The Role of Friction in Orthodontic Appliances










CHAPTER
“Smooth shapes are very rare in the wild but extremely important in the
ivory tower and the factory.”
— Benoit Mandelbrot
“The gem cannot be polished without friction, nor man perfected without trials.”
— Confucius
“We have got onto slippery ice where there is no friction and so in a certain sense
the conditions are ideal, but also, just because of that, we are unable to walk.
We want to walk so we need friction!”
— Ludwig Wittgenstein
“Simplicity is the ultimate sophistication.”
— Leonardo da Vinci
OVERVIEW
The Role of
Friction in
Orthodontic
Appliances
19
Because frictional forces are part of any orthodontic force system, friction must be both studied
and understood. In a continuous arch, wires continually slide through bracket slots, which produce
frictional forces. Frictional forces act parallel to the long axis of a wire and are produced by normal
forces at 90 degrees to the wire. Some frictional force is produced by the tying mechanism, but
most is associated with normal forces that are needed for tooth movement: labial and lingual, oc-
clusal or apical, or various moments and torques. Fundamental classic equations govern the deter-
mination of frictional force. Frictional force equals the coefcient of friction times the normal
force. Classic theory, although limited in the real world, is a good introduction for the clinician.
Frictional force varies during canine retraction. Four stages can be described, from tipping to root
movement. The frictional force is different in all stages, with the smallest during tipping. For forc-
es alone, friction is independent of bracket width. For moments used to prevent canine tipping
and rotation, the wider the bracket width, the lower the friction. Many biologic considerations
will inuence friction, including root length. The role of vibratory motion to reduce friction is also
discussed in this chapter. Friction can be both good and bad clinically, but the biggest problem
with friction is that it is unknown. If known, many times it can be overridden.
453
453

19
The Role of Friction in Orthodontic Appliances
454
There has been an increasing interest in under-
standing and controlling friction during the use of
orthodontic appliances. Frictional forces can oper-
ate along with active tooth-moving forces or from
the restraint of the tying mechanism. Friction can be
both good and bad. It is the intent of this chapter
to delineate the role of friction on a scientic ba-
sis so that the clinician can optimize treatment and
better evaluate the utility of so-called low-friction
brackets and wires. Understanding friction can help
us select a new appliance or improve our use of an
existing appliance system. It determines in part the
efciency of tooth movement and anchorage, and
it is a factor in eliminating undesirable side effects.
Moreover, understanding friction can help to reduce
commercialism in the marketing of appliances and
techniques.
Frictional Forces, Their Origin,
and Classic Formulas
If a force is applied to a canine from a chain elastic
or a coil spring (Fig 19-1), the tooth will not feel the
full force if there is friction in the appliance. What
the tooth feels is the effective force (F
E
), not the ap-
plied force (F
A
):
F
E
= F
A
Frictional force (F
F
)
When the frictional force is the same as the applied
force, the tooth will feel no force from the spring.
As long as there is frictional force, effective force is
always less than the applied force. Of course, it is
the effective force that is relevant for the clinician.
Tooth movement is an intermittent start-and-stop
phenomenon; hence, we are interested in static fric-
tion. Measurement of friction along moving surfac-
es (dynamic or kinetic friction) will give somewhat
smaller values. Rolling friction involves wheels and
is not relevant to our appliances.
Where do frictional forces come from? The nature
of friction is still being debated between adhesion
and interlocking theory, even among modern phys-
icists; however, classic friction theory tells us that
forces perpendicular to the archwire are responsi-
ble for friction. Figure 19-2a shows a canine sliding
along an archwire. For simplicity, all moments are
ignored. The applied force (F
A
) is 100 g. F
N
is a nor-
Fig 19-1 If a force is applied to a tooth, the tooth will not feel the
applied force (F
A
) if there is friction (F
F
) in the appliance. What the
tooth feels is the effective force (F
E
).
Fig 19-2 (a) In classic friction theory, the friction is calculated from the coefcient of friction (µ) and normal forces (F
N
) perpendicular to the
archwire: frictional force (F
F
) = coefcient of friction (µ) × normal force (F
N
). (b) The bracket is pushing on the wire in an occlusal direction
with an equal and opposite magnitude according to Newton’s Third Law.
a b

455
Frictional Forces, Their Origin, and Classic Formulas
mal force perpendicular to the wire; the bracket is
pushing on the wire in an occlusal direction, and,
according to Newton’s Third Law, an equal and op-
posite force is pushing on the bracket (Fig 19-2b).
The classic law of friction is also known as Amon-
tons-Coloumb Law and is very simple:
F
F
= Coefcient of friction (µ) × Normal force (F
N
)
There are no terms in the formula regarding the
amount of contact area, duration of contact, tem-
perature, or sliding speed. The coefcient of friction
is not an inherent property of a material, such as
modulus of elasticity. It is a dimensionless property
that represents the amount of friction between two
materials and is determined by experiment only and
not by theory. If the material used at the interface
of two materials reduces the coefcient of friction,
it is called a lubricant. If it increases the coefcient
of friction, it is called an adhesive. For a stainless
steel wire and stainless steel bracket in the mouth,
an average value for the coefcient of friction (µ) is
0.16. The magnitude of normal force can be unpre-
dictable because of the many variables, including
three material interfaces that can be present: wire,
bracket, and polymeric O-ring. Suppose a 50-g nor-
mal force is applied to a bracket. The frictional force
(see Fig 19-2a) can be calculated, and the effective
distal force is 92 g.
F
F
= 50 g × 0.16 = 8 g
F
E
= 100 g – 8 g = 92 g
Figure 19-3 shows a bracket with forces acting on
it. Note that as the applied force is increased, the
frictional force increases at the same rate up to a
certain level of force called the maximum static
friction force. Frictional force increases the same
amount as the applied force but in the opposite
direction. If the applied force increases above the
maximum static friction force, the bracket will start
to move. The applied force must overcome this max-
imum frictional force for any tooth to move. The
maximum static friction force is observed just before
movement starts. If movement continues, frictional
force values decrease slightly, and so-called kinetic
friction is observed. Either static or kinetic friction
values are applicable as long as we understand that
wire-bracket interfaces are responding to static fric-
tion. Tooth movement is not continuous; rather, it is
an intermittent start-and-stop phenomenon; hence,
static friction is the most relevant for us. In this
chapter, frictional force and maximum static friction
force are used interchangeably.
Plots of frictional force versus applied force are
more irregular than that shown in Fig 19-3. The ac-
tual plot (green) in Fig 19-4a demonstrates uctuat-
ing frictional force. This is explained by the stick-slip
phenomenon, where the surfaces adhere together
and then separate (break) apart. This behavior can
explained at the microscopic level, where jagged
surfaces induce up and down motion during sliding
(Fig 19-4b).
The coefcient of friction is the lowest with stain-
less steel wires and the highest with beta-titanium
wires. Ceramic brackets have higher coefcients than
Fig 19-3 Applied force (F
A
) plotted against frictional force (F
F
). The
frictional force and applied forces are proportional up to a certain
level of force called the maximum static friction force. Frictional
force increases the same amount as the applied force but in the op-
posite direction. If the applied force increases above the maximum
static friction force, the bracket will start to move with slightly de-
creased frictional forces (kinetic friction).

19
The Role of Friction in Orthodontic Appliances
456
stainless steel, and the high variation is related to
design and manufacturing methods. It is often as-
sumed that the smoother the material, the lower is
the coefcient of friction; however, the relationship
is not so simple. The schematic graph in Fig 19-5
shows that at the extremes, high- and low-roughness
materials have high coefcients of friction. It is well
known that highly polished surfaces show very high
coefcients of friction, which is well understood by
adhesion theory at the ultramicroscopic level. Only
at intermediate roughness does a good correlation
exist between roughness and coefcient of friction.
Fig 19-4 (a) The actual plot from experimental data (green) demonstrates uctuating frictional force. The average of the data is the red
curve. (b) The uctuating curve in part a is better understood with interlocking theory at the microscopic level, where jagged surfaces must
slide past each other.
Fig 19-5 The schematic graph shows that at the extremes, both
rough and highly smooth materials have high coefcients of fric-
tion. This phenomenon is well understood by adhesion theory at
the ultramicroscopic level. In the intermediate roughness, a good
correlation exists between roughness and coefcient of friction.
Fig 19-6 If the forces are high, destructive changes can
occur in either the bracket or the wire, and the subse-
quent behavior will not follow classic friction theory.
Fig 19-7 Ion impregnation by nitrogen bombarding on
beta-titanium wire increases the hardness and reduces
the coefcient of friction of a wire.
a b
Stick-slip
phenomenon
Displacement
Frictional force

457
Source of Normal Forces
Hardness is typically related to a low coefcient;
nevertheless, Teon is a soft material, and yet its co-
efcient of friction is low.
The classic formulas presented in this chapter only
operate within reasonable ranges of perpendicular
forces. If the forces are high, destructive changes
can occur in either the bracket or the wire, chang-
ing the subsequent behavior. Examples include wire
notching, as depicted in Fig 19-6. A tipped tooth can
notch a wire, producing effects not easily predicted.
Some surface treatments, such as ion impregna-
tion by nitrogen bombarding, increase the hardness
and reduce the coefcient of friction of a wire. Fig-
ure 19-7 shows a group of beta-titanium archwires;
the various colors are produced after titanium ni-
tride particles are distributed in the wire’s surface by
ion impregnation.
Source of Normal Forces
Frictional forces are evident at all stages of ortho-
dontic treatment. They involve any mesiodistal slid-
ing between wire and bracket. This occurs not only
with purposeful sliding mechanics such as canine re-
traction but also in alignment arches where, if the
wire cannot slide, buccal or lingual forces can be
attenuated. Friction can also be employed to open
space in cases of arch length discrepancies. Not all
friction is bad.
Forces perpendicular to the wire can come from
a number of sources and in any direction: buccal,
lingual, occlusal, or apical (Fig 19-8). The O-ring pro-
duces a lingual force in Fig 19-9 that can lead to a
frictional force. Thus, the ligation method is only
one source of friction. Any other forces required for
tooth movement, if perpendicular to the archwire,
can also lead to friction and in many situations can
produce much more friction than the ligature tie.
Of particular importance are forces originating
from pure moments or couples. By denition, cou-
ples are equal and opposite forces not in the same
line of action. Normal forces exist on the wire, al-
though the sum of the forces is zero (Fig 19-10). Mo-
ments are used in a rst-order direction to rotate
teeth, in a second-order direction to change axial
mesiodistal inclinations, and in a third-order direc-
tion to change buccolingual axial inclinations. A mo-
ment (couple) at the bracket is required to give an
equivalent force system for full control of a tooth.
This moment is one major source of friction with the
edgewise appliance. Some brackets are designed
to allow a tooth to tip or rotate. With this type of
bracket, this source of friction can be eliminated,
but control of tooth movement is lost as a result.
Sometimes we hear the phrase “friction-free
brackets.” These brackets use a locking cap mecha-
nism instead of a ligature tie. But is “friction free”
possible under typical clinical conditions? These
brackets, when placed on a wire, slide easily because
no normal forces from ligation or moments from
the bracket are present. In Fig 19-11, a low-friction
self-ligating bracket has been used to rotate a sec-
ond premolar. The ideal-shaped frictionless archwire
will produce approximately a couple that should
rotate the premolar around its center of resistance
(CR), near the center of the crown. However, a fric-
tional force operates at the distal of the bracket
in a mesial direction (Fig 19-11a). Notice that the
frictional force produced a side effect that opened
Fig 19-8 The normal force can come
from a number of sources and in any
direction: buccal, lingual, occlusal, or
apical.
Fig 19-9 In the passive wire, the
O-ring produces a lingual force that
can lead to a frictional force. Thus, the
ligation method is only one source of
friction.
Fig 19-10 Of particular importance are forces origi-
nating from pure moments or couples. Normal forces
exist on the wire in three dimensions.
F
N

19
The Role of Friction in Orthodontic Appliances
458
up space and that the crown moved mesially (Fig
19-11b). This demonstrates once again that other
frictional forces operate beyond the ligation mech-
anism. In other words, we should be careful in us-
ing the terms friction-free or frictionless brackets to
describe actual clinical situations. In most clinical sit-
uations, the archwire will deliver normal forces and
moments to the teeth to produce tooth movement;
the reactive perpendicular forces on the wire are a
major source of friction, not just the ligature tie.
Some orthodontists differentiate between simple
normal forces and normal forces from couples. Clas-
sical friction theory allows couples to be handled
like any other forces. Terms such as binding should
not be used to suggest a different theoretical mech-
anism at work in the situation where a tipping mo-
ment or torque is applied.
Canine Retraction
An in-depth consideration of canine retraction us-
ing sliding mechanics provides the opportunity to
develop how friction works with a major treatment
phase. Without a wire for control, a distal force on
a canine produces well-known side effects. The ca-
nine rotates distal in, and the crown tips distally. To
prevent the unwanted effects, an archwire can be
placed; the archwire elastically deforms and, during
recovery, prevents or minimizes the rotation and tip-
ping by exerting couples on the teeth (Figs 19-12a and
19-12b). Figures 19-12c and 19-12d show the same
diagram with the couples (curved arrows) replaced
by two normal forces to further show the origin of
the frictional force. In Fig 19-13, as the tooth tips
distally, energy is stored in the wire, and the wire
curves. As the curved wire straightens out, normal
forces control tooth movement and prevent tipping.
The same forces and moments that give control also
give frictional forces as these normal forces act on
the wire. In short, no friction during sliding mechan-
ics means no control.
The “control” couples will vary depending on what
is required. The yellow arrow in Fig 19-14a is the
location of the force if translation is the objective.
An equivalent force system at the bracket requires
large equal and opposite vertical forces (a couple).
This is contrasted in Fig 19-14b with a tipping move-
ment around the apex (as the center of rotation),
where the needed moment is much smaller. Because
the control moment is smaller, there will be less fric-
tion during tipping than during translation.
To gure out how much frictional force occurs
during canine retraction, we must consider the
phase of canine retraction as evaluated from both
the facial and occlusal views. Four phases can be
recognized (Fig 19-15). After a distal force is placed,
the canine may have play between the wire and
the bracket, and initially the tooth will display un-
controlled tipping. This is phase I. No moments or
normal forces operate in this plane. For now, liga-
tion forces are ignored. The tooth continues to tip
more, and the play is eliminated. Increasing mo-
ments are created by the elastically deformed wire,
and a controlled tipping phase is produced (phase
II). Perhaps we have a tipping center of rotation at
the apex. Note that normal forces are produced in
phase II as the tipping is being minimized, but only
low levels of friction are produced. When the tooth
tips some more and a sufciently high moment is
delivered by the wire, translation occurs (phase III).
The greatest frictional forces are produced during
Fig 19-11 (a) Even in a low-friction self-ligating bracket, frictional
force operates at the distal of the bracket in a mesial direction. (b)
The frictional force produced a side effect that opened up space,
and the crown moved mesially. In clinical situations, forces on the
wire are a major source of friction, not just the ligature tie.
a b

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CHAPTER “Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory.” — Benoit Mandelbrot“The gem cannot be polished without friction, nor man perfected without trials.” — Confucius“We have got onto slippery ice where there is no friction and so in a certain sense the conditions are ideal, but also, just because of that, we are unable to walk. We want to walk so we need friction!” — Ludwig Wittgenstein“Simplicity is the ultimate sophistication.” — Leonardo da VinciOVERVIEWThe Role of Friction in Orthodontic Appliances 19Because frictional forces are part of any orthodontic force system, friction must be both studied and understood. In a continuous arch, wires continually slide through bracket slots, which produce frictional forces. Frictional forces act parallel to the long axis of a wire and are produced by normal forces at 90 degrees to the wire. Some frictional force is produced by the tying mechanism, but most is associated with normal forces that are needed for tooth movement: labial and lingual, oc-clusal or apical, or various moments and torques. Fundamental classic equations govern the deter-mination of frictional force. Frictional force equals the coefcient of friction times the normal force. Classic theory, although limited in the real world, is a good introduction for the clinician. Frictional force varies during canine retraction. Four stages can be described, from tipping to root movement. The frictional force is different in all stages, with the smallest during tipping. For forc-es alone, friction is independent of bracket width. For moments used to prevent canine tipping and rotation, the wider the bracket width, the lower the friction. Many biologic considerations will inuence friction, including root length. The role of vibratory motion to reduce friction is also discussed in this chapter. Friction can be both good and bad clinically, but the biggest problem with friction is that it is unknown. If known, many times it can be overridden.453453 19The Role of Friction in Orthodontic Appliances454There has been an increasing interest in under-standing and controlling friction during the use of orthodontic appliances. Frictional forces can oper-ate along with active tooth-moving forces or from the restraint of the tying mechanism. Friction can be both good and bad. It is the intent of this chapter to delineate the role of friction on a scientic ba-sis so that the clinician can optimize treatment and better evaluate the utility of so-called low-friction brackets and wires. Understanding friction can help us select a new appliance or improve our use of an existing appliance system. It determines in part the efciency of tooth movement and anchorage, and it is a factor in eliminating undesirable side effects. Moreover, understanding friction can help to reduce commercialism in the marketing of appliances and techniques.Frictional Forces, Their Origin, and Classic FormulasIf a force is applied to a canine from a chain elastic or a coil spring (Fig 19-1), the tooth will not feel the full force if there is friction in the appliance. What the tooth feels is the effective force (FE), not the ap-plied force (FA):FE = FA – Frictional force (FF)When the frictional force is the same as the applied force, the tooth will feel no force from the spring. As long as there is frictional force, effective force is always less than the applied force. Of course, it is the effective force that is relevant for the clinician.Tooth movement is an intermittent start-and-stop phenomenon; hence, we are interested in static fric-tion. Measurement of friction along moving surfac-es (dynamic or kinetic friction) will give somewhat smaller values. Rolling friction involves wheels and is not relevant to our appliances.Where do frictional forces come from? The nature of friction is still being debated between adhesion and interlocking theory, even among modern phys-icists; however, classic friction theory tells us that forces perpendicular to the archwire are responsi-ble for friction. Figure 19-2a shows a canine sliding along an archwire. For simplicity, all moments are ignored. The applied force (FA) is 100 g. FN is a nor-Fig 19-1 If a force is applied to a tooth, the tooth will not feel the applied force (FA) if there is friction (FF) in the appliance. What the tooth feels is the effective force (FE).Fig 19-2 (a) In classic friction theory, the friction is calculated from the coefcient of friction (µ) and normal forces (FN) perpendicular to the archwire: frictional force (FF) = coefcient of friction (µ) × normal force (FN). (b) The bracket is pushing on the wire in an occlusal direction with an equal and opposite magnitude according to Newton’s Third Law.a b 455Frictional Forces, Their Origin, and Classic Formulasmal force perpendicular to the wire; the bracket is pushing on the wire in an occlusal direction, and, according to Newton’s Third Law, an equal and op-posite force is pushing on the bracket (Fig 19-2b). The classic law of friction is also known as Amon-tons-Coloumb Law and is very simple:FF = Coefcient of friction (µ) × Normal force (FN)There are no terms in the formula regarding the amount of contact area, duration of contact, tem-perature, or sliding speed. The coefcient of friction is not an inherent property of a material, such as modulus of elasticity. It is a dimensionless property that represents the amount of friction between two materials and is determined by experiment only and not by theory. If the material used at the interface of two materials reduces the coefcient of friction, it is called a lubricant. If it increases the coefcient of friction, it is called an adhesive. For a stainless steel wire and stainless steel bracket in the mouth, an average value for the coefcient of friction (µ) is 0.16. The magnitude of normal force can be unpre-dictable because of the many variables, including three material interfaces that can be present: wire, bracket, and polymeric O-ring. Suppose a 50-g nor-mal force is applied to a bracket. The frictional force (see Fig 19-2a) can be calculated, and the effective distal force is 92 g. FF = 50 g × 0.16 = 8 gFE = 100 g – 8 g = 92 gFigure 19-3 shows a bracket with forces acting on it. Note that as the applied force is increased, the frictional force increases at the same rate up to a certain level of force called the maximum static friction force. Frictional force increases the same amount as the applied force but in the opposite direction. If the applied force increases above the maximum static friction force, the bracket will start to move. The applied force must overcome this max-imum frictional force for any tooth to move. The maximum static friction force is observed just before movement starts. If movement continues, frictional force values decrease slightly, and so-called kinetic friction is observed. Either static or kinetic friction values are applicable as long as we understand that wire-bracket interfaces are responding to static fric-tion. Tooth movement is not continuous; rather, it is an intermittent start-and-stop phenomenon; hence, static friction is the most relevant for us. In this chapter, frictional force and maximum static friction force are used interchangeably.Plots of frictional force versus applied force are more irregular than that shown in Fig 19-3. The ac-tual plot (green) in Fig 19-4a demonstrates uctuat-ing frictional force. This is explained by the stick-slip phenomenon, where the surfaces adhere together and then separate (break) apart. This behavior can explained at the microscopic level, where jagged surfaces induce up and down motion during sliding (Fig 19-4b).The coefcient of friction is the lowest with stain-less steel wires and the highest with beta-titanium wires. Ceramic brackets have higher coefcients than Fig 19-3 Applied force (FA) plotted against frictional force (FF). The frictional force and applied forces are proportional up to a certain level of force called the maximum static friction force. Frictional force increases the same amount as the applied force but in the op-posite direction. If the applied force increases above the maximum static friction force, the bracket will start to move with slightly de-creased frictional forces (kinetic friction). 19The Role of Friction in Orthodontic Appliances456stainless steel, and the high variation is related to design and manufacturing methods. It is often as-sumed that the smoother the material, the lower is the coefcient of friction; however, the relationship is not so simple. The schematic graph in Fig 19-5 shows that at the extremes, high- and low-roughness materials have high coefcients of friction. It is well known that highly polished surfaces show very high coefcients of friction, which is well understood by adhesion theory at the ultramicroscopic level. Only at intermediate roughness does a good correlation exist between roughness and coefcient of friction. Fig 19-4 (a) The actual plot from experimental data (green) demonstrates uctuating frictional force. The average of the data is the red curve. (b) The uctuating curve in part a is better understood with interlocking theory at the microscopic level, where jagged surfaces must slide past each other.Fig 19-5 The schematic graph shows that at the extremes, both rough and highly smooth materials have high coefcients of fric-tion. This phenomenon is well understood by adhesion theory at the ultramicroscopic level. In the intermediate roughness, a good correlation exists between roughness and coefcient of friction.Fig 19-6 If the forces are high, destructive changes can occur in either the bracket or the wire, and the subse-quent behavior will not follow classic friction theory.Fig 19-7 Ion impregnation by nitrogen bombarding on beta-titanium wire increases the hardness and reduces the coefcient of friction of a wire.a bStick-slipphenomenonDisplacementFrictional force 457Source of Normal ForcesHardness is typically related to a low coefcient; nevertheless, Teon is a soft material, and yet its co-efcient of friction is low.The classic formulas presented in this chapter only operate within reasonable ranges of perpendicular forces. If the forces are high, destructive changes can occur in either the bracket or the wire, chang-ing the subsequent behavior. Examples include wire notching, as depicted in Fig 19-6. A tipped tooth can notch a wire, producing effects not easily predicted.Some surface treatments, such as ion impregna-tion by nitrogen bombarding, increase the hardness and reduce the coefcient of friction of a wire. Fig-ure 19-7 shows a group of beta-titanium archwires; the various colors are produced after titanium ni-tride particles are distributed in the wire’s surface by ion impregnation.Source of Normal ForcesFrictional forces are evident at all stages of ortho-dontic treatment. They involve any mesiodistal slid-ing between wire and bracket. This occurs not only with purposeful sliding mechanics such as canine re-traction but also in alignment arches where, if the wire cannot slide, buccal or lingual forces can be attenuated. Friction can also be employed to open space in cases of arch length discrepancies. Not all friction is bad.Forces perpendicular to the wire can come from a number of sources and in any direction: buccal, lingual, occlusal, or apical (Fig 19-8). The O-ring pro-duces a lingual force in Fig 19-9 that can lead to a frictional force. Thus, the ligation method is only one source of friction. Any other forces required for tooth movement, if perpendicular to the archwire, can also lead to friction and in many situations can produce much more friction than the ligature tie.Of particular importance are forces originating from pure moments or couples. By denition, cou-ples are equal and opposite forces not in the same line of action. Normal forces exist on the wire, al-though the sum of the forces is zero (Fig 19-10). Mo-ments are used in a rst-order direction to rotate teeth, in a second-order direction to change axial mesiodistal inclinations, and in a third-order direc-tion to change buccolingual axial inclinations. A mo-ment (couple) at the bracket is required to give an equivalent force system for full control of a tooth. This moment is one major source of friction with the edgewise appliance. Some brackets are designed to allow a tooth to tip or rotate. With this type of bracket, this source of friction can be eliminated, but control of tooth movement is lost as a result.Sometimes we hear the phrase “friction-free brackets.” These brackets use a locking cap mecha-nism instead of a ligature tie. But is “friction free” possible under typical clinical conditions? These brackets, when placed on a wire, slide easily because no normal forces from ligation or moments from the bracket are present. In Fig 19-11, a low-friction self-ligating bracket has been used to rotate a sec-ond premolar. The ideal-shaped frictionless archwire will produce approximately a couple that should rotate the premolar around its center of resistance (CR), near the center of the crown. However, a fric-tional force operates at the distal of the bracket in a mesial direction (Fig 19-11a). Notice that the frictional force produced a side effect that opened Fig 19-8 The normal force can come from a number of sources and in any direction: buccal, lingual, occlusal, or apical.Fig 19-9 In the passive wire, the O-ring produces a lingual force that can lead to a frictional force. Thus, the ligation method is only one source of friction.Fig 19-10 Of particular importance are forces origi-nating from pure moments or couples. Normal forces exist on the wire in three dimensions.FN 19The Role of Friction in Orthodontic Appliances458up space and that the crown moved mesially (Fig 19-11b). This demonstrates once again that other frictional forces operate beyond the ligation mech-anism. In other words, we should be careful in us-ing the terms friction-free or frictionless brackets to describe actual clinical situations. In most clinical sit-uations, the archwire will deliver normal forces and moments to the teeth to produce tooth movement; the reactive perpendicular forces on the wire are a major source of friction, not just the ligature tie.Some orthodontists differentiate between simple normal forces and normal forces from couples. Clas-sical friction theory allows couples to be handled like any other forces. Terms such as binding should not be used to suggest a different theoretical mech-anism at work in the situation where a tipping mo-ment or torque is applied.Canine Retraction An in-depth consideration of canine retraction us-ing sliding mechanics provides the opportunity to develop how friction works with a major treatment phase. Without a wire for control, a distal force on a canine produces well-known side effects. The ca-nine rotates distal in, and the crown tips distally. To prevent the unwanted effects, an archwire can be placed; the archwire elastically deforms and, during recovery, prevents or minimizes the rotation and tip-ping by exerting couples on the teeth (Figs 19-12a and 19-12b). Figures 19-12c and 19-12d show the same diagram with the couples (curved arrows) replaced by two normal forces to further show the origin of the frictional force. In Fig 19-13, as the tooth tips distally, energy is stored in the wire, and the wire curves. As the curved wire straightens out, normal forces control tooth movement and prevent tipping. The same forces and moments that give control also give frictional forces as these normal forces act on the wire. In short, no friction during sliding mechan-ics means no control.The “control” couples will vary depending on what is required. The yellow arrow in Fig 19-14a is the location of the force if translation is the objective. An equivalent force system at the bracket requires large equal and opposite vertical forces (a couple). This is contrasted in Fig 19-14b with a tipping move-ment around the apex (as the center of rotation), where the needed moment is much smaller. Because the control moment is smaller, there will be less fric-tion during tipping than during translation. To gure out how much frictional force occurs during canine retraction, we must consider the phase of canine retraction as evaluated from both the facial and occlusal views. Four phases can be recognized (Fig 19-15). After a distal force is placed, the canine may have play between the wire and the bracket, and initially the tooth will display un-controlled tipping. This is phase I. No moments or normal forces operate in this plane. For now, liga-tion forces are ignored. The tooth continues to tip more, and the play is eliminated. Increasing mo-ments are created by the elastically deformed wire, and a controlled tipping phase is produced (phase II). Perhaps we have a tipping center of rotation at the apex. Note that normal forces are produced in phase II as the tipping is being minimized, but only low levels of friction are produced. When the tooth tips some more and a sufciently high moment is delivered by the wire, translation occurs (phase III). The greatest frictional forces are produced during Fig 19-11 (a) Even in a low-friction self-ligating bracket, frictional force operates at the distal of the bracket in a mesial direction. (b) The frictional force produced a side effect that opened up space, and the crown moved mesially. In clinical situations, forces on the wire are a major source of friction, not just the ligature tie.a b 459Canine RetractionFig 19-12 During canine retraction, the canine rotates distal in, and the crown tips distally. The archwire elastically deforms and, during re-covery, prevents or minimizes the rotation (a) and tipping (b) by exerting couples on the teeth. (c and d) The same diagram with the couples (curved arrows in a and b) replaced by two normal forces (arrows) to further show the origin of the frictional force.Fig 19-13 As the canine tips distally, energy is stored in the wire, and the wire curves. As the curved wire straightens out, normal forces control tooth movement and prevent tipping (red arrows).a bcdFig 19-14 (a) The yellow arrow is the location of the force if translation is the objective. An equivalent force system at the bracket requires vertical forces (a couple). (b) A tipping movement around the apex (as the center of rotation), where the needed moment is smaller.a b 19The Role of Friction in Orthodontic Appliances460translation. During phase IV, as the force is reduced, no more distal sliding occurs, and the axial inclina-tion is corrected. Here, of course, there is a high fric-tional force that is acceptable because sliding is not desired at this stage (see also Fig 14-9).In short, frictional force varies depending on the stage of canine retraction: none initially with play and the highest levels during translation. Even with rigid edgewise arches, a retracted tooth will go through these four phases; however, the angle of tip will be smaller. The angle of tip during transla-tion is mainly a function of wire stiffness and the applied distal force. Clinically, it may appear that the tooth has translated in one phase. In reality, how-ever, it has rst tipped, then translated, and then nally uprighted. Ligation forces and forces in oth-er planes are considered separately in this chapter. As the bracket width decreases, the friction will in-crease because the normal force must increase to provide the same amount of moment. However, the mechanism of narrow brackets (eg, Begg bracket) is different. They produce only a single force and negligible frictional forces because they do not pre-vent tooth tipping (no control moments) and do not demonstrate phases II, III, and IV of space closure. In Begg treatment, a separate individual root spring is used for tooth uprighting during phase IV.From the facial view, frictional forces are devel-oped because the CR is apical to the bracket. In a similar evaluation from the occlusal view, the brack-et is labial to the CR and, hence, a distal force will rotate the canine distal in. The archwire prevents or minimizes canine rotation in four phases (Fig 19-16). During phase I, if play exists between the wire and the bracket, the canine is free to rotate. No wire re-straining of the rotation occurs; therefore, there is no friction in this phase in the occlusal view. During phase II, the tooth continues to rotate; however, the archwire is minimizing the rotation by elastic de-formation. Because of the restraining archwire mo-ments, friction increases and nally reaches its max-imum during phase III translation. No sliding occurs in phase IV when the rotation is being corrected.The amount of frictional force from the occlusal view depends on the perpendicular distance of the bracket to the CR. The greater this distance, the larger is the moment rotating the canine and the greater is the moment needed from the archwire to Fig 19-15 Four phases can be recognized during canine retraction (facial view). Phase I: The canine may have play between the wire and the bracket, and initially the tooth will display uncontrolled tipping. Phase II: Increasing moments are created by the elastically deformed wire, and controlled tipping occurs. Phase III: When the tooth tips some more and a sufciently high moment is delivered by the wire, translation occurs. Phase IV: The force is reduced, no more distal sliding occurs, and the axial inclination is corrected. Note that the largest moment occurs during phase III translation.Fig 19-16 In the occlusal view, the same four phases can be recog-nized during canine retraction.Fig 19-17 The amount of frictional force from the occlusal view depends on the perpendicular distance of the bracket to the CR. 461Torque and Frictionprevent this rotation (Fig 19-17). The patient in Fig 19-18a had blocked-out canines; if canine retraction were started with their initial labial positions, high friction levels would be anticipated for three rea-sons: (1) lingual and downward normal forces, (2) normal forces from the couple preventing tipping in the facial view, and (3) a moment preventing and correcting distal-in rotation of the canine. Note that the large distance from the applied force to the ca-nine CR, as observed from the occlusal view (Figs 19-18b and 19-18c), leads to an unusually large mo-ment. Because the frictional forces are additive from the facial and occlusal views, a canine abnormally ared to the buccal creates larger frictional forces than average. It is usually wise to reduce intercanine width as soon as possible before full canine retrac-tion.Torque and FrictionIt has been seen that moments associated with the prevention of tipping and rotation of a canine can lead to high frictional forces. In addition, third-order moments (ie, torque) can lead to particularly high frictional forces. Figure 19-19 compares two acti-vations on a canine; both have the same moment magnitude of 1,000 gmm, but one is in the bending mode (Fig 19-19a), and the other is in the torsion mode (Fig 19-19b).The torque produces the largest vertical force of 2,000 g because the distance is small across the wire cross section. Because the normal forces from torque are greater than those from the second-order couple, the friction will be eight times higher in torque than tipping for the same moment. (In this example, the ratio of the moment arms is 4 mm/0.5 mm = 8; hence, the normal force is eight times greater.) For this rea-son, it is not recommended to use edgewise wires that fully engage the brackets (with possible un-wanted torque) for canine retraction. The high fric-tion can potentially make for inefcient or unpre-dictable retraction. Round or undersized wires are preferable to eliminate possible unwanted torque problems.Fig 19-18 If canine retraction were started with these initial labial positions, high frictional levels would be anticipated for three reasons: lin-gual and occlusal forces (a), a couple in the facial view, and a couple preventing distal-in rotation on the canine in the occlusal view (b and c). Fig 19-19 (a) The moments associated with the prevention of tipping and rotation of a canine can lead to high frictional forces. (b) Third- order moments (ie, torque) can lead to particularly high frictional forces. Note that the same moment magnitude of 1,000 gmm requires very high normal forces for torsion.aa b cb 19The Role of Friction in Orthodontic Appliances462Fig 19-20 Methods of ligation of the wire. (a) A wire can be placed passively into a bracket by a locking mechanism. No force is ex-erted on the tooth, and the tie function is purely restraint. (b) The tie mechanism activates the wire, producing an active force for desired tooth movement. (c) After the wire is fully seated, a greater ligature tie force does not increase the force to move the tooth. This wedging causes high friction, and sometimes it can be used to keep teeth from sliding.Fig 19-21 Leonardo da Vinci’s illustration showing that the size of the contact area does not change the frictional force because the normal force (weight) does not change.Bracket Design and FrictionLet us consider two bracket design parameters: (1) method of ligation and (2) bracket width. A wire can be placed passively into a bracket, and a ligature or locking mechanism holds it in place. No force is exerted on the tooth, and the tie function is purely restraint (Fig 19-20a). In Fig 19-20b, the tie mecha-nism activates the wire, producing an active force for desired tooth movement. Displacing the ligature tie with more force will cause the wire to more fully seat in the bracket. After the wire is fully seated, a greater ligature tie force does not increase the force to move the tooth (Fig 19-20c). The added perpen-dicular force will only produce a frictional force that most likely is not required or wanted. This friction from tight ties is sometimes used to keep teeth from sliding. Normal force from metal ligature ties are dif-cult to control if predictable ligating forces are to be achieved. Elastomeric O-rings can deliver initially higher forces than a lightly tied metal ligature wire. However, elastomers will undergo degradation (or relaxation) over time, making the ligation force un-predictable; after degradation, their normal forces may be as low as some self-ligating brackets. If one only considers friction from ligation, so-called self- ligating brackets do have the advantage of more predictably delivering lighter restraining forces (forces at 90 degrees to the archwire) and, hence, lower friction. Both active and passive self-ligating systems can produce lower normal forces by ligation alone than elastomeric rings or metal ties. On the other hand, after degradation, elastomers can deliv-er low tie forces; also, some clinicians are very adept at forming light metal ties. If the frictional forces are known, they can be overridden. It should be re-membered that, during treatment, the orthodon-tist applies forces perpendicular to the arch during wire placement and that it is these forces that can produce the most friction during sliding mechan-ics; self-ligating brackets are not an exception. The same forces are required for delivering the correct force system with self-ligating brackets as with more traditional brackets; hence, friction is similar.Which bracket produces the most friction: a wide bracket or a narrow bracket during retraction? It depends on the phase of space closure. Many clini-cians believe that the size of the contact area be-tween the bracket and the wire affects the friction. Yet in the 15th century, Leonardo da Vinci correctly observed that the frictional force is proportional to the contact load and independent of the contact area. The classic friction formula states that for the same normal force, the size of the contact area does not make any difference. Therefore, the orientation of the wire or replacement of rectangular wire with round wire does not reduce the friction, provided that the restraining or active normal forces are the same. Note that in Leonardo da Vinci’s illustration (Fig 19-21), the amount of contact area does not change the frictional force because the normal force (weight) does not change. The selection of a ribbon or edgewise wire orientation must have another ra-a b c 463Is Friction Always Bad?tionale for its correct usage. Wire shape and dimen-sion can affect friction only if it alters wire stiffness.Narrow brackets may show faster tooth move-ment initially; therefore, it may be assumed to have less friction, but this concept is wrong. The tooth movement in this case is not directly related to the friction. The reason narrow brackets seem to show initial faster tooth movement during sliding me-chanics is due to the play between the bracket slot and the wire in phase I of sliding mechanics (Fig 19-22). With the same amount of play (clearance) between the bracket and the wire, the narrow bracket can tip (rotate) more during phase I of space closure. In this phase, the friction comes only from the normal force ligature mechanism. To nd the frictional force, we must use a moment (couple) that produces vertical forces. The formula isFF = µ × N = µ × 2M Wwhere FF is frictional force, N is normal force, M is moment at the bracket, and W is bracket width.Figure 19-23 compares two brackets: a narrow 2-mm bracket and a wide 4-mm bracket. Let us sup-pose both teeth need a counterclockwise moment of 1,000 gmm for translation. The narrow bracket requires equal and opposite 500-g forces (500 g × 2 mm = 1,000 gmm), and the wide bracket needs 250-g forces (250 g × 4 mm = 1,000 gmm). The nar-row bracket has twice the frictional force because the normal force is two times that of the wide bracket. Therefore, the wide bracket has less friction during phases II and III of space closure. Smaller cross-section wires may have more clear-ance between the wire and the bracket and there-fore may have an extended phase I (no friction). Also, these wires have lower wire stiffness and as-sociated lower normal forces during other phases of canine retraction. But remember that the lower friction found in small round wires is not caused by the smaller contact area.Is Friction Always Bad?Orthodontists may commonly think of friction-al forces as bad. In reality, however, they are not always bad. Let us use canine retraction as an ex-ample. In Fig 19-24, a 200-g distal force is applied along with a counterclockwise moment of 1,000 gmm. If a 5:1 moment-to-force (M/F) ratio is deliv-ered to the bracket of the canine as the applied force, it would be expected that the canine would tip back with a center of rotation approaching the apex (Fig 19-24a). Let us now calculate the friction-al forces (Fig 19-24b). The effective force is reduced to 94 g. Is this good or bad? The plan was controlled tipping with an M/F ratio of 5; however, transla-tion occurred. Not only has the force magnitude Fig 19-22 Narrow brackets may show initial faster tooth move-ment than wide brackets, but that does not mean they have less friction. The quicker tooth movement is due to the play between the bracket slot and the wire during phase I of sliding mechanics. The narrow bracket (a) tips more than the wide bracket (b) because of the increased play.Fig 19-23 A narrow 2-mm bracket (a) and a wide 4-mm bracket (b) are compared. Both teeth need a counterclockwise moment of 1,000 gmm for translation. The narrow bracket requires equal and opposite 500-g forces (500 g × 2 mm = 1,000 gmm), while the wide bracket requires 250-g forces (250 g × 4 mm = 1,000 gmm). The narrow bracket has twice the frictional force because the nor-mal force is two times that of the wide bracket. Therefore, the wide bracket has less friction during phases II and III of space closure.a ba b 19The Role of Friction in Orthodontic Appliances464changed, but so has the M/F ratio. The new ratio of 10.6 could translate the canine, since the force has been reduced. So the effective force system might be better if less tipping is desired. The negative aspect of friction is that it makes our appliances less predictable. There can be a large dif-ference between the applied force system and the effective force system. Perhaps in some situations, friction is so great that there is no effective force at all. Sometimes teeth do not respond because of tooth-bone ankylosis; sometimes, it could be the ap-pliance that is ankylosed.Overriding FrictionIf the clinician knows all of the frictional forces, force can be added during canine retraction to com-pensate for the frictional forces. This is called a fric-tion override. An example is shown in Fig 19-25a. An effective force of 200 g is needed for canine retrac-tion. An M/F ratio of 6 is estimated for the tipping phase around the center of rotation at the apex in the facial view, and an M/F ratio of 4 is estimated to prevent rotation of the canine in the occlusal view. The ligature tie has a normal force of 500 g. Let us assume a coefcient of friction (µ) of 0.2 and a 4-mm bracket width.FF (facial view) = 200 g × 6 mm × 2 × 0.2 = 120 g 4FF (occlusal view) = 200 g × 4 mm × 2 × 0.2 = 80 g 4FF (ligature tie) = 500 g × 0.2 = 100 g∑FF = 120 g + 80 g + 100 g = 300 gBecause the sum of the frictional forces is 300 g, 500 g must be applied in order to produce an effec-tive force of 200 g (Fig 19-25b). This override is only for the tipping at the apex that is phase II of canine retraction. More (an additional 80 g) is needed for phase III translation, as a rough estimate.Fig 19-24 (a) A 5:1 M/F ratio is delivered to the bracket of the canine, and canine tip-back with a center of rotation approaching the apex is expected. (b) The calculated effective force is reduced to 94 g. The ef-fective force system might be better if less tipping is desired. The negative aspect of friction is that it makes our appliances less predictable.Fig 19-25 An effective force of 200 g is needed for canine retraction. Because the sum of all frictional forces is 300 g (a), a total applied force of 500 g must be used in order to override the 300 g of frictional force (b).aabb 465Friction and Anatomical VariationUnfortunately, clinically it is not always accurate or practical to calculate the frictional forces to es-timate the override needed. The frictional force is continually changing during the different phases of retraction. It is difcult to measure ligation force, and it can change. Anatomically, teeth vary in mor-phology and support. The coefcient of friction is difcult to determine, and other factors can be pres-ent. However, the principal of the override can be a useful clinical concept.Thorstenson and Kusy1 showed that a conven-tional twin bracket with a metal ligature tie with a 200-g normal load produces about 30 g more frictional force during retraction compared with a self-ligating bracket. If this is known, an override could be easy and practical. A 30-g overload is add-ed to the applied load when canine retraction is ini-tiated (phase I). The major problem that confronts the clinician is that most of the time a thorough un-derstanding of frictional forces is not possible. Still, some average friction data could be helpful. More helpful would be more predictably designed ortho-dontic appliances. They do not have to be friction-less; known friction is acceptable with an override.Occlusal Forces, Vibration, and FrictionIt could be theorized that vibration in the mouth could relieve some frictional forces. This certainly is a commonly observed phenomenon in laboratory friction. Liew et al2 has shown a 60% to 85% reduc-tion of frictional force using O-rings and round wire (Fig 19-26). O’Reilly et al3 also demonstrated a 19% to 85% friction reduction in both rectangular and round wires.Different phenomena may operate to reduce the magnitude of friction. The horizontal component of occlusal forces can produce lateral tooth displace-ment that can loosen the ligature tie or O-ring. Thus, vibration or tooth displacement could be an important factor in eliminating the frictional force from the ligation mechanism. The frictional forces produced in response to tipping during sliding of a tooth along an archwire are an entirely different phenomenon, because it is the elastically bent wire that produces the normal forces, not the force from ligation. Occlusal forces may not relieve the friction unless the chewing force is placed in a direction to temporarily reduce the normal force between the wire and the bracket. This suggests once again that friction from the ligation mechanism may not be as important as friction from tooth-moving forces—the forces from the elastically bent wires. One of the main advantages of a self-ligating bracket is that the ligation mechanism produces less normal force in the passive state of the wire. This advantage may be minimized because vibratory forces seem to be successful in reducing friction from conventional ligature ties or O-rings.Friction and Anatomical VariationPatients could have identical brackets, malocclu-sions, and wires and still not have the same fric-tional forces based on anatomical variation in root length and alveolar and periodontal support. Let us Fig 19-26 Vibration in the mouth could relieve some frictional forces. Liew et al2 demonstrated a 60% to 85% reduction of fric-tional force using O-rings and round wire. 19The Role of Friction in Orthodontic Appliances466only consider the translation phase during canine retraction for the four teeth in Fig 19-27. To trans-late the teeth, a force must be placed through the CR (yellow arrows). That force is usually replaced at the bracket level with a force and a couple (red arrows). The magnitude of this couple is the force times the distance from the bracket to the CR. Thus, the greater the M/F ratio, the higher are the vertical normal forces that create the frictional force.The tooth in Fig 19-27a is a typical tooth with av-erage periodontal support as a reference. The CR is away from the bracket; therefore, a high M/F ratio at the bracket is required. This moment produces much friction, as discussed in this chapter. The teeth in Figs 19-27b and 19-27c have shorter roots, with their CRs closer to the bracket. Here, the M/F ratios are low with subsequent low frictional force. Root resorption (see Fig 19-27c) is certainly unwanted, but it does have the advantage of minimizing the friction produced at the level of the bracket.The tooth from an adult showing alveolar bone loss (Fig 19-27d) has the largest distance to the CR and would have the greatest friction during transla-tion. Clinically, the tooth might not move so rapidly by translation, and we would be disappointed in the response. We might blame the poor response on the age of the patient and biologic factors, but perhaps the greater frictional force is the real culprit.Anchorage and FrictionThe claim is sometimes made that larger friction at the molar can lead to prevention of anchorage loss during space closure in an extraction case. Let us consider for simplicity just two teeth—a canine and a rst molar (Fig 19-28a)—in which a chain elastic is used. All of the forces are acting on the same line of action. The applied force is slowly increased from 0 g (red arrows). The forces are equal and opposite on the molar and canine (Newton’s First Law). Also, the frictional force (purple arrows) increases with equal and opposite force (Newton’s Third Law). Once the applied force overcomes one of the maximum stat-ic friction forces between the two brackets, sliding of a tooth along the archwire can occur. There are two possible interfaces either at the molar or the ca-nine bracket; sliding will only occur at the interface that overcomes the lower maximum static friction force. Let us assume for now that the lower max-imum static friction force is at the canine bracket (FFmax at the molar > FFmax at the canine). The canine slides because the applied force is greater than the maximum static friction force at the canine brack-et (Fig 19-28b). On the molar, however, the applied force is less than the maximum static friction force, and therefore sliding does not occur at that inter-face. The sliding occurs only at the interface with the smaller frictional force, where the applied force is greater than the frictional force. Even if the slid-ing occurs at only one interface (ie, at the canine or at the molar), the canine can still move distally, or the molar can move mesially, with sliding occurring at the canine bracket interface.This is easily seen with a simple experiment. Place a ruler or any rigid rod on your ngers, as depicted in Fig 19-29a. Let us assume that the ruler is a wire and the ngers are the brackets. The coefcient of friction between the ruler and the ngers is the same; therefore, the frictional force will be propor-tional to the normal force. Now move the ngers closer together very slowly, still keeping static equi-librium. Let us assume that the left nger has less maximum static friction force to begin with. Only the left nger starts to slide toward the center of the ruler. As the left nger moves to the center, the normal force will be increased (Fig 19-29b). There-fore, sliding is stopped and the right nger starts to slide. The sliding occurs alternately between the left and right ngers, and the two ngers will nal-ly meet at the center. The normal force changes as the ruler is placed off-center, and only the nger at Fig 19-27 Patients could have identical brackets and wires but not have the same frictional forces based on anatomical variation in root length and alveolar and periodontal support. (a) A typical tooth with average periodontal support as a reference. (b and c) Teeth with shorter roots, with their CRs closer to the bracket. Here, the M/F ratios are low with subsequent low frictional force. (d) A tooth from an adult showing alveolar bone loss has the largest distance to the CR and would have the greatest friction during translation.a b c d 467Anchorage and Frictionthe contact with less friction slides. Note that both ngers never slide at the same time. Therefore, as long as the friction is higher at the molar either by higher normal force from a tight ligature or by a higher coefcient of friction, it never slides. But just because it is not sliding does not mean that it is not moving. In the experiment above, the sliding occurs alternately between the left and right ngers, but the movement of the ngers is continuous. Suppose the left nger is glued to the ruler and the sliding will occur on the right nger only; both ngers still move, and the glued left nger does not feel high-er resistance to moving due to higher friction. The same is true with a wire. The higher-friction side does not feel higher resistance to moving.In Fig 19-30a, an omega stop was placed immedi-ately anterior to the molar tube for visualization of innite friction. Sliding does not occur at the molar tube, but sliding does occur at the canine bracket, and the applied force at the molar will be reduced by the frictional force at the canine (Fig 19-30b).Fig 19-28 The applied force is slowly increased from 0 g (red arrows). (a) The forces are equal and opposite on the molar and canine (New-ton’s First Law). Also, the frictional force (purple arrows) increases with equal and opposite force (Newton’s Third Law). (b) Once the applied force overcomes one of the maximum static friction forces between the two brackets, sliding of a tooth along the archwire can occur.abFig 19-29 (a) Place a ruler or any rigid rod on your ngers. Slowly move the ngers closer together, still keeping static equilibrium. Only one nger will start to slide toward the center of the ruler. As the nger moves to the center, the normal force will be increased. Therefore, sliding is stopped and the other nger will start to slide. (b) The sliding occurs alternately between the left and right ngers, and the two ngers will nally meet at the center. abFig 19-30 An omega stop was placed immediately anterior to the molar tube for visualization of innite friction. (a) Sliding will not occur at the molar tube. (b) However, sliding does occur at the canine bracket, and the applied force at the molar will be reduced by the frictional force at the canine. The differential friction at the two interfaces never produces differential space closure.ab 19The Role of Friction in Orthodontic Appliances468It is not too surprising that friction does not usu-ally inuence anchorage loss. Note the clinical sit-uation in Fig 19-28. The key to understanding is to remember that the archwire is in equilibrium. With-out friction, the applied forces from the chain elastic sum to zero force on the wire. There are two pos-sible frictional forces on the wire: the molar push-ing the wire forward and the canine pushing the wire backward. They must sum to zero for equilib-rium, and hence, both must be equal and opposite in magnitude. This is independent of the interface (gate), where sliding can occur, as explained above. In short, Newton’s First Law of equilibrium does not allow the possibility of differential frictional forces. Differential frictional forces acting from the molar and the canine would accelerate both wire and pa-tient into outer space.The maximum static friction force may be differ-ent from the canine and the molar; however, the magnitudes of frictional forces are always equal and opposite. Under these conditions, the friction does not inuence the anchorage. In Fig 19-29, the ruler is different than an orthodontic wire, where moments can be present at each end along with the vertical force; however, the same principle is true.Now let us assume that the sliding interface is at the molar, so friction is very high at the canine. With these boundary conditions, en masse retraction of the incisors and canine can still occur. The forces on the molar and anterior segment will still be equal and opposite; therefore, less friction at the molar tube never produces more anchorage loss. In the special situation where deep bite is present, anchor-age loss may occur (Fig 19-31), but not because of higher friction at the canine. The deep bite prevents the maxillary incisors from retracting, and the maxil-lary molar is now free to slide anteriorly. A differen-tial coefcient of friction is possible, but differential frictional force is not possible. Even with differential coefcients of friction, differential space closure will not occur.In some clinical applications, archwires are re-quired to slide through many brackets. Under these conditions, friction is very complicated and, hence, predictive modeling is difcult.Reducing Friction During Space Closure Space can be closed using sliding mechanics even if there are frictional forces. The problem with friction is that it makes the force system more unpredict-able. There are a number of approaches that can be employed to reduce frictional forces and make the force system more predictable. We have already discussed bracket design and the use of wider brackets and lower ligation forc-es. Some cases do not require translation, and then tipping can be allowed. Tipping and suitable rota-tion such as distal-in canine rotation can require less friction, because less moment requires less frictional force. If the force is placed closer to the CR, it is not necessary for the archwire to produce the anti-tip and antirotation moments, and subsequent friction will be eliminated. The applied force can be placed more apically by an extension arm or by an equiva-lent force system at the bracket from an additional wire or spring. Apical levers and lingual placement of the force can readily be utilized. The spring to store and release energy can be part of the canine retraction spring and its apical extension (Fig 19-32). To eliminate or minimize the friction from canine retraction, rotational forces from a chain elastic or a coil spring can be attached on the lingual surface of the canine (Fig 19-33). If an auxiliary retraction spring or loop is used, ac-tivations can be placed to minimize tipping and ro-tation during canine retraction three-dimensionally so that the sliding archwire can deliver a smaller fric-tional force. An archwire is still present to give posi-tive control with minimal friction (Fig 19-34).En masse space closure requires sliding of the archwire at the posterior brackets. Because the me-sial force is buccal to the CR of the posterior teeth, molars tend to rotate mesial in (Fig 19-35). The use of a buccal archwire can barely prevent this side ef-Fig 19-31 In the special situation where deep bite is present, an-chorage loss may occur where higher maximum friction is at the canine. This anchorage loss is not due to higher friction at the ca-nine, however, but is rather a result of the deep bite preventing the maxillary incisors from retracting, meaning the maxillary molar is free to slide anteriorly. 469Reducing Friction During Space Closurefect, and friction will be produced. Lingual or trans-palatal arches can preserve arch form without pro-ducing friction from a wire observed in the occlusal view (Fig 19-36).Finally, space closure can be accomplished without sliding or friction mechanics by a so-called friction-less spring. In Fig 19-37, canine retraction springs were used. All needed anti-tip and antirotation moments are bent and twisted into the springs. No sliding on an archwire is required. With sliding mechanics, the required moments are obtained by perpendicular normal forces from the archwire in-evitably producing friction. With frictionless springs, the same forces and moments may be required and are present, but because no sliding occurs, there is no friction (see also Fig 14-13).Fig 19-33 A chain elastic or a coil spring can be attached on the lingual surface of the ca-nine to reduce the friction in the occlusal view.Fig 19-35 En masse space closure requires sliding of the archwire at the posterior brack-ets. Because the mesial force is buccal to the CR of the posterior teeth, molars tend to ro-tate distal out.Fig 19-32 Apical levers and lingual placement of the force can readily be utilized for reduction of friction.Fig 19-34 If an auxiliary retraction spring or loop is used for canine retraction, three-dimensional activations can be placed to minimize tipping and rotation. The archwire delivers additional vertical and lateral normal forces for control.Fig 19-36 Lingual or transpalatal arches can preserve arch form without producing friction from a wire observed in the occlusal view.Fig 19-37 Space closure can be accomplished without sliding or friction mechanics by a fric-tionless spring. All needed anti-tip and antiro-tation moments are bent and twisted into the springs. 19The Role of Friction in Orthodontic Appliances470Friction During Initial Alignment and FinishingFrictional forces can be present and inuence results at all stages of treatment from leveling to nishing. Two effects that occur with lighter alignment arches merit mention. Frictional forces produce a compo-nent of force that is parallel to the archwire (Fig 19-38). Sometimes this is good and other times bad. The positive effect of mesiodistal forces due to friction is the opening of space for tooth alignment (Fig 19-39). Many patients have moderate crowding, and an in-crease of arch length is desirable. If the wire is not free to slide, the wire will open space by pushing teeth laterally, causing an increase in arch length. It is a well-known principle that teeth cannot be aligned or rotated unless there is enough space for them. Because there are limitations in the ability of a main archwire to sufciently increase arch length, auxiliary or secondary wires such as coil springs, in-trusion arches, and bypass arches can be used to in-crease arch length. If there is adequate space, low friction in an archwire is desirable.The negative effect of friction during leveling is that the wire may not be free to slide mesially or distally through the brackets; therefore, the desired Fig 19-38 (a and b) Frictional forces pro-duce a component of force that is parallel to the archwire. (c) As the bracket is displaced occlusogingivally, not only vertical force but also signicant horizontal force is produced by the friction. Ni-Ti, nickel-titanium.cFig 19-39 The positive effect of mesiodis-tal forces is the opening of space for tooth alignment (purple arrows).Fig 19-40 (a) The negative effect of friction during leveling is that the wire may not be free to slide mesially or distally through the brackets; therefore, the desired buccal forces are not free to express themselves. (b) Friction at the canine and the rst molar prevents the wire from fully deactivating.a ba b 471Friction During Initial Alignment and Finishingbuccal forces are not free to express themselves. Longitudinal frictional forces prevent deactivation of the wire (Fig 19-40a). Large lateral deections of the wire that cannot be recovered to the original shape because of friction necessitate removal and reinsertion of the archwire. Friction at the canine and the rst molar prevents the wire from fully de-activating (Fig 19-40b). If full deactivation does not occur and the wire does not slide spontaneously, it can be removed and retied. Leaving a wire in place to deactivate it can open space and relieve the of-fending friction; however, these mesiodistal forces may not be efcient or wanted. A reverse articulation of the maxillary lateral in-cisor is treated by a nickel-titanium (Ni-Ti) overlay wire (Fig 19-41). If the ligature is too tight, the Ni-Ti wire cannot fully deactivate. It is important to allow sliding at the tie (green arrows in Figs 19-41a to 19-41c). Note that the overlaid Ni-Ti wire has a hook on each side (blue arrows in Figs 19-41a to 19-41c) and that the elastics are activated with light force in the direction of the axis of the wire. The me-siodistal forces to the wire will thereby unlock the friction and will allow full labial force expression to the lateral incisor (Figs 19-41c and 19-41d). Anoth-er approach is to remove the Ni-Ti overlay and retie the ligature to eliminate the unwanted longitudinal forces.Tying of archwires into irregular teeth can either increase the arch length or reduce the arch length, even when identical forces are applied, because of friction. To simplify this explanation, let us consider a cantilever force system with a single force deliv-ered at the free end. Figure 19-42 shows an intru-sion arch with a V-bend placed anterior to the molar tube. Its conguration after initial intrusion will also produce aring of the incisors; however, let us not consider this effect. We could assume that the intru-sion force is acting at the CR of the anterior teeth. Because it is a cantilever, the location of the V-bend is not very important. It can be placed at many lo-cations further anteriorly along the intrusion arch to produce identical intrusive forces; yet different congurations would produce varying amounts of horizontal force from the described friction effect during deactivation.In Fig 19-42a, it is assumed that the wire and the bracket do not have any friction. An occlusal acti-vation force brings the intrusion arch to the level of the incisor brackets; the wire is allowed to freely slide through the molar tube so that the wire just touches the labial of the incisor brackets, exerting no horizontal force. After being tied to the incisors with a ligature, the wire will initially produce only an intrusive force; no labial or lingual (horizontal) forces are possible.Next, innite friction on the molar tube is as-sumed; the wire is not free to slide through the tube after tying of the incisors. Where does the fric-tion come from? The large moment and force (red) acting at the molar tube generate high frictional forces. In Fig 19-42b, the same deactivated shape is placed with the above method. Initially the force at the incisors will feel only intrusion because no hor-izontal force is present, but as the archwire deacti-vates, it becomes straighter and longer; hence, the incisors will gradually feel a labial force as the in-trusion proceeds. The shape at full deactivation is a straight line. Note that it is longer horizontally than the curved activated shape.Figure 19-42c has a gradual curvature rather than a sharp V-bend formed into the intrusion arch. With this shape during deactivation, the intrusion arch will get shorter, and a lingual force will be produced. Fig 19-41 (a to d) A reverse articulation of a maxillary lateral incisor is treated by a Ni-Ti overlay wire. It is important to allow sliding at the tie (green arrows). Note that the overlaid Ni-Ti wire has a hook on each side (blue arrows) and that elastics are ac-tivated with light force in the direction of the axis of the wire. The mesiodistal forces at the wire will thereby unlock the friction, allowing full labial force expres-sion to the lateral incisor.bac d 19The Role of Friction in Orthodontic Appliances472Different congurations initially could deliver the same force system, but if friction is present, over time the force system can change signicantly when new horizontal forces are produced. Of course in re-ality, the frictional force is nite; still, the same phe-nomenon will be observed. The example given was for a cantilever, but this effect can operate between other bracket geometries involving forces and mo-ments at each bracket.Brackets and archwires are needed for three-dimensional control where both forces and couples are required. In some situations, only a single force is needed, and an archwire placed into a bracket can complicate the mechanics not only by added moments but also by added unavoidable friction-al forces. The canine in Fig 19-43a requires distal movement and rotation into an extraction site, as depicted by the red arrows. A very simple single dis-tal force at the bracket without an archwire produc-es the force system that we want (Fig 19-43b). From the occlusal view, wire engagement is not needed for the rotational moment. Tying the wire into the bracket would potentially make the situation worse (Fig 19-43c). The frictional mesial force added to the mesial-in moment could move the canine CR to the mesial, which is not indicated. The additional mo-ment can also restrict effective distalization of the canine, slowing down retraction. The clinical case in Fig 19-11 showed the undesirable effect of moving the CR to the wrong position because of friction.Fig 19-43 (a) The canine requires distal movement and rotation into an extraction site, as depicted by the red arrows. (b) A very simple single distal force at the bracket produces the desired force system. (c) Tying the wire into the bracket would potentially make the situation worse due to the friction.a b cFig 19-42 (a) An intrusion arch with a V-bend placed anterior to the molar tube. It is assumed that the wire and the bracket do not have any friction. After the wire is tied to the incisors with a liga-ture, the wire will initially produce only an intrusive force. No labial or lingual (horizontal) forces are possible. (b) Innite friction on the molar tube is assumed. The same deactivated shape is placed with the above method. The incisors will gradually feel a labial compo-nent of force as the intrusion proceeds. (c) When a gradual curva-ture rather than a sharp V-bend is formed into the intrusion arch, a lingual component of force will be produced.a bc 473ConclusionConclusionThis chapter has discussed the role of classic fric-tion in understanding the biomechanics of an or-thodontic appliance. Basic formulations have been presented to give clinicians a rational basis for how frictional forces operate so they can more efciently use any appliance. These simple formulas must not be assumed to fully give all the restraining forces to sliding. It is far more complicated. Tribologists, specialized engineers who study friction in depth, still debate its effects, principles, and mechanisms. There are also many research papers regarding fric-tion in the orthodontic eld. It is interesting to nd that some results are contradictory even though the research methods are similar. This is because there are too many variables to control in research of stat-ic and kinetic friction. Saliva, for example, acts as a lubricant or adhesive depending on the materials used. Even at low forces where little permanent de-formation or wear occurs, classic theory may be too limited. The measurement of coefcients of friction is difcult and may not be reproducible, hence giv-ing potentially inconsistent values in the literature. The force system in vivo is continually changing over time as teeth displace. Force decay is inherent in our wires and appliances. Actual loading conditions may be different and many times more complicated than envisioned. We have discussed here only four stages of canine retraction. If the arch is not fully leveled before retraction, the force system will be different than described in this chapter.Resistance to sliding can involve more than classic engineering formulas if heavier loads are present in the mouth. Wires or even brackets can be per-manently deformed, wear, and undergo abrasion. Here prediction or calculation of sliding resistance becomes very difcult.Our discussion of friction has mainly described in-terbracket distance activity that generates forces between brackets. Intrabracket forces occurring be-tween the wings of a bracket can also be signicant sources of friction. Wedging was briey mentioned in Fig 19-20; wedging (Fig 19-44) occurs when a lig-ature tie is too tight or a wire cross section is slightly larger than the slot size. Wedging is common even when undersized wires are used. Examples are given in Fig 19-45. Archwires are sometimes placed with a curvature such as a curve or reverse curve of Spee, which can ll up the bracket slot (Fig 19-45a). A permanent deformation of the wire between two brackets can result from heavy mastication (Fig 19-45b). Any small bends or torque inside the brack-et, possibly the result of a nick by a plier, must be considered as another source of signicant friction (Fig 19-45c).Other forces from the cheeks, lips, and tongue may inuence the cyclic unlocking of friction. Brief-ly we have discussed the importance of cyclic and Fig 19-44 Intrabracket forces occurring between the wings of a bracket can be a signicant source of friction. One example is wedging, where a ligature tie is too tight or a wire cross section too large.Fig 19-45 (a) Wedging occurs even with undersized wire. A curvature such as a curve or reverse curve of Spee can ll up the bracket slot. (b) A permanent deformation of the wire between two brackets caused by heavy mastication. (c) An unnoticed nick by a plier must be considered as another potential source of signicant friction.a b c 19The Role of Friction in Orthodontic Appliances474occlusal forces in frictional force reduction. Unfor-tunately, our understanding makes for poor predic-tion because of its complexity. Nevertheless, an un-derstanding of classic friction and the formulas that underlie it can go a long way to explain much that is seen clinically and help clinicians in the selection and design of the individualized orthodontic appli-ances for their patients.References1. Thorstenson GA, Kusy RP. Resistance to sliding of self- ligating brackets versus conventional stainless steel twin brackets with second-order angulation in the dry and wet (saliva) states. Am J Orthod Dentofacial Orthop 2001; 120:361–370.2. Liew CF, Brockhurst P, Freer TJ. Frictional resistance to slid-ing archwires with repeated displacement. Aust Orthod J 2002;18:71–75.3. O’Reilly D, Dowling P, Langerstrom L, Swartz ML. An ex-vivo investigation into the effect of bracket displace-ment on the resistance to sliding. Br J Orthod 1999;26:219–227.Recommended ReadingBurstone CJ. Biomechanical rationale of orthodontic therapy. In: Melsen B (ed). Current Controversies in Orthodontics. Chi-cago: Quintessence, 1991;131–146.Burstone CJ. Precision lingual arches: Active applications. J Clin Orthod 1989;23:101–109.Burstone CJ. Self-ligation and friction: Fact and fantasy. Pre-sented at the 37th Moyers Symposium on Effective and Ef-cient Orthodontic Tooth Movement, Ann Arbor, MI, 26 Jan 2011.Burstone CJ. The segmented arch approach to space closure. Am J Orthod 1982;82:361–378.Burstone CJ, Hanley KJ. Modern Edgewise Mechanics Seg-mented Arch Technique. Glendora, CA: Ormco, 1986. Burstone CJ, Koenig HA. Creative wire bending—The force system from step and V bends. Am J Orthod Dentofacial Or-thop 1988;93:59–67.Burstone CJ, Koenig HA. Force systems from an ideal arch. Am J Orthod 1974;65:270–289.Burstone CJ, Koenig HA. Optimizing anterior and canine re-traction. Am J Orthod 1976;70:1–19.Choy K, Pae EK, Kim KH, Park YC, Burstone CJ. Controlled space closure with a statically determinate retraction system. Angle Orthod 2002;72:191–198.Gottlieb EL, Burstone CJ. JCO interviews Dr. Charles J. Burstone on orthodontic force control. J Clin Orthod 1981;15:266–268.Iwasaki LR, Beatty MW, Randall CJ, Nickel JC. Clinical ligation forces and intraoral friction during sliding on a stainless steel archwire. Am J Orthod Dentofacial Orthop 2003;123:408–415.Kusy RP, Whitley JQ. Coefcients of friction for arch wires in stainless steel and polycrystalline alumina bracket slots. Am J Orthod Dentofacial Orthop 1990;98:300–312.Nägerl H, Burstone CJ, Becker B, Kubein-Messenburg D. Cen-ters of rotation with transverse forces: An experimental study. Am J Orthod 1991;99:337–345.Park JB, Yoo JA, Mo SS, et al. Effect of friction from differing vertical bracket placement on the force and moment of NiTi wires. Korean J Orthod 2011;41:337–345.Ronay F, Kleinert MW, Melsen B, Burstone CJ. Force system developed by V bends in an elastic orthodontic wire. Am J Orthod Dentofacial Orthop 1989;96:295–301.Smith RJ, Burstone CJ. Mechanics of tooth movement. Am J Orthod 1984;85:294–307.Tanne K, Koenig HA, Burstone CJ. Moment to force ratios and the center of rotation. Am J Orthod Dentofacial Orthop 1988;94:426–431.Tanne K, Nagataki T, Inoue Y, Sakuda M, Burstone CJ. Patterns of initial tooth displacements associated with various root lengths and alveolar bone heights. Am J Orthod Dentofacial Orthop 1991;100:66–71.Tanne K, Sakuda M, Burstone CJ. Three-dimensional nite ele-ment analysis for stress in the periodontal tissue by orthodon-tic forces. Am J Orthod Dentofacial Orthop 1987;92:499–505.Thorstenson GA, Kusy RP. Comparison of resistance to sliding between different self-ligating brackets with second-order angulation in the dry and saliva states. Am J Orthod Dentofa-cial Orthop 2002;121:472–482.Timoshenko S, Goodier JN. Theory of Elasticity, ed 2. New York: McGraw-Hill, 1951. 475PROBLEMSDisregard all forces out of the plane of the diagrams. For problems 1 through 4, 600 g of normal force is acting on the canine and the rst molar. The coefcient of friction is 0.2. 1. What is the maximum static friction force? 2. 100 g is applied at the canine by a coil spring from canine to molar. How much force is applied at the molar? Calcu-late the magnitude of the frictional forces at each tooth.3. Calculate the magnitude of force to override the friction.4. How much force does each tooth feel in phase I of space closure when 300 g of force is applied at the canine? 19The Role of Friction in Orthodontic Appliances476For problems 5 through 7, 600 g of normal force is acting on the canine.5. 1,200 g of ligature force is applied at the molar. How much force would the canine and molar feel in phase I of space closure?6. Assume that the normal force of the molar tube is com-pletely removed. How much force would the canine and molar feel in phase I of space closure?7. Assume that the canine bracket from problem 6 is replaced with a ceramic bracket and the coefcient of friction be-tween the wire and bracket is 0.5 at the canine. 300 g is applied at the canine. How much force would the canine and molar feel?8. The canine and the rst molar are to be translated. Calcu-late the maximum static friction force on the canine and molar. How much applied force is needed to translate the teeth? Where would sliding occur?9. A 10:1 M/F ratio at the bracket will translate the molar and canine. A 100-g force is placed at the extension hooks (lever arms). What is the effective force on the molar and canine?

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