces a moment at
the point of attachment. In orthodontics >>"critical moment", as it
is the largest moment involved and is often responsible for breakage in an archwire at that
particular point.
Load (force) on diving board produces bending moments along the board, with the
maximum moment being located closest to the point of attachment.
85. Since moments are products of force times
distance, as stated so frequently thus far, you
will notice that the moment keeps decreasing
along the diving board and finally reaches zero
directly underneath the individual (load)
standing on the board. This is because the
distance at that point is zero.
The bending moments reduce as the distance from the load decreases.
86. Now, as the load moves forward to the end of
the diving board, the critical moment doubles
due to the fact that the distance has doubled.
The load is still the same, but force times twice the
original distance produces twice the moment (critical
moment). Again, note that the individual produces only a
pure force acting through the point at which the load is
positioned.
87. Cantilever Principle
What we have just discussed is known as a
cantilever system, characterized by a pure force
acting at one end, and an equal and opposite force
at the other end accompanied by a moment. We
can utilize this system in orthodontics and make
modifications for practical purposes. The pure
force can be used for overbite correction while the
differential torque can be utilized for intraoral
anchorage control. The latter and its application
will be discussed later.
88. To demonstrate the relationship of wire length to
load/deflection (stiffness), fabricate a rectangular
segment of wire with a tipback bend. This visual
demonstration should help you to remember the
significance of "bypassing" teeth as one dramatic means
of controlling force levels.
A. With the sectional arch inserted in a molar tube on a typodont, measure the force necessary
to raise the wire to bracket level at the anterior end. B. Move the measuring device half the
distance to the molar and note the force measurement now needed.
89. Constant Load versus Constant Deflection
To seek an exact force level requires varying the deflection of
the archwire (Fig. 1). This means that 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) (Fig. 2).
Fig. 1 Fig. 2
90. With all of this in mind, the auther prefer the application
of constant bends (angular) because they are easy to do,
readily reproducible, intraorally activated (light wires
only), and offer low force ranges when the orthodontist is
familiar with the "by-pass" approach to force control. It is
necessary to get rid of the idea that "light" wires, by
themselves, produce "light" forces. As we know, small
interbracket distances can produce very high magnitudes
of force with the so called "light wires". Bypassing teeth is
one method of increasing interbracket distance.
Individuals often use single wing brackets for this purpose,
but when all teeth are banded all of the time and an
archwire engaged in every bracket automatically, there is
little alternative for reducing force levels.
91. In short, constant bends are VERY practical,
easy, useful, and effective— IF the operator
understands the various principles governing
"force control". Although the range of force
levels will be broad, the entire range can be
maintained at a very low level.
92. Clinical Application of the Diving
Board Concept (cantilever principle)
If the tipback activation is constant, such as a 45° angle, then
as the distance doubles, so does the deflection (Fig. ).
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. With wire sizes of .016, the
magnitudes at times become so low, you wonder if
"anything" will happen with the overbite. It is common to
have forces in the range of 20-30 grams and lower.
93. If we apply a total force on an incisor segment
of 30 grams (intrusion), for example, we
produce equal and opposite forces on the
molars. But, one-half goes to each molar,
meaning that each molar in this example
would incur only 7½ grams of force— enough
to allow the molars to erupt during vertical
growth, but not enough to overcome the
forces of occlusion.
94. Affect on Forces and Moments
Because the anterior-posterior arch length
varies from patient to patient, when bicuspids
and cuspids are bypassed the length becomes a
variable and, thus, so do the magnitudes of the
intrusive and extrusive forces at each end of the
archwire, which we have already seen to be
greatly affected by changes in wire length.
However, the entire range of force is so low that
low magnitudes of force may pose a greater
problem than attaining higher levels of force. In
fact, it may even require going to archwires of
greater diameter to produce a required force and
desirable response.
95. The moment on the molars, however, cannot
be ignored, as it is possible to tip back molars
undesirably, if not cautious. Be careful not to
use too large a tipback bend (angle), as this in
combination with duration (time) of use can
result in excessive tipback of the molar teeth.
However, if molars are tipped back without
the use of forces that cause such teeth to
"overerupt“.
96. Pure Force
A pure force will not occur if the design of the
archwires is improper. In a case where only the
molars and incisors are banded/bonded, direct
insertion of the archwire into the incisor brackets,
following the placement of a tipback bend at the
molar area, does not produce a pure intrusive
force to the incisor teeth. Initially, the wire will
cross the lateral incisor brackets at a slight angle,
resulting in a more complex system in which
forces and moments are introduced in
combination. The exact force is unknown and in
certain cases might not even exist.
97. The cantilever in this (Fig.)-pure force- is in use with the lower
arch. An anterior segment has been placed with an archwire
overlay containing a tipback bend. But the upper archwire has
been inserted directly into the incisor brackets and, as a result, a
pure force is no longer introduced at the bracket level . Instead,
intrusive forces in combination with moments are introduced
and the system is therefore not a cantilever system. Notice the
effect of the moments on the lateral incisors. This is routinely
seen when the archwire containing a tipback bend is inserted
directly into the incisor brackets. But it is practical, the forces
remain light, and the lateral incisor inclination is easily corrected
following correction of the overbite.
99. Case treated with light forces using a noncantilever
approach and bypassing bicuspids and cuspids
In addition to providing light forces, the bypassing allows
erupting teeth to adjust to their environment without direct
interference from an appliance. Again, the effect of the
moments can be seen on the lateral incisors. Remember, it
was pointed out earlier that there is a large moment
produced on the molar teeth from the tipback bend. When
the archwire is tied securely to the molar tubes, this
moment tends to tip all of the teeth distally, as they are
forced to "follow" the molars. This "distalization" tendency
is 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.
101. Following treatment, with bands removed and
removable retainers placed, note the improvement
occurring as the distobuccal cusps of the maxillary
molars begin to "seat" themselves (Fig. ). This is a
regular occurrence when molars have been tipped
back without the use of excessive forces. Nothing
more than a 2×4 appliance (incisors and molars) was
used in this case, and it can be seen that the cuspids
still have a distal crown inclination.
Case shown after treatment
102. • remember crown movement tends to precede
root movement. So we do have an overall
advantage if we apply common sense. In fact,
in most Class II malocclusions, the molars
require some degree of tipping (uprighting) .
103. Since overbite would normally be required with the
use of a tipback bend, and since tipback bends are
sometimes desired in cases having little or no overbite
for a number of reasons— many yet to be discussed—
the intrusive components of force can be eliminated by
the use of:
1- "up and down" elastics in the anterior of the mouth.
These elastics do not erupt teeth— unless their
extrusive components exceed the intrusive
components in the archwire. When balanced properly,
the extrusive components of force from the elastics
simply cancel out the intrusive components of force
from the two archwires, upper and lower, when
tipback bends are used in both arches.
104. 2- When the tipback bend in an arch is
combined with anterior lingual root torque in
the same arch, the vertical forces will
disappear whenever each of the activations
produces equal and opposite moments (static
equilibrium).
105. a case with some interesting sidelights
• Because of the large moment produced at each molar, during
overbite correction it is not uncommon to see "distalization" of an
entire arch. Non-banded teeth, as mentioned earlier, make useful
reference points on a clinical level.
a case showing use of light forces with both a cantilevered and non-cantileveredapproach.
106. • When the archwire is tied back at the molar tubes, the incisor segment is
"forced" to follow the molars as they tip back— if the molar crowns are
allowed to tip back rather than the roots moving forward (some
combination would normally be expected). Note the position of the lower
incisors relative to the cuspids. Also note that the unbanded lower cuspids
are tipping distally quite significantly during the overbite correction. At the
same time, teeth are erupting nicely.
107. It was seen that partial appliances offer many distinct
advantages over full appliances. This is not to say that
full appliances cannot be utilized near the end of
treatment but rather to point out that many effective
tooth movements can be achieved in the earlier stages
of treatment which would not be achieved if a full
appliance were introduced at the initiation of
orthodontic treatment.
108. Distalization With Differential Torque
• 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". We have observed the
"rowboat effect", which is the tendency for the
maxillary teeth to move forward during anterior
lingual root torque
109. 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
Reversing the mechanics results in distalization.
110. 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.
Rectangular wire with anterior lingual root torque will produce that movement when
engaged in molar tube
111. 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.
112. 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. An .016 wire in an .022 × .028 slot is obviously
a "loose" fit, but as you will see in time, the slots need
not be filled. Now, when this wire with tipbacks is
inserted into the molar tubes and then engaged into the
incisor brackets, mesial root torque will be produced on
the molars. But since crown movement tends to precede
root movement, there is a tendency for distal crown
movement. If the archwire is tied to the molar tubes,
there is a distalization tendency for the entire upper
arch, although teeth do not tend to move distally with
the same ease as they seem to move mesially or labially.
113. 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.
First molars are tipped back without
impacting second molars.
114. If the first molars are allowed to extrude as
they tip back, they will literally be lifted and
tipped back over the second molar crowns. If
the teeth are not permitted to extrude, they
will tip ack and literally push the unerupted
second molar even further back.
115. To give you an idea of how easy it is to
increase extrusive forces without even
realizing it, think of this. The stiffness
(load/deflection rate) of an .016 square wire is
nearly twice that of an .016 round wire. Labial
root torque increases anterior intrusive forces
and therefore increases molar extrusion.
Remember that lingual root torque increases
incisor eruption and molar intrusion? Labial
root torque is simply the opposite.
116. • Note here that the unerupted second molars not only were
not impacted, but were pushed back due to the large
moment (distal crown torque) on the molars and erupted in
a tipped-back configuration. Also, note that the unbanded
bicuspids and cuspids have tipped back dramatically,
relative to mandibular plane. This clearly indicates the
direction of thrust resulting from the differential torque.
Extreme tipback of first molars did not impact second molars.
117. • It is true that an intrusive force with round wire produces
labial crown torque (lingual root torque) on the incisors, but
with the archwire tied back, the molar moments are not only
in control, but will cause the incisor crowns to maintain their
anterior-posterior position or retract. Instead of seeing flared
incisors, the opposite effect is experienced. In fact, more
often than not, correction of a deep overbite in this manner
(2 × 4) results in a flattening of the incisors rather than
flaring. In spite of an excessive tipback, Figure shows that the
molars returned to a level position following appliance
removal. I have not yet failed to see this occur.
118. • many patients can be included in nonextraction
treatment if you could simply gain another 1½
to 2 millimeters of space in each quadrant(Fig. )
. Since differential torque can do this,
particularly where molars require some
uprighting, the combination of "E" space with
that gained mechanically is significant.
119. • The space opening that was created with the
tipback bend in the cases shown was
accomplished by gradually increasing the
length of the archwires. As clinical evidence
showed the tipback effects, the tie-back loops
were gradually unrolled or unwound, which
caused the archwire to become longer and
accommodate the additional arch length.
Space gain through differential torque in an adult.
120. Class II Correction Without Headgear or Elastics
• It is important to understand that the Class II
correction is coincidental during overbite
correction. This is not a means of eliminating
headgear or elastics. The simple fact is that
where headgear is planned, you will be
surprised, many times, to find that the
amount of headgear treatment originally
planned is either reduced, some times
dramatically, or even eliminated.
121. • The first case (Figure) is a girl who exhibited
what I refer to as a "Super" Class II or
"Double“ Class II malocclusion. Since the Class
II malocclusion involves a significant degree of
tipping and the overbite is extremely deep,
the auther considered this the ideal type of
case to use differential torque with a tipback
bend.
122. • Headgear treatment was instituted prior to
the conclusion of treatment, but substantial
progress was achieved prior to the use of any
headgear or elastics (Fig.). You won't see this
type of case very frequently, but when much
molar uprighting is required in such a case, be
ready for a welcome surprise.
Progress on case shown , prior to use of headgear or elastics.
123. • Also interesting is the fact that tipback bends
were used in both arches, and still Class II
correction occurred (Fig.). Movement is
usually more responsive in the maxillary arch,
although in this case much of the upper
movement only required tipping (uprighting).
Class II correction occurred using tipback bends in both arches.
124. • For the benefit of the few remaining doubters,
incisors can be intruded as evidenced in this
Figure . The reciprocal teeth during incisor
intrusion are the molars. Therefore, the
unbanded cuspids provide good clinical clues
as to what is happening.
Incisor intrusion on case
125. • shows a girl with a 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.
126. The lower arch was reasonably satisfactory, so only
upper incisors and molars were banded and the case
treated with an .016 archwire (upper 2 x 4 appliance
only )with a tipback bend. Anterior alignment in itself
following treatment
127. Case with Class II division 2 malocclusion> In this case , no headgear or elastics were ever used
Case following overbite correction.
128. • This case is shown to demonstrate, on a
clinical level, the tipping back of incisor crowns
with this force system, as opposed to the labial
flaring seen in the traditional full strapup with
the use of an archwire containing a reverse
curve of Spee.
The Case a year after appliance removal.
129. • With a reverse curve of Spee, the incisors do flare, but
the force system is not the same as that of
• a tipback. There is no differential torque and, thus, the
intrusive force acting through the incisor
• brackets produces labial crown torque on the incisor
segment with resultant flaring. With the
• tipback, this anterior torque is "overwhelmed" by the
molar moment, and the molars are favorites to
• win the "Tug of War" that follows.
130. Summary
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. As in any treatment with round wire, the
other effects must be guarded against as discussed
earlier in this series.
131. Wire/Bracket Relationships
• 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
Various angular wire/bracket relationships.
132. • We cannot eliminate "common sense":
however, since identical force systems can
produce different responses due to the
biologic nature of the environment. Teeth
extrude more readily than they intrude.
Certain rotations occur more easily than
others in different planes of space.
133. It seems appropriate at this time to go into a greater
degree of "exactness" . For, if we can understand what is
exact, we can then deviate from exactness and begin to
know the value of applying the same principles in
"nonexact" terms, in order to achieve our objectives in a
practical way. In other words, we will avoid producing a
complex appliance to satisfy academic needs. Instead,
we will keep the appliance simple and "read" the
relationships involved adjacent to the archwire bends as
though only two teeth were involved. "practicality", let
us not get lost with details that do not pose a "clinical"
threat. If you will read an article titled, "Force Systems
from an Ideal Arch" by Burstone and Koenig (AJO, March
1974), you will appreciate the true complexity of force
systems in orthodontics. At the same time, I think you
will want to utilize what you can in an efficient and
simple manner
134. Basically, we deal with various wire/bracket
relationships created by the malocclusion,
archwire bends, or both. For practical reasons,
I prefer 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.
135. Let us consider the variations. If we begin by
using a constant interbracket width (any
width) and a center bend, it can be seen in
Figure1 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.I prefer aligning the brackets and
then determining my own systems by placing
the bends where needed.
The same wire/bracket relationship can be created by a bend in the wire or a straight wire in
relation to a malocclusion.
136. Look at the next Figure2 , 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 3 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.
Fig.2 Fig.3
137. everything that lies between the relationships
in Figures 1and 3 is merely a transitioning of
force systems. Dr.Charles Burstone referred to
Figure 1 as a symmetric bend relationship. I
have adopted the term center bend or gable
bend. He referred to Figure 2 as an asymmetric
bend and Figure 3 as a step relationship. I refer
to the asymmetric bend as an off-center bend.
If we can see what forces and moments MUST
exist in the two extremes under discussion (Figs.
1 and 3), then we can accept the systems that
exist "in between".
138. 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— by applying the requirements
for static equilibrium. Once we can prove
these systems are present, by necessity, we
can resume our discussion of mechanics on a
practical level. But it is only fair that you see,
first, what occurs technically.
139. Looking at Figure 4, a center bend, we can see that
forces must be applied at four separate points for
wire/bracket engagement. Since three requirements
(previously discussed) MUST be met and ARE met to
establish the static equilibrium that will and DOES
exist, we can go through each step in order. Let us
start by "assuming" all four forces are equal. We
don't know, yet, if they are, but we must start
somewhere. Only when all three requirements of
static equilibrium are met, will we have discovered
what the actual forces are. We are not interested in
any actual figures, but only relative magnitudes.
Figure 4,
140. If all four forces (activational) are equal, then
the first requirement for static equilibrium is
fulfilled. That is, the sum of the vertical forces
must equal zero. Since there are no horizontal
forces necessary to engage the wire into the
brackets, the second requirement is
automatically fulfilled. That is, the sum of the
horizontal forces must equal zero. Since the
third requirement says that the sum of all the
moments, measured from ANY point must also
equal zero, let us choose the center point for
convenience.
141. Now we will determine the moments produced around
this point by each force (line of force) acting at a
perpendicular distance to such point. 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. Therefore, we have met all three requirements for
static equilibrium, and the orginally "assumed" forces are
proven to be correct. So, we can now determine the
activational force system at each bracket.
142. Since Forces A and B produce a couple (pure moment)
which is clockwise, and since Forces C and D produce a
counterclockwise couple (Fig. 5 A), we have now
arrived at the net activational force system— two
moments, equal and opposite in magnitude. Tooth
movement occurs as the result of deactivation, as in
(Figure 5 B). From now on we can refer to this system
when we discuss the center bend and know that it
must exist in order to conform with the requirements
of static equilibrium.
Figure 5
143. Step Bend Force System
we will go through the same analysis, again using
aligned brackets with the bends placed in the wire (Fig.
6 A). Since we must start somewhere, we will 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. All that remains now is to determine
that all the moments produced around a common
point also equal zero, the third and final requirement.
Fig.6
144. 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.
145. Figure 6 B shows the ONLY system that meets all
three requirements. First, 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. But, 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. The important thing to
realize is that the net activational forces at each bracket
are unequal, unlike the center bend.
146. we can analyze the individual brackets for the
net activational force system. Forces A and B
produce a clockwise moment at the left bracket
and a net force, as shown in Fig. 7 A. At the right
bracket, Forces C and D form a clockwise moment
also, with the magnitudes being the same, as well
as a net force equal and opposite to the force at
the left bracket. Now that the net activational
system has been determined at each bracket,
simple reversal (Fig. 7 B) gives the force system
acting on the teeth (deactivation).
Fig. 7
147. Clinical Demonstrations
If you look ONLY at the two teeth mentioned, Figure 8
illustrates various center bend relationships produced
by the malocclusion itself. Anterior-posterior
relationship must also be considered, as demonstrated
in Figure 8 with full wire/bracket engagement, such as
with a rectangular wire.
Figure 8 Various center bend relationships produced by malocclusions.
148. • Figure 9 illustrates step relationships when
applying the same approach. The single off-
center bend (as opposed to the step bend
which actually contains two off-center bends)
has already been demonstrated many times.
Figure 9 Various step bend relationships produced by malocclusions.
149. Figure 10 shows a rotated central incisor. A wire
tied only into the two central incisors would
automatically create the off-center relationship.
But, to keep matters simple, all of the relationships
mentioned and formed by the malocclusion are, for
the most part, disregarded in obtaining INITIAL
bracket alignment. In some cases, however, it would
be foolish to disregard them.
Fig. 10 A wire tied into rotated central Incisors would create off-center relationship.
150. The force system in the single off-center bend
lies somewhere in between the center bend and
step relationships, depending on the EXACT
wire/bracket angular relationship (Fig. 11). In
spite of the fact that using a constant bend, as
already discussed, with variable interbracket
distances produces moments that vary, as seen in
Figure 11 B, the complication is taken out of it by
utilizing the differential in the system, as
demonstrated with use of the tipback bend in
overbite correction.
Fig. 11
