The effects of third-order torque and self - Saint Louis University

THE EFFECTS OF THIRD-ORDER TORQUE AND SELF-LIGATING 

ORTHODONTIC BRACKET TYPE ON SLIDING FRICTION: A COMPARATIVE 

STUDY 

Michael J. Chung, D.D.S. 

An Abstract Presented to the Faculty of the Graduate School 

of Saint Louis University in Partial Fulfillment 

of the Requirements for the Degree of 

Master of Science in Dentistry 

2007

Abstract 

Few studies have evaluated the effect of wire-slot 

torque on sliding friction. Apparently, no studies have 

been published to date that compare friction across 

categories of self-ligating brackets when third-order 

positioning is controlled. The purpose of this study was 

to determine the effects of wire-slot torque and type of 

self-ligating bracket on the average kinetic friction in 

sliding mechanics with a 0.019- x 0.025-inch stainless 

steel archwire. Five sets of crown-attachments (including 

In-Ovation R, Time2, Damon 3MX, SmartClip and Victory 

brackets) were tested for frictional resistance in a 

simulated posterior dental segment with -15, -10, -5, 0, 

+5, +10, and +15 degrees of torque placed in the maxillary 

right second-premolar bracket. 

Increasing the torque from 0 to ±15 degrees produced 

significant increases of frictional resistance in all five 

of the tested attachment-sets. At 0 degrees of torque, the 

sets with passive self-ligating brackets produced less 

friction than the sets with active self-ligating brackets, 

and all four self-ligating bracket sets produced 

significantly less friction than the set with 

elastomerically ligated Victory brackets. At ±10 degrees

of torque, all five attachment sets displayed similar 

resistances with the exception of the In-Ovation R set at 

+10 degrees. At ±15 degrees of torque, the In-Ovation R 

and the SmartClip sets produced significantly larger 

frictional resistances than the other three sets. 

The data suggest that the presence of third-order 

torque can influence the kinetic frictional resistances in 

posterior dental segments during anterior retraction using 

sliding mechanics with self-ligating brackets and that 

frictional resistance will increase at a greater rate when 

the torque exceeds ±10 degrees with the present combination 

of sizes of slots and wire. Furthermore, whether a self- 

ligated bracket is active or passive may not be clinically 

significant regarding friction in the presence of torque 

approaching and exceeding 15 degrees.

THE EFFECTS OF THIRD-ORDER TORQUE AND SELF-LIGATING 

ORTHODONTIC BRACKET TYPE ON SLIDING FRICTION: A COMPARATIVE 

STUDY 

Michael J. Chung, D.D.S. 

A Thesis Presented to the Faculty of the Graduate School of 

Saint Louis University in Partial Fulfillment 

of the Requirements for the Degree of 

Master of Science in Dentistry 

2007

COMMITTEE IN CHARGE OF CANDIDACY: 

Assistant Professor Donald R. Oliver, 

Chairperson and Advisor 

Assistant Professor Ki Beom Kim, 

Adjunct Professor Robert J. Nikolai 

i

To my wife, Sahrip, and my parents... 

Thank you for all your love and support. 

ii

ACKNOWLEDGEMENTS 

The author wishes to acknowledge all of the 

individuals who assisted him with this project. He would 

like to thank Dr. Donald R. Oliver, Dr. Robert J. Nikolai, 

Dr. Ki Beom Kim, Mr. Joe Tricamo, Dr. Heidi Israel, and 

Dr. Binh Tran. 

The author would also like to thank Mr. John Sherrill 

and Ormco Corporation, Mr. Kevin Harrison and 3M/Unitek 

Corporation, Mr. Ted Reed and GAC International, and Mr. 

Brian Horn and American Orthodontics for supplying the 

brackets for this study. 

iii

TABLE OF CONTENTS 

List of Tables...........................................v 

List of Figures.........................................vi 

CHAPTER 1: INTRODUCTION..................................1 

CHAPTER 2: REVIEW OF THE LITERATURE 

Classical friction............................3 

Friction in orthodontics......................5 

Factors influencing friction .................9 

Archwires..................................9 

Brackets..................................15 

Ligation..................................19 

Other factors influencing friction........27 

Summary......................................34 

References...................................35 

Tables.......................................47 

CHAPTER 3: JOURNAL ARTICLE 

Abstract.....................................48 

Introduction.................................50 

Materials and Methods........................56 

Results......................................62 

Discussion...................................64 

Conclusions..................................70 

References...................................72 

Tables.......................................80 

Figures......................................84 

Vita Auctoris...........................................90 

iv

LIST OF TABLES 

Table 2-1: Partial Overview of Self-Ligating 

Brackets................................. 47 

Table 3-1: Frictional-force means and standard 

deviations in grams at seven torque angles 

at the second premolar from five sets of 

crown-attachments.........................80 

Table 3-2: Significance levels (α = 0.05) of 

differences in mean frictional forces across 

pairs of cells, each cell defined by a 

torque-angle, from five sets of crownattachments...............................81 

Table 3-3: Summary from Kruskal-Wallis analyses of 

variance of frictional forces for seven 

torque-angles across five sets of crownattachments...............................82 

Table 3-4: Mean differences in frictional resistances 

in grams and significance levels (α = 0.05) 

between attachment sets at each of the seven 

torque angles.............................83 

v

LIST OF FIGURES 

Figure 3-1: Four cylinders mounted in aluminum base 

plate of the friction testing device......84 

Figure 3-2: Bracket-slot positioning template.........84 

Figure 3-3: Control of the third-order position of the 

second premolar bracket-slot..............85 

Figure 3-4: SLBUCCAL tube.............................85 

Figure 3-5: Damon 3MX bracket.........................85 

Figure 3-6: SmartClip bracket.........................86 

Figure 3-7: In-Ovation R bracket......................86 

Figure 3-8: Time2 bracket.............................86 

Figure 3-9: Victory bracket...........................87 

Figure 3-10: Friction testing setup mounted to the 

Instron Universal Testing Machine.........87 

Figure 3-11: Plots of mean kinetic frictional force 

within the dental segment vs. torque angle 

at the second premolar from five sets of 

crown-attachments.........................88 

Figure 3-12: Cross-section diagrams of a 0.019- x 0.025inch 

wire. The buccolingual dimension of 

the wire when rotated 10 degrees (line BD) 

is calculated by multiplying cosΦ2 by the 

hypotenuse AB.............................89 

vi

CHAPTER 1: INTRODUCTION 

The specialty of orthodontics has been going through a 

period of considerable research interest in the role of 

friction during tooth movement. Within the past 30 years, 

studies have focused on both the contact between the wire 

and the bracket- or tube-slot as a potential source of 

frictional resistance during sliding mechanics and the many 

associated factors that can affect that resistance to tooth 

movement. These experiments have identified variables in 

the archwire, bracket, ligature and oral environment as 

contributors to frictional forces. 

With recent advances in orthodontic technologies, such 

as new self-ligating bracket designs and archwire alloys, 

orthodontists have developed systems aimed at maximizing 

the efficiency of treatment. Today fewer archwires are 

placed, and treatment phases have been merged that were 

previously carried out individually. The gaining 

popularity of sliding mechanics has made further research 

on the role of friction necessary. 

Previous studies have evaluated friction by pulling 

the wire through the bracket-slot and measuring the force 

required to produce the sliding displacement. Many 

investigations have examined single brackets with various 

1

combinations of bracket-slot and wire materials, ligature 

type, slot-positioning and other pertinent parameters. 

Research designs have recently attempted to simulate 

clinical environments with multiple crown-attachments 

placed in series or in an archform. 

The present research was designed to answer several 

timely questions about friction in orthodontics. 

Apparently no studies have been published to date that 

compare friction across categories of self-ligating 

brackets with third-order positioning controlled. The 

purpose of this study was to determine the effect of wire- 

slot torque on friction in self-ligating brackets with an 

engaged, 0.019- x 0.025-inch, stainless steel archwire. In 

addition, the influence of the design of various ligating 

mechanisms on kinetic friction with active torque present 

in the wire and/or slot was also evaluated. 

2

CHAPTER 2: REVIEW OF THE LITERATURE 

Classical Friction 

In the orthodontic literature, friction was discussed 

as early as 1960 when Stoner 1 warned of the difficulty in 

determining the amount of force to be applied to a tooth 

because of the role of frictional resistance. Our current 

understanding of friction impairing tooth movement is based 

largely on long-standing theories, not directly related to 

orthodontics, by Leonardo Da Vinci, Guillaume Amontons, and 

Charles-Augustin Coulomb. Although Da Vinci’s work was not 

published until the other investigators had carried out 

friction experiments, he left behind the earliest known 

studies on the subject in a collection of journals in which 

he detailed his research. 2 Collectively, these scientists 

are credited with establishing the classical laws of 

friction, or the Amontons-Coulomb laws, which state the 

following: 1. Frictional force is proportional to normal 

force; 2. Frictional force is independent of contact-area; 

3. Frictional force is independent of sliding velocity. 2,3 

Friction is defined as the resistance to motion 

when one object moves or tends to move tangentially 

relative to another object. 4 The total contact-force 

3

etween the objects is expressed as two components when 

there is attempted or actual relative displacement between 

surfaces in contact. One component, the normal force, is a 

pushing force with an orientation perpendicular to the 

shared contact-surface. The frictional force component 

impedes the motion between the surfaces and is, therefore, 

opposite in direction to that of intended or actual motion. 5 

The maximum static or the kinetic frictional force (F) 

tangent to the two surfaces is often hypothesized as 

proportional to the normal force, as expressed by the 

equation F = µN, where µ is the coefficient of friction 

between the surfaces, and N is the normal-force magnitude 

against the contact-surface of the object to be displaced. 6 

Each of two coefficients of friction is a constant which is 

related to characteristics of the contacting surfaces of 

the objects; they are known as the static and kinetic 

coefficients of friction. 7 Ordinarily in static situations, 

the frictional force is just large enough to prevent 

relative tangential movement. Maximum static friction 

refers to the resistance to displacement encountered at the 

onset of motion; it corresponds to the smallest action 

required to initiate motion between surfaces that are at 

rest. Kinetic friction is the frictional force that 

impedes displacement during sliding motion between the 

4

surfaces. 6 The magnitudes of the coefficients of friction 

are generally between zero and one. 5 

Friction in Orthodontics 

Because frictional force acts in a direction opposite 

to the intended path of the object to be displaced, and 

sliding mechanics are commonplace in orthodontic therapy, 

an understanding of friction is necessary to achieve 

optimal clinical results. Fixed-appliance therapy usually 

involves some relative wire-slot displacement in various 

phases of treatment; hence, the generation of friction 

during tooth movement can be problematic for the 

orthodontist. Because a portion of the force for delivery 

to a tooth-crown may be necessary to overcome frictional 

resistance, the orthodontist must be sure to use a force of 

sufficient magnitude to also initiate a biological response 

in the supporting tissues. 7 Frictional resistance is 

thought play a role in delayed tooth movement, undesired 

movement and loss of anchorage. 6 Examination of its effect 

on orthodontic anchorage, however, reveals that, in some 

situations, the presence of friction at the anchor teeth 

can be desirable, because it helps to prevent unwanted 

movement of those teeth. Even so, a problem lies in the 

5

fact that the magnitude of resistance is unknown. The 

orthodontist is, then, guessing how much force is needed to 

move teeth without straining anchorage. 8 

The application of sliding mechanics in orthodontics 

has increased since the introduction of the pre-adjusted 

edgewise appliance system. 9 The process can involve the 

guidance of a tooth along a continuous archwire or the 

movement of the wire through crown-attachment slots. In 

particular, overjet reduction and space closure have been 

traditionally accepted applications of sliding mechanics. 

In a first premolar extraction case, a space is created 

between the canine and the second premolar. In the 

presence of maximum anchorage, the canine would first be 

retracted bodily with the archwire guiding its 

displacement. This single-tooth movement would likely 

create unwanted friction that could cause “side effects” 

such as uncontrolled tipping, loss of posterior anchorage, 

or deepening of the overbite. 10 Forces acting posteriorly 

on the anterior portion of the archwire would then be 

created to retract the incisors into the remaining spaces 

while allowing the excess wire to slide through the 

posterior brackets and tubes. Any friction in the buccal 

segments would hinder the movement of the incisal segment 

and, therefore, could delay space closure. 11 

6

Since the introduction to orthodontics in the 1970s of 

nickel-titanium alloy archwires, sliding mechanics can also 

be present in the initial stages of orthodontic treatment. 

These very flexible archwires have gradually replaced 

multi-loop stainless steel wires for leveling and aligning 

teeth. Nickel-titanium alloy wires exhibit small load- 

deformation rates and “superelasticity.” These properties 

enable relatively light and nearly constant forces over 

large deflections without significant permanent deformation 

of the wire, permitting easy engagement into misaligned 

bracket-slots. 12 The activated wire can then be left to 

guide the teeth into position as it returns to its 

original/pre-engagement shape. The objective of this stage 

of therapy is to produce simultaneous tooth movements such 

as leveling the arch, extruding “high” canines, correcting 

tooth rotations and modifying archforms. 13 A misaligned 

dental arch will require greater lengths of wire than a 

well-aligned arch to compensate for enlarged interbracket 

distances. As the brackets come into alignment, the teeth 

move into their correct spatial positions, and segments of 

an unstopped archwire that were “reaching” to the 

misaligned positions will slide through the adjacent 

bracket-slots and tubes. 11,14,15 In 1997 Meling et al. 14 found 

that friction in a crowded dental arch would reduce the 

7

sizes of forces delivered to the crowns by the wire during 

deactivation, especially with a light leveling wire. The 

authors concluded that careful ligation to minimize 

friction was important for delivery of expected force 

magnitudes. It is as early as placement of this initial 

wire that friction becomes a concern to the orthodontist. 

The classical laws of friction offer only a partial 

explanation of friction in orthodontic systems. The 

original theories by Amontons and Coulomb were derived from 

dry friction mechanics with distinct static and kinetic 

frictional phases, defined by zero velocity and constant 

velocity, respectively. Tooth movement in orthodontics, 

however, occurs at such low velocities, that these two 

phases are clinically interrelated. 3 Although the first two 

laws of friction would be unaffected by this application, 

the third law of friction may not accurately describe 

orthodontic friction in vivo. As the velocity of tooth 

movement approaches zero, instability in steady sliding is 

likely, due to interlocking and shearing of asperities, the 

peaks of microscopic surface irregularities. This effect 

is evident in the phenomenon known as “stick-slip motion”; 

a cycle involves a “stick state” where elastic loading 

occurs, and a “slip” where sudden sliding and stress- 

relaxation occur. 3,8 Nonetheless, Rossouw’s group 3 concluded 

8

that the application of the Amontons-Coloumb laws is 

justified in orthodontic in vitro analyses if sliding 

velocity is assumed constant. 

Factors Influencing Friction in Orthodontics 

The now frequent presence of sliding mechanics in 

orthodontic therapy has produced considerable research 

interest in friction generated between crown-attachment 

slot and archwire. Many studies have collectively 

identified factors that can contribute to friction within 

the fixed orthodontic appliance. Although it is known that 

many of these influences are interrelated, discussing them 

individually perhaps helps to better clarify their 

relationships to friction. 

Archwires 

During the past century, orthodontists have made 

selections from a wide range of marketed archwires. From 

gold wires that dominated early in the twentieth century to 

today’s ß-titanium and nickel-titanium alloys, the 

broadening of wire property values has continually changed 

the way orthodontics is practiced. 16 A number of archwire 

parameters have been found to contribute to friction at the 

9

interface of wire and crown-attachment slot. These 

parameters are alloy composition, surface-roughness, and 

cross-sectional shape and size. 

Alloy Composition 

At angulations in which second-order binding existed 

of the wire within the bracket-slot, Frank and Nikolai 5 

found that nickel-titanium alloy wires produced smaller 

maximum static frictional forces than did a stainless steel 

wire of the small size, likely due to the smaller modulus 

of elasticity of the former alloy. One of the many 

important findings from this study was that, due to 

variances in modulus of elasticity and surface roughness 

across as-received wires, archwire-alloy influenced 

frictional resistance. Since then, dozens of studies have 

compared frictional force values generated across wires 

differing by alloy. Some experimental studies have 

suggested that, typically within stainless steel slots, 

stainless steel wires tend to produce less sliding friction 

than nickel-titanium alloy wires. 17-30 When testing with 

second-order angulations that produce binding within the 

bracket-slot, however, other studies have reported less 

friction with the nickel-titanium alloy wires. 4,5,31-34 This 

behavior is related to the modulus of elasticity for the 

10

archwires. At binding angulations, two contacts form at 

the ends of the bracket-slot, one on the occlusal face of 

the wire and one on the gingival face. As the wire 

deflects upon activation, those wires with a greater 

modulus of elasticity will produce larger normal bracket- 

wire contact forces at those contact points. 5,48 Several 

investigations have found that ß-titanium alloy wires have 

greater resistance to sliding than either stainless steel 

or nickel-titanium alloy wires, particularly in the absence 

of binding. 18,20-24,26,27,29,35,36 Tspelepsis and associates 33 

failed to detect any such differences across the three 

alloys. 

Surface Characteristics 

Frank and Nikolai 5 found that, with small, nonbinding 

angulations and in stainless steel slots, stainless steel 

wires exhibited less sliding frictional resistance than 

nickel-titanium alloy wires. This difference was thought 

to be related to the roughness of the wire-alloy surface. 

This property of a wire is determined by characteristics of 

the alloy, the manufacturing process, any surface treatment 

and, for some materials, the shelf-time and/or use-time. 5 

Other researchers have speculated that the greater friction 

produced by titanium alloy wires when compared to stainless 

11

steel wires could be a result of the relative roughness of 

the contacting wire and slot surfaces. 5,18,23 

Kusy et al. 37 used a laser-spectrometer and the 

specular-reflectance technique to measure surface- 

roughnesses of wires of four materials, and found the 

surface of a nickel-titanium alloy wire to be the roughest 

followed, in order, by wire surfaces of ß-titanium, 

chromium-cobalt, and orthodontic stainless steel alloys. 

Using the same procedure, Kusy and Whitley 38 assessed the 

effect of surface topography on coefficients of friction 

for these alloys, and concluded that low wire surface 

roughness was not a sufficient condition for a small 

frictional coefficient. Prososki, Bagby and Erickson 11 

showed similar results, finding no statistically 

significant correlation between surface-roughness and 

frictional resistance from as-received archwires of common 

alloys. Although the surface of a ß-titanium archwire is 

less rough than that of nickel-titanium alloys, researchers 

have consistently shown greater in-slot frictional 

resistance to sliding from the former wire. 11,24,38,39 

Burstone and Farzin-Nia 40 have suggested that the relative 

softness of the ß-titanium alloy wire-surface compared to 

the harder stainless steel surface is a reason for the 

former’s greater frictional resistance. 

12

A phenomenon known as “cold welding” has been proposed 

as an explanation for greater friction potentials found 

with nickel-titanium and ß-titanium alloy wires. As the 

fraction of titanium in the alloy increases, the reactivity 

of its surface with other alloy-surfaces increases; nickel- 

titanium and ß-titanium alloys have titanium contents of 

about 50% and 80%, respectively. 41 Kusy and Whitley 24 found 

adhesions in the bracket-slots from scanning electron 

micrographs after drawing ß-titanium alloy wires through 

stainless steel bracket-slots in order to calculate the 

coefficients of friction. X-ray spectra of this debris 

were obtained, and they showed elements of the ß-titanium 

alloy. The authors concluded that the primary cause for 

high frictional resistance with ß-titanium wires was the 

reactivity of the titanium content of the alloy with 

stainless steel, leading to “cold welding” of the 

contacting surfaces. 20,24,39 

The effort to reduce friction in the fixed appliance 

has led to trials with a process called ion-implantation, a 

method of increasing the hardness and altering the surface- 

chemistry of an alloy by implanting nitrogen ions into that 

surface. In laboratory studies, this process had been 

shown to decrease friction significantly. 40,42 Clinical 

split-mouth studies, however, did not show a significant 

13

difference in rate of tooth movement on the side with ion- 

implanted ß-titanium alloy wires engaged. 43 

Cross-sectional Shape and Size 

Many studies have suggested that the cross-sectional 

size of an archwire and frictional-resistance potential may 

be directly related. 5,23,31,34,36,44,45 In 2003 Smith, Rossouw 

and Watson 34 found significantly greater friction with 

larger archwires than smaller ones, and they attributed 

this difference to greater flexural stiffnesses of the 

wires having larger cross-sections. 

Rectangular wires permit the orthodontist to exert 

third-order control during treatment. These wires are 

stiffer than round wires with similar cross-sectional 

dimensions. 46 The shape of the archwire cross-section 

influences its bending characteristics. Changes in shape 

from round to square to rectangular (e.g., while 

maintaining second-order slot-clearance), and the 

corresponding increases in stiffnesses, can cause increases 

in frictional resistance. Frank and Nikolai 5 found, 

however, that the smaller contact areas between the wire 

and bracket-slot with binding angulations in 0.020-inch 

round wires produced greater friction than the stiffer 

rectangular wires. They suggested that the point-contacts 

14

of round wire with the slot created larger intensities of 

normal force than did the line-contacts of the rectangular 

wires. 

Brackets 

Orthodontic brackets are marketed in various designs, 

dimensions and materials, and a wealth of information 

exists in the literature regarding the effect of bracket- 

parameters on sliding friction. Influences discussed below 

include bracket material composition, slot size, and 

bracket width. 

Bracket Material Composition 

Clinicians have many choices when selecting the 

material composition of appliances. Stainless steel is the 

most common material of orthodontic brackets. These 

brackets are available to practitioners as cast or 

sintered. Traditionally, stainless steel brackets have 

been manufactured as castings; thereafter, specific 

surfaces are milled. Sintering is a process within which 

the stainless steel particles are compressed at elevated 

temperature into the desired shapes. When compared with 

previous research 23 using the same apparatus and wires, 

Vaughan et al. 29 found that the slots of sintered brackets 

15

produced about 40% to 45% less friction than slots of cast 

brackets. 

Ceramic brackets are a popular choice for many adults 

because of their esthetic appearance. Like stainless steel 

brackets, ceramic brackets are also available in multiple 

designs. Whether they (including the slots) are single- 

crystal sapphire, polycrystalline alumina or zirconia, 

these brackets have generally been found to produce more 

friction than stainless steel brackets with the same wires 

at nonbinding angulations. 4,25-27,36,51,54,80-82 Some 

investigators have not found a difference in frictional 

resistance between stainless steel and ceramic brackets. 35,83 

In an effort to maintain the esthetic advantages of 

ceramic brackets, but reduce the friction potentials 

associated with them, some polycrystalline alumina brackets 

are manufactured with metallic slots. One of these, with a 

stainless steel slot, the Clarity bracket (3M/Unitek 

Corporation, Monrovia, CA), was compared by Cacciafesta’s 

group 36 with conventional ceramic and stainless steel 

brackets. They reported that the steel-slot/ceramic 

bracket produced less friction than the conventional all- 

ceramic bracket, but more than the stainless steel bracket 

with stainless steel, nickel-titanium alloy or ß-titanium 

alloy wires. Kusy and Whitley 84 found that both the Clarity 

16

acket and the gold-lined Luxi bracket (Rocky Mountain 

Orthodontics, Denver, CO) exhibited frictional resistances 

similar to that of stainless steel brackets. In general, 

ceramic brackets with metallic slots were found to be 

acceptable alternatives to all-ceramic brackets. 36,84 

Orthodontic brackets have been manufactured from other 

materials for various reasons. Esthetic plastic brackets 

are available with or without metallic inserts. These 

brackets have generally been found to produce less friction 

than ceramic brackets, although deformation with tight 

ligation (i.e., toward torque control) has been a problem. 7 

Titanium brackets were introduced in response to concerns 

about corrosion and potential sensitivity to the nickel in 

stainless steel. These brackets were found to be very 

similar in frictional resistance to stainless steel 

brackets. 19,85 

Bracket Width and Slot Size 

There is conflicting information in the literature as 

to the effect of bracket width on friction in the fixed 

appliance. Andreasen and Quevedo 44 measured the friction 

produced with three brackets of different slot widths and 

six wires at four second-order angulations and found no 

significant differences in frictional resistance across the 

17

ackets. Peterson’s group 31 also found that bracket width 

had no effect on friction. Frank and Nikolai, 5 however, 

found that frictional force increased as bracket width 

increased. This outcome was allegedly due to decreased 

interbracket distance and to the wider bracket binding at a 

smaller angulation. Other researchers found a similar 

effect, but thought the cause was the mesiodistal slot 

dimension of the wider bracket resulting in greater 

stretching of the ligature, which in turn, lead to 

increased normal forces of ligation. 23 A third group of 

studies found that narrower brackets produced more friction 

than wider brackets. 21,22,81 Drescher’s group 22 believed that 

the increased tipping seen in narrow brackets resulted in 

greater frictional forces. Using biomechanical analysis 

and mathematical formulations, Schlegal 86 determined that 

neighboring brackets had an extraordinary influence on 

friction within a bracket, and, due to this influence, 

single-bracket studies could not accurately determine how 

bracket width affected friction. He concluded that 

interbracket distance, wire stiffness and relative bracket 

position must also be considered when determining the ideal 

slot width. 

Bracket width may have an indirect influence on 

friction due to its relationship with interbracket distance 

18

and wire stiffness. As bracket width increases, the 

distance(s) to the adjacent bracket(s) will decrease, 

resulting in shorter and stiffer sections of wire. 5,7 The 

influence of bracket width is more pronounced at greater 

angulations. 

Slot size has not been found to influence frictional 

resistance in the fixed appliance. 21,27 Kusy, Whitley and 

Prewitt 27 evaluated several factors, and they concluded that 

there was no substantial difference overall in frictional 

resistance between a 0.018-inch and a 0.022-inch bracket- 

slot when each is paired with a comparable-sized archwire. 

Ligation 

Ligation has become a popular topic among researchers 

in the field of orthodontics. Orthodontic products have 

been developed toward reducing friction potential in the 

fixed appliance and some seemingly have suppressed a major 

contributor by augmenting traditional methods of ligation 

within modern bracket designs. Current, common categories 

of ligation are 1) small, ductile, stainless steel wire- 

segments, 2) elastomeric o-rings and ties and 3) self- 

ligation. 

19

Conventional Ligation 

Orthodontic ligatures existed prior to the use of the 

modern fixed appliance. In 1728, Fauchard published a book 

called “Le Chirurgien Dentiste” in which he described his 

“Bandeau” device. Ligatures were extended from this 

horseshoe-shaped device to facilitate simple tooth 

movement. Angle’s edgewise appliance was introduced in 

1925, and the original design has evolved to the most 

commonly used orthodontic appliance today. It was the 

first fixed appliance to feature ligatures as an essential 

part of the appliance. Early ligatures were materially 

precious metals. 49,50 

In modern clinical orthodontics, the conventional 

methods of tying archwires into bracket-slots are with 

either small stainless steel wires or elastomeric ties. 

These ligatures, although relatively inexpensive and easy 

to place, have been criticized with the recent interest in 

orthodontic friction. Studies have shown a relationship 

between normal forces of ligation and resistance to 

sliding. Using a pneumatically controlled surface to 

simulate the force of ligation on a sliding wire, Stannard 

et al. 17 discovered a proportional increase in friction with 

increasing ligating force. Keith, Jones and Davies, 51 with 

three magnitudes of ligating force, found a similar 

20

ligation-friction relationship. The importance of ligating 

technique was demonstrated by Frank and Nikolai 5 ; they found 

ligature-tie force to be the greatest contributor to 

friction at small wire-slot angulations. Berger 52 also 

concluded that, at nonbinding angulations, ligature-force 

was a major contributor to frictional resistance. 

Of the two conventional methods of archwire-ligation, 

elastomeric ligatures have been the more popular because of 

the ease and speed at which they can be placed and removed. 

In addition, patients have enjoyed selecting from the 

numerous colors available. In terms of their effect on 

friction, however, the difference between stainless steel 

and elastomeric ligation has not been so clear. Some 

studies have been unable to show a difference in frictional 

forces generated between these two methods of ligation. 5,53 

Others have reported that elastomeric ties produced less 

friction. 45 Another group of studies found stainless steel 

ligatures to show less friction. 54-57 The inability to 

obtain consistent results might be blamed on differences in 

experimental methods. 56 In addition, it is possible that 

the difficulty in controlling and maintaining ligating 

forces could be another cause of the inconsistency. 17 

Stainless steel ligating forces have been reported to range 

between 0 and 300 grams, depending upon how tightly the 

21

ligature is wound. 7 The force of ligation with elastomeric 

ties has been estimated to be from approximately 50 grams 

to 225 grams with subsequent decay due to “relaxation” of 

the elastomeric material. 34,58 

Recently, an alternative type of separate ligation has 

become available to the orthodontic community, which is 

claimed to retain the ease of elastomeric ligation 

placement and removal while reducing the resistance to 

sliding. This ligature, called the Slide (Leone Orthodontic 

Products, Sesto Fiorentino, Firenze, Italy), is an 

injection-molded polyurethane device that hooks onto the 

tie wings and is placed over the facial surface of a 

conventional bracket-slot. By ligating across the slot 

instead of directly over the wire, the Slide places no 

normal force of ligation, and essentially converts the 

bracket into a tube. An in vitro study showed that this 

ligature produces significantly less sliding friction 

compared to conventional ligation techniques. 59 

Self-Ligation 

In 1933, Boyd filed a patent for the first self- 

ligating bracket, the “Boyd band bracket,” which featured a 

moving bar that passively entrapped the archwire in the 

bracket-slot. Since then, more than 40 self-ligating 

22

designs have been introduced to the orthodontic community. 

Many of the early designs featured variations of three 

basic ligating mechanisms: a passive door, a passive “C- 

clip” and an active spring. 49,60 

It was not until the invention of the Edgelok bracket 

(Ormco Corporation, Glendora, CA) by Wildman in the early 

1970s that self-ligating designs gained widespread exposure 

to orthodontists. Wildman’s design featured a movable cap 

that closed over the facial portion of the slot to 

passively trap the archwire. Because of its passive 

nature, orthodontists found precise control of tooth 

movement to be a challenge. Ormco responded by marketing 

auxiliary rotational collars to help address the 

limitation. 49,60,61 

In 1977, clinical trials began on a new self-ligating 

design called the SPEED bracket (Strite Industries Ltd., 

Cambridge, Ontario, Canada). Developed by Hanson, 62 this 

bracket was innovative in that it featured the first 

bracket-mounted stainless steel spring-clip which held the 

archwire in the slot with a lingually directed force. The 

claimed benefit of this active ligation system was improved 

rotational control. 60,62 

Several modern self-ligating bracket designs have been 

commercially available for the past 30 years, but until 

23

ecently such brackets have had limited sales. The design 

of orthodontic products specifically aimed at minimizing 

friction has resulted in the reintroduction of self- 

ligating bracket systems to mainstream orthodontics. Since 

the introduction of the Damon 2 (Ormco Corporation, 

Glendora, CA) and the In-Ovation (GAC International, 

Bohemia, NY) brackets in 2000, the use of self-ligating 

systems in orthodontic practices has become more common. 63 

Most major orthodontic vendors now offer a self-ligating 

system in addition to traditional, open-slot, bracket 

designs. These newer brackets are claimed to reduce 

friction, contribute to improved hygiene, lessen anchorage 

loss, and shorten chair- as well as treatment-time. 55,63-66 

Several studies have reported that self-ligating brackets 

contribute to lessened sliding-friction potential compared 

to that from traditionally tied brackets. 9,48,55,57,67-70 

Since the recent gain in popularity of self-ligation, 

several new designs have become commercially available to 

the orthodontist. In general, these brackets fall into one 

of two categories based on the design of the slot-closure 

(Table 2-1). An “active” clip is a resilient spring-clip 

that snaps closed and reduces the depth of the slot to 

approximately 0.018 inches. Because this clip can store 

energy when it is activated by a lingual malalignment, a 

24

otated tooth or a twisted rectangular wire, it has the 

potential to deliver lingual force to the wire and help 

bring the tooth into its proper position. 60 The Speed 

bracket, the In-Ovation R bracket and the Time2 bracket 

(American Orthodontics, Sheboygan, WI) all feature active 

clips within their designs. It is suggested by product 

literature that active ligation helps deliver full torque 

expression when a rectangular wire is engaged and pressed 

against the base of the slot. Critics of the clip design 

say, however, that introducing an active component into the 

ligation unnecessarily increases frictional resistance. 

Some investigators have found that any advantage from 

decreased friction with active self-ligating brackets is 

reduced when rectangular wires are placed. 9,48,65,71-74 Other 

researchers have found the same to be true for the passive 

Damon SL II. 75 It has also been suggested that the 

cantilevered clip delivers a diagonally directed force to 

the archwire, in effect reducing the torquing efficiency 

and causing errors in torque expression. 63 

In contrast, “passive” ligating mechanisms, like those 

of the Damon 2, Damon 3 and Damon 3MX brackets and the 

SmartClip bracket (3M/Unitek Corporation, Monrovia, CA), do 

not invade the slot and place no inherent normal force on 

the archwire. These systems feature one of two basic 

25

designs. The passive-slide design of the Damon series of 

brackets utilizes a sliding “door” that closes the slot, 

effectively transforming the bracket into a tube. The 

SmartClip bracket features a nickel-titanium alloy “C-clip” 

lateral to each of the mesial and distal tie-wings 76 ; an 

archwire that is snapped into the bracket-slot may remain 

passive in the lumens of the clips. The claimed benefit of 

passive self-ligation is reduced friction with a variety of 

wire sizes, resulting in faster tooth movement. 77 With the 

lack of a lingually directed force on the archwire, 

however, some critics argue that controlling torque could 

be a problem. 58 In addition, Harradine 63 points out that, in 

theory, a passively ligated bracket with an engaged 

rectangular wire, having a faciolingual dimension of 0.025 

inches, could bring a facially displaced tooth only to 

within 0.002 inches of the adjacent teeth because of its 

slot depth; usually it is approximately 0.027 inches. An 

active clip would, theoretically, not have this problem 

because it “squeezes” in the slot an archwire as small as 

0.018 inches in the faciolingual dimension. Harradine 63 

stated, however, that a remaining, clinically significant 

malalignment was unlikely. In two investigations, no 

significant difference between either the SmartClip bracket 

or the Damon 2 bracket and a conventional bracket in regard 

26

to incisor irregularity after initial alignment was 

found. 78,79 

Other Factors Influencing Friction 

Saliva 

Although the role of saliva as a potential lubricant 

for the sliding of wires through slots has been studied by 

several researchers, there has been no clear answer as to 

the effect of saliva on intraoral friction. In one of the 

earliest studies, Andreasen and Quevedo 44 found no 

significant difference in friction between “wet” and “dry” 

samples. Possible explanations for this finding were the 

following: 1. Saliva may not be good lubricant for the slot 

and wire materials; or 2. Forces at the contact area shared 

by the wire and bracket-slot were so great that the fluid 

was expelled from that area. Tselepis, Brockhurst and 

West 33 found a significant reduction in friction in the 

“wet” state. Saunders and Kusy 87 similarly found a decrease 

in friction when saliva was introduced between two 

contacting titanium surfaces. Others have found, however, 

some increases in frictional resistance with the addition 

of saliva. 17,53,83 These conflicting results were suggested 

by Kusy, Whitley and Prewitt 27 to be related to the surfaces 

in contact. They found that the lubricating or adhesive 

27

ehavior of saliva depended on the material composition of 

the slots and wires. For example, when saliva was 

introduced in stainless steel slots, it produced decreases 

in frictional resistance with ß-titanium alloy wires, but 

an adhesive effect with stainless steel wires. 

Occlusal Forces 

In the human dentition, the deformable periodontal 

ligament allows minute movements of the teeth to aid in 

distribution of forces from occlusal function. These 

forces, that can arise as a result of speaking, swallowing, 

or normal masticatory function, are heavy (1 kg to 50 kg) 

and intermittent, occurring thousands of times per day for 

one second or less. 8,88 These brief movements of the teeth 

alter the normal forces between the crown-attachment slot 

and wire, constantly breaking and resetting “friction 

locks.” 5 Studies have been conducted to determine the 

effect of perturbations (extraneous, small actions 

simulating mastication, swallowing) on frictional forces in 

the orthodontic appliance. Braun’s group, 88 with an in 

vitro model, found a reduction in sliding resistance 

proportional to the magnitude of extraneous forces. Using 

a half-arch model, Lingenbrink 89 found an average decrease 

in kinetic frictional forces of 49% when perturbations were 

28

added. Similarly, Bunkall 15 noted reductions in average 

kinetic friction and maximum static friction of 35 to 70%. 

Second-Order Angulation, Binding and Notching 

Several studies have shown that, as second-order 

angulation between the bracket-slot and the archwire 

increases, friction also increases. 5,21,24,31,33,44,80,90 

Classical friction from ligating force is largely 

responsible for frictional resistance when the second-order 

angulation is less than the angle at which binding occurs. 5 

This angle is called “critical” and is defined as the 

second-order angulation at which the wire just contacts two 

diagonally opposing edges of the bracket-slot, reducing the 

wire-slot clearance to zero. 91 When the angle exceeds the 

critical value for the bracket-archwire combination, 

binding becomes an influential factor in resistance to 

sliding. 92 Factors that affect binding are archwire size, 

bracket-slot geometry, and interbracket distances. 57 

Thorstenson and Kusy 93 reported that ligation type seemed to 

have an effect on only classical friction because they did 

not influence binding when the brackets were positioned at 

an angulation beyond the critical contact angle. 

If the wire-slot angulation substantially exceeds the 

critical contact angle, a physical deformation of a round 

29

wire at one or both of its contact points with the edge of 

the slot, known as mechanical notching, can occur, further 

adding to the resistance to sliding. 70,94 In a clinical 

study, this damage to the archwire was found to be related 

to the design of the orthodontic bracket. 95 The main effect 

of archwire-notching on friction is the creation of 

“obstacles” that impede relative wire-slot sliding. 96 It 

appears that notching may be a function of the materials in 

contact. Kusy et al. 30 found that ceramic brackets cause 

more notching than stainless steel brackets. Similarly, 

Articolo’s group 96 found that notching of archwires was 

three times more prevalent and severe with ceramic brackets 

than with stainless steel brackets. 

Third-Order Torque 

The term “third-order torque” in orthodontics pertains 

to the rotational control and movement of a tooth crown or 

root faciolingually. This type of tooth movement can occur 

subsequent to twisting a square or rectangular archwire 

along its longitudinal axis, required to place it into the 

slot of a crown-attachment. In this process, two contact 

forces acting on the occlusal and gingival walls of the 

slot by partial archwire deactivation create a third-order 

30

couple, resulting in the delivery in the faciolingual plane 

of torsional forces to the tooth. 97,98 

The preadjusted edgewise appliance is designed with a 

specific amount of slot-/pre-torque for each tooth in the 

arch to aid in achieving optimal crown- and root- 

positioning. Theoretically, this torque will be expressed 

when a full-size archwire is allowed to deactivate 

completely over time after being seated in the slot of a 

properly placed bracket. When a rectangular wire not 

completely filling the slot is engaged, a certain amount of 

rotation around the longitudinal axis of the wire can occur 

before the occlusogingival clearance within the slot 

becomes zero and third-order rotational forces are 

transmitted to the crown-attachment. This clearance-angle 

is known as “slop” or “play,” and its magnitude is 

primarily dependent on the shape and dimensions of the wire 

and slot, as well as the amount of edge-bevel in the wire 

cross-section. 99-101 The difference between the appliance- 

torque and this clearance-angle gives the effective torque, 

the estimated amount of third-order torque that the 

bracket-wire combination will express after deactivation of 

the wire. 98 Because most orthodontic treatment is 

undertaken with less than full-size archwires, some 

preadjusted brackets include accentuated torque in the 

31

maxillary- incisor brackets so that finishing with 0.019- x 

0.025-inch wires will still result in optimal root 

positioning. 102 

The vendor-stated sizes of both the wire and the slot 

are nominal dimensions because of manufacturing tolerances 

that exist in the fabrication processes. Actual dimensions 

are not reported by the vendor. Sebanc et al. 98 measured 

dimensions of bracket-slots with a traveling microscope and 

the dimension(s) of various orthodontic-wire cross-sections 

with a micrometer. They found that slot dimensions were 

generally larger than their nominal values. Actual wire 

dimensions were generally found to be equal to or smaller 

than nominal sizes, but all were within 0.0005 inches. 

Meling and Ødegaard. 100 found a range of ±0.0005 inches in 

actual wire heights across the wires of seven wire-vendors. 

Kusy and Whitley 94 measured archwires and bracket-slots, and 

they found that 30% of the wire specimens were larger than 

suggested by their nominal dimension(s). Of the bracket- 

slots tested, 15% of the measurements were smaller than the 

vendor-stated values. The abilities of the manufacturers, 

or lack thereof, to accurately produce wires of stated 

dimensions can affect the amount of torque expressed in the 

bracket-slots. 101,103 

32

Another factor that influences bracket-wire torque 

expression is the elastic modulus of the bracket-slot. 

Harzer, Bourauel and Gmyrek 104 compared slot-deformations, 

polycarbonate brackets versus stainless steel brackets, and 

found higher torque losses and smaller torquing moments in 

the plastic brackets. Others found similar results. 105,106 

Kapur, Sinha and Nanda 107 compared the structural integrity 

of titanium brackets with that of stainless steel brackets 

when both were subjected to torsional forces from an 

archwire, and concluded that the titanium brackets 

demonstrated less deformation. 

The effect of third-order discrepancies in bracket 

alignment on frictional resistance has not been extensively 

evaluated in the orthodontic literature. Using an Instron 

testing machine, Moore, Harrington and Rock 108 discovered a 

significant increase in sliding friction with increased 

third-order torque in a single-bracket study. Sims and 

colleagues 68 also evaluated friction produced with wires 

sliding through three consecutive bracket-slots, with the 

middle bracket given predetermined torque values. They 

reported that, with third-order activation present, the 

self-ligating Activa bracket (‘A’- Company, San Diego, CA) 

showed consistently less resistance to mesiodistal sliding 

than did sets of two conventionally ligated brackets. 

33

Summary 

The literature supports the thought that many factors 

play a role in the friction generated between the wire and 

bracket-slot in orthodontic treatment. These factors 

include properties related to the archwire, bracket, 

ligation type, and oral environment. 

New products, such as low-friction, self-ligating 

brackets, are being developed to help reduce sliding 

resistance associated with tooth movement. To obtain a 

thorough understanding how to best use these products in 

clinical orthodontics, it is important to study them in a 

simulated dental arch with the variables influencing 

friction controlled. It is for this reason, the present 

study has been undertaken. 

34

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resistance in titanium and stainless steel brackets. Am J 


86. Schlegel V. Relative friction minimization in fixed 

orthodontic bracket appliances. J Biomech 1996;29:483-491. 

87. Saunders CR, Kusy RP. Surface topography and frictional 

characteristics of ceramic brackets. Am J Orthod 


88. Braun S, Bluestein M, Moore BK, Benson G. Friction in 

perspective. Am J Orthod Dentofacial Orthop 1999;115:619- 

627. 

89. Lingenbrink JC. The effect of extraneous intra-oral 

force on wire-slot friction potentially impeding leveling 

and aligning during orthodontic therapy. Master’s Thesis. 

Center for Advanced Dental Education. Saint Louis 

University. St. Louis, MO. 2006. 

90. Ogata RH, Nanda RS, Duncanson MG, Jr., Sinha PK, 

Currier GF. Frictional resistances in stainless steel 

bracket-wire combinations with effects of vertical 

deflections. Am J Orthod Dentofacial Orthop 1996;109:535- 

542. 

91. Kusy RP, Whitley JQ. Assessment of second-order 

clearances between orthodontic archwires and bracket slots 

via the critical contact angle for binding. Angle Orthod 

1999;69:71-80. 

92. 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 


44

93. Thorstenson GA, Kusy RP. Effects of ligation type and 

method on the resistance to sliding of novel orthodontic 


states. Angle Orthod 2003;73:418-430. 

94. Kusy RP, Whitley JQ. Influence of archwire and bracket 

dimensions on sliding mechanics: derivations and 

determinations of the critical contact angles for binding. 

Eur J Orthod 1999;21:199-208. 

95. Hansen JD, Kusy RP, Saunders CR. Archwire damage from 

ceramic brackets via notching. Orthod Rev 1997;11:27-31. 

96. Articolo LC, Kusy K, Saunders CR, Kusy RP. Influence of 

ceramic and stainless steel brackets on the notching of 

archwires during clinical treatment. Eur J Orthod 

2000;22:409-425. 

97. Nikolai RJ. Bioengineering analysis of orthodontic 

mechanics. Philadelphia: Lea & Febiger, 1985:pp 53-56. 

98. Sebanc J, Brantley WA, Pincsak JJ, Conover JP. 

Variability of effective root torque as a function of edge 

bevel on orthodontic arch wires. Am J Orthod 1984;86:43-51. 

99. Johnson E. Relative stiffness of beta titanium 

archwires. Angle Orthod 2003;73:259-269. 

100. Meling TR, Odegaard J. On the variability of crosssectional 

dimensions and torsional properties of 

rectangular nickel-titanium arch wires. Am J Orthod 


101. Meling TR, Odegaard J, Meling EO. On mechanical 

properties of square and rectangular stainless steel wires 

tested in torsion. Am J Orthod Dentofacial Orthop 

1997;111:310-320. 

45

102. McLaughlin RP, Bennett JC, Trevisi HJ. Systemized 

orthodontic treatment mechanics. Edinburgh, Scotland, 

Mosby, 2001. 

103. Gioka C, Eliades T. Materials-induced variation in the 

torque expression of preadjusted appliances. Am J Orthod 


104. Harzer W, Bourauel C, Gmyrek H. Torque capacity of 

metal and polycarbonate brackets with and without a metal 

slot. Eur J Orthod 2004;26:435-441. 

105. Feldner JC, Sarkar NK, Sheridan JJ, Lancaster DM. In 

vitro torque-deformation characteristics of orthodontic 

polycarbonate brackets. Am J Orthod Dentofacial Orthop 

1994;106:265-272. 

106. Sadat-Khonsari R, Moshtaghy A, Schlegel V, Kahl-Nieke 

B, Moller M, Bauss O. Torque deformation characteristics of 

plastic brackets: a comparative study. J Orofac Orthop 

2004;65:26-33. 

107. Kapur R, Sinha PK, Nanda RS. Comparison of load 

transmission and bracket deformation between titanium and 

stainless steel brackets. Am J Orthod Dentofacial Orthop 

1999;116:275-278. 

108. Moore MM, Harrington E, Rock WP. Factors affecting 

friction in the pre-adjusted appliance. Eur J Orthod 

2004;26:579-583. 

46

Tables 

Table 2-1: Partial Overview of 

Self-Ligating Brackets. 

Year Bracket 

47 

Mode of 

Action 

1933 Boyd band bracket Passive 

1933 Ford lock Passive 

1952 Russell appliance Passive 

1953 Schurter device Passive 

1957 Rubin device Passive 

1966 Branson Passive 

1972 SPEED System Active 

1972 Edgelok bracket Passive 

1979 Mobil-Lock bracket Passive 

1986 Activa bracket Passive 

1995 Time bracket Active 

1996 Damon bracket Passive 

1998 Twinlock bracket Passive 

2000 In-Ovation bracket Active 

2000 Damon 2 bracket Passive 

2002 In-Ovation R bracket Active 

2004 Time2 bracket Active 

2004 Damon 3 bracket Passive 

2005 SmartClip bracket Passive 

2006 Damon 3MX bracket Passive 

Modified from Woodside, Berger and Hanson, 2005 60

CHAPTER 3: JOURNAL ARTICLE 

Abstract 

Few studies have evaluated the effect of wire-slot 

torque on sliding friction. Apparently, no studies have 

been published to date that compare friction across 

categories of self-ligating brackets when third-order 

positioning is controlled. The purpose of this study was 

to determine the effects of wire-slot torque and type of 

self-ligating bracket on the average kinetic friction in 

sliding mechanics with a 0.019- x 0.025-inch stainless 

steel archwire. Five sets of crown-attachments (including 

In-Ovation R, Time2, Damon 3MX, SmartClip and Victory 

brackets) were tested for frictional resistance in a 

simulated posterior dental segment with -15, -10, -5, 0, 

+5, +10, and +15 degrees of torque placed in the maxillary 

right second-premolar bracket. 

Increasing the torque from 0 to ±15 degrees produced 

significant increases of frictional resistance in all five 

of the tested attachment-sets. At 0 degrees of torque, the 

sets with passive self-ligating brackets produced less 

friction than the sets with active self-ligating brackets, 

and all four self-ligating bracket sets produced 

48

significantly less friction than the set with 

elastomerically ligated Victory brackets. At ±10 degrees 

of torque, all five attachment sets displayed similar 

resistances with the exception of the In-Ovation R set at 

+10 degrees. At ±15 degrees of torque, the In-Ovation R 

and the SmartClip sets produced significantly larger 

frictional resistances than the other three sets. 

The data suggest that the presence of third-order 

torque can influence the kinetic frictional resistances in 

posterior dental segments during anterior retraction using 

sliding mechanics with self-ligating brackets and that 

frictional resistance will increase at a greater rate when 

the torque exceeds ±10 degrees with the present combination 

of sizes of slots and wire. Furthermore, whether a self- 

ligated bracket is active or passive may not be clinically 

significant regarding friction in the presence of torque 

approaching and exceeding 15 degrees. 

49

Introduction 

Friction is defined as the resistance to motion when 

one object moves or tends to move tangentially relative to 

another object. 1 The total contact-force between the 

objects may be expressed as two components when there is 

attempted or actual relative motion between surfaces in 

contact. One component, the normal force, is a pushing 

force with an orientation perpendicular to the shared 

contact-surface. The frictional force component impedes 

movement between the surfaces and is, therefore, opposite 

in direction to that of intended or actual motion. 2 The 

maximum static or the kinetic frictional force (F) tangent 

to the two surfaces is often hypothesized as proportional 

to the normal force, as expressed by the equation F = µN, 

where µ is a coefficient of friction between the surfaces, 

and N is the normal force at the shared contact surface of 

the objects. 3 The coefficient of friction is a constant 

which is related to characteristics of the contacting 

surfaces of the objects. 4 

Because frictional force acts in a direction opposite 

to the intended path of the object to be displaced, and 

sliding mechanics are commonplace in orthodontic therapy, 

an understanding of friction is necessary to achieve 

50

optimal clinical results. Fixed-appliance therapy involves 

at least some relative (mesiodistal) wire-slot displacement 

in various phases of treatment; hence, the generation of 

friction during tooth movement can be problematic for the 

orthodontist. Because a portion of the force for delivery 

to a tooth-crown to be displaced may be necessary to 

overcome frictional resistance, the orthodontist must be 

sure to use a force of sufficient magnitude to also 

initiate a biological response in the supporting tissues. 4 

The application of sliding mechanics in orthodontics 

has increased since the introduction of the pre-adjusted 

edgewise appliance system. 5 The process can involve the 

guidance of a tooth along a continuous archwire or the 

movement of the wire through the crown-attachment slot(s). 

In particular, overjet reduction and space closure have 

been traditionally accepted applications of sliding 

mechanics. In a first premolar extraction case, a space is 

created between the canine and the second premolar. When 

maximum anchorage is desired, the canine would first be 

retracted bodily with the archwire guiding its 

displacement. This single tooth movement would likely 

create unwanted friction that could cause “side effects” 

such as uncontrolled tipping, loss of posterior anchorage, 

or deepening of the overbite. 6 Forces acting posteriorly on 

51

the anterior portion of the archwire would then be created 

to retract the incisors into the remaining spaces while 

allowing the excess wire to slide through the posterior 

brackets and tubes. Any wire-slot friction in the buccal 

segments would hinder the movement of the anterior segment 

and, therefore, could delay space closure. 7 

The popularity of sliding mechanics in orthodontics 

has produced considerable research interest in frictional 

forces generated between bracket-slot and archwire. Many 

studies have identified multivalued factors that can 

contribute to or affect friction within the fixed 

orthodontic appliance. These parameters include alloy- 

composition, 1,8-27 surface-roughness, 2,7,9,14,15,28-31 archwire 

cross-sectional shape and size, 2,14,22,25,27,32-34 ligation 

method, 2,4,5,8,25,34-46 bracket/slot material surface 

properties, 1,10,16-18,20,27,35,37,47-52 bracket width, 2,4,12,13,22,33,49 

lubrication, 8,18,24,53-55 extraneous occlusal forces, 56-58 

second-order angulation, 2,12,15,22,24,33,46-48,59,60 and third-order 

torque. 44,61 

Several modern self-ligating bracket designs have been 

commercially available for the past 30 years, but until 

recently such brackets did not have widespread use. The 

design of orthodontic products specifically aimed at 

minimizing friction has resulted in the reintroduction of 

52

self-ligating bracket systems to mainstream orthodontics. 

These newer brackets are claimed to reduce friction, 

contribute to improved oral hygiene, lessen anchorage loss, 

and shorten chair- time as well as treatment-time. 38,62-65 

Several studies have reported that self-ligating brackets 

generate less sliding friction than elastomerically tied 

brackets. 5,38,40,42-46 

In general, self-ligating brackets fall into one of 

two categories based on the design of the slot-closure. An 

“active” design features a resilient spring-clip that snaps 

closed and reduces the faciolingual slot depth to 

approximately 0.018 inches. Because this clip can store 

energy when it is activated by a lingual malalignment, a 

rotated tooth or a twisted rectangular wire, it has the 

potential to exert lingual force on the wire and help bring 

the tooth into its proper position. 66 Critics of the clip- 

design say, however, that introducing an active component 

into the ligation unnecessarily increases frictional 

resistance. 67 Some investigators have found that any 

advantage from decreased friction with active self-ligating 

brackets is reduced when rectangular wires are 

placed. 5,43,63,68-71 It has also been suggested that the 

asymmetric design of the cantilevered clip delivers a 

diagonally directed force to the archwire, in effect 

53

educing the torquing efficiency and causing errors in 

torque-expression. 64 

In contrast, a “passive” ligating mechanism does not 

reduce the depth of the slot and places no inherent normal 

force on the archwire. These systems have one of two basic 

designs. The passive-slide design utilizes a sliding 

“door” that closes the slot, effectively transforming the 

bracket into a tube. 67 Another passive ligation design 

features a nickel-titanium alloy “C-clip” mechanism lateral 

to each of the mesial and distal tie-wings 72 ; an archwire 

that is snapped into the bracket-slot may remain passive in 

the lumens of the clips. The claimed benefit of these 

passive self-ligation systems is reduced friction with all 

wire sizes, resulting in faster tooth movement. 73 With the 

absence of a lingually directed force against the archwire, 

however, some critics argue that the inability to control 

torque could be a problem. 41 For this reason, passive self- 

ligating brackets are manufactured with a faciolingual 

slot-dimension as small as 0.027 inches, instead of the 

traditional 0.028 inches minimum. 

In orthodontics, friction arises when there is contact 

and a tendency for mesiodistal sliding of an archwire 

relative to the slot. When a small rectangular wire not 

completely filling the slot is engaged, some amount of 

54

unconstrained rotation around the longitudinal axis of the 

wire can occur. If and when the occlusogingival clearance 

within the slot becomes zero, third-order rotational forces 

are created to be transmitted to the crown-attachment 

through direct contact with the slot. Moore, Harrington, 

and Rock 61 measured friction in two different brackets with 

predetermined tip and torque. The group discovered a 

significant increase in friction in the presence of active, 

third-order torque. Using an Instron testing machine, Sims 

and colleagues 44 also evaluated friction produced with wires 

sliding through bracket-slots positioned to input specific 

torque values. They reported that, with torsion, the self- 

ligating Activa bracket (‘A’ Company, San Diego, CA) showed 

consistently less resistance to sliding than the two 

conventionally ligated brackets. 

Apparently no studies have been published to date that 

compare friction across categories of self-ligating 

brackets when third-order positioning is controlled. The 

purpose of this study was to determine the effect of wire- 

slot torque on friction in 0.022-inch crown-attachment sets 

that included self-ligating brackets with a 0.019- x 0.025- 

inch stainless steel archwire engaged. The effect of the 

design of the various ligating mechanisms on kinetic 

55

friction with active torque present in the wire and/or slot 

was also evaluated. 

Materials and Methods 

The posterior maxillary right quadrant with a first 

premolar extracted and canine retracted was simulated to 

evaluate the friction produced in a buccal segment during 

retraction of the half-incisal segment; third-order torque 

was generally activated at the second premolar position. A 

0.019- by 0.025-inch stainless steel wire was selected for 

this study because it is frequently selected as the 

retraction archwire. The two independent variables 

controlled in this study were the bracket ligation design 

and the third-order torque angle at the second premolar 

bracket. The dependent variable was the kinetic friction 

generated in the appliance when a wire was slowly pulled 

posteriorly through the crown-attachments. 

The friction testing device is described in the 

Master’s thesis by Bunkall. 58 The device consists of a 

series of aluminum cylinders (“teeth”) mounted into a base- 

plate in an archform representing a maxillary quadrant. 

Through each cylinder is an adjustable stainless steel rod 

with an attached brass faceplate that simulates the facial 

56

surface of a tooth-crown. The construction of the cylinder 

subassembly allows the faceplate to be positioned in all 

three dimensions of space. The mechanism was fabricated to 

enable the control of multiple bracket-slot locations and 

orientations. In the present study, four aluminum 

cylinders, representing the maxillary right canine, second 

premolar, first molar and second molar, were inserted into 

the four posterior mounting holes in the aluminum base- 

plate (Figure 3-1). The stainless steel rod and knuckle- 

joint set-screw were rotated 90 degrees on each “tooth” to 

aid in the third-order positioning of the 0.022-inch 

brackets and tubes. Crown-attachments were bonded to the 

brass faceplates. 

Seven bracket-positioning templates were fabricated 

from 0.022-inch-thick steel plates. Each template was 

prepared to enable control of the positions of the slots of 

the four crown-attachments; the slots were temporarily 

“engaged” and “filled” by the working edge of the template. 

At the site of the second-premolar bracket-slot, a 

rectangular section of the steel plate was cut away, 0.025 

inches from the working edge of the template. The cutout 

left a 0.022- by 0.025-inch cross-section within each of 

the six templates; the small “bar” was inelastically 

rotated along its central longitudinal axis to one of six 

57

specific angles relative to the plane of the template to 

enable torque-placement in the second-premolar slot (Figure 

3-2). The seventh template was left uncut to place zero 

degrees of torque at the second premolar. Each template as 

a whole was initially flat and shaped to place the canine 

and first-molar attachment-slots in zeroed first- and 

second-order positions, while also controlling the location 

of the second-premolar bracket-slot (Figure 3-3). The 

second-molar tube was aligned with a 0.021- by 0.025-inch, 

straight wire-segment cantilevered from the three adjacent 

attachment-slots set at zero degrees of torque. 

Each “test specimen” consisted of two brackets, two 

molar tubes and a stainless steel archwire. Affixed at the 

first-molar site was a self-ligating first-molar tube with 

a facial slide mechanism and a 0.022-inch slot (SLBUCCAL, 

Ormco Corporation, Glendora, CA; Figure 3-4). This crown- 

attachment can be opened like a standard converted molar- 

tube; it permitted the insertion of the slot-positioning 

template, and the slide was closed during testing to enable 

its functioning as a standard unconverted four-walled 

buccal tube. The second-molar attachment was a 0.022-inch 

slot, maxillary single tube (Part Number 68-172-82; GAC 

International, Bohemia, NY). The archwires were 0.019- by 

58

0.025-inch NuBryte Standard Arch stainless steel wires 

(Part Number 03-925-51; GAC International, Bohemia, NY). 

Because transmission of third-order torque-forces is 

directly influenced by wire size, ten percent of the test- 

wires (21 wires) were arbitrarily chosen and measured with 

a digital micrometer (Model APB-2D, Mitutoyo Corporation, 

Kanagawa, Japan). Their average cross-sectional dimensions 

were calculated toward third-order clearance estimates. 

Five different pairs of canine and second-premolar 

brackets, all with 0.022-inch slots, were selected for this 

study. The “passive” self-ligating attachments were Damon 

3MX brackets (Ormco Corporation, Glendora, CA) with passive 

facial slides (Figure 3-5) and SmartClip brackets 

(3M/Unitek Corporation, Monrovia, CA) with passive C-clips 

(Figure 3-6). The “active” self-ligating attachments were 

In-Ovation R brackets (GAC International, Bohemia, NY; 

Figure 3-7) with sliding spring-clips and Time2 brackets 

(American Orthodontics, Sheboygan, WI; Figure 3-8) with 

rotating spring-clips. The traditional crown-attachments 

were the Victory-series MBT brackets (3M/Unitek 

Corporation, Monrovia, CA; Figure 3-9); wires were tied in 

the slots with silver Unistick elastomeric ligatures (Part 

Number 854-262; American Orthodontics, Sheboygan, WI). 

59

Individual test-subsamples had the second-premolar 

bracket-slot oriented at third-order torque values of -15, 

-10, -5, 0, +5, +10, and +15 degrees; the other three slots 

were fixed at zero torque. (A negative/positive torque- 

angle should produce lingual/facial tooth-crown tipping.) 

One set of four crown-attachments was used for testing at 

all torque values. The order of torque values during the 

testing of each set was randomized to reduce the bias due 

to slot-wear on the results. The research design consisted 

of all combinations of the five crown-attachment/ligation 

sets and seven torque values. Based on previous results, 44 

six replications for each bracket-torque combination (210 

total tests) were anticipated to be sufficient. 

Brackets and molar tubes were affixed to the brass 

faceplates with cyano-acrylate adhesive (Loctite Super Glue 

Gel, Henkel Consumer Adhesives, Gulph Mills, PA). The 

brackets and tubes were positioned, collectively aligned, 

with the slot-positioning templates and the previously 

mentioned wire-segment. A new archwire was engaged in the 

attachment-slots and ligated for each test. New 

elastomeric ligatures were placed prior to each test with 

Victory brackets using a Straight Shooter ligature gun (TP 

Orthodontics, LaPorte, IN) to produce the same amount of 

short-term prestretch in all elastomeric ties. With the 

60

test-archwire in place and ligated, the simulated dental 

segment was mounted to the fixed head of a universal 

testing machine (Model 1011, Instron Corporation, Canton, 

MA) with the posterior, held end of the archwire oriented 

vertically. A custom attachment was fastened to the 

moveable head of the Instron testing machine (Figure 3-10), 

equipped with a ten-pound load transducer. This attachment 

was fabricated with a four-pronged “pencil chuck,” by which 

one posterior end of the test-wire was grasped. The 

testing machine and an attached chart recorder (Model 2310- 

069, Instron Corporation) were turned on simultaneously. 

The wire was pulled posteriorly through the crown- 

attachments at a rate of one millimeter per minute for 90 

seconds while the chart recorder produced a force-versus- 

displacement plot. Testing was performed in the dry state 

and at room temperature. The load range was set at 0 to 

1000 grams. The testing machine was initially calibrated 

and checked after changes of crown-attachment sets. From 

each test the mean load, which was virtually equal to the 

frictional-force magnitude, was determined from ten plot- 

points taken at six-second intervals between the 30-second 

and 90-second marks on the plot. 

61

Results 

The data were analyzed using SPSS software, version 

14.0 (SPSS, Inc., Chicago, IL). The mean frictional 

resistances and standard deviations thereof, associated 

with five individual crown-attachment sets and each of the 

seven torque values, are shown in Table 3-1. Figure 3-11 

displays the mean frictional resistances from each of the 

crown-attachment sets; the seven means (associated with 

torque-angles) for an individual set are connected in order 

by straight lines. Significant differences in mean 

frictional resistances across pairs of third-order torque 

values from each set were statistically analyzed with the 

Mann-Whitney U test (Table 3-2). Kruskal-Wallis one-way 

analyses of variance and post-hoc Tukey comparisons 

determined significant differences (p < 0.05) between 

frictional resistances across the five crown-attachment 

sets at each of the seven torque angles and are presented 

in Tables 3-3 and 3-4. 

Actual test-archwire dimensions were determined to be 

equal to their nominal sizes. The average width and height 

of the wires were 0.0190 and 0.0250 inches, respectively. 

Neither +5 nor -5 five degrees of third-order rotation 

resulted in significant changes in frictional force from 

62

aseline values at 0 degrees of torque with the exception 

of the SmartClip set, significantly greater at both the 

positive and negative torques, and the Time2 set, but only 

at +5 degrees of torque (Table 3-1). Increasing torque 

from 0 to ±10 degrees produced significant increases in 

frictional resistance from all four sets of self-ligating 

attachments (Table 3-2). Among the self-ligating sets, the 

In-Ovation R and the SmartClip sets showed significantly 

more friction from a further increase from both +10 to +15 

and -10 to -15 degrees of torque; the Time2 set displayed a 

significant increase only from -10 to -15 degrees. The 

elastomerically ligated Victory sets showed the smallest 

overall increase in friction when torque-angle was 

increased, ranging from 303 grams at 0 degrees to 551 grams 

at -15 degrees. The SmartClip sets displayed the smallest 

mean frictional force of 55 grams at 0 degrees, but also 

provided the greatest resistance increase, producing a 

force of 744 grams at +15 degrees (Table 3-1). 

At +5, 0 and -5 degrees of torque, the Victory crown- 

attachment set generally produced significantly more 

friction than the four self-ligating sets; the single 

exception was the Time2 set at +5 degrees (Table 3-4). The 

Damon 3MX and SmartClip sets produced the smallest mean 

frictional forces at 0 degrees of torque. 

63

There were no significant differences in mean 

frictional forces produced across the five attachment-sets 

at -10 degrees of torque. At +10 degrees, however, the In- 

Ovation R set produced significantly greater frictional 

resistance than each of the other four attachment-sets. 

At +15 and -15 degrees of torque, the In-Ovation R and 

SmartClip sets generated significantly greater mean 

frictional forces than the other three sets; the forces 

from each of these two sets were statistically equal at 

these torque angles (Table 3-4). The In-Ovation R and 

SmartClip sets produced forces of 757 grams and 744 grams, 

respectively, and 752 grams and 736 grams, respectively, at 

+15 and -15 degrees (Table 3-1). The Victory, Time2 and 

Damon 3MX sets produced mean frictional forces that were 

statistically equal to each other at these angulations. 

Effect of Torque 

Discussion 

Increasing torque in the second-premolar slot from 0 

to and beyond ±10 degrees caused increases in frictional 

forces from all of the tested attachment-sets except the 

Victory set from 0 to -10 degrees. This effect was not 

seen from most of the sets when the torque-angle was 

64

increased to only five degrees. These observations tend to 

support the suggestion 61 that torque will not have a 

dramatic effect on mesiodisal sliding friction until it 

exceeds the third-order clearance angle of the wire-slot 

combination. Reportedly, the clearance torque-angle for a 

fully drawn, 0.019- x 0.025-inch wire in a 0.022-inch open 

slot is about 10 degrees. 74 Presently, beyond 10 degrees of 

third-order rotation, an increase in friction due to the 

creation of occlusogingival normal forces between the wire 

and the bracket-slot would be expected because of the 

torsional couple transmitted from the twisted archwire. 75 

In addition, geometric calculations suggest that a 0.019- x 

0.025-inch wire rotated 10 degrees in a bracket-slot would 

occupy a buccolingual dimension of 0.0276 inches (Figure 3- 

12). With the Damon 3MX and Smartclip brackets having slot 

depths of 0.027 and 0.0275 inches, respectively, the slots 

of the two passive self-ligated brackets are 

“buccolingually filled,” implying that the ligating 

mechanism can play a role in frictional resistance with 

active torques approaching and exceeding 10 degrees. 

Active self-ligating attachments, such as the Time2 

and the In-Ovation R brackets, may behave differently from 

passive brackets when third-order rotations are introduced. 

Each clip is cantilevered occlusogingivally such that it 

65

enters the slot asymmetrically, contacting a rectangular 

wire along either a gingival or occlusal edge. An engaged 

0.019- x 0.025-inch archwire with zero torque would be 

expected to deflect the clip of either bracket. 76 A third- 

order rotation of the slot relative to the archwire, 

depending upon its sense, could potentially cause more or 

less deflection of the clip, thereby affecting the 

faciolingual normal forces exerted by the wire and the 

accompanying components of the frictional force system. 

The Time2 set generated larger frictional forces at +5 

degrees than at -5 degrees of torque. When comparing 

frictional resistances at +10 degrees and -10 degrees of 

torque, both the Time2 and In-Ovation R brackets showed 

greater forces at the positive third-order angulation. 

This finding might be explained by the asymmetrical nature 

of the clip-designs. 

The Victory set also produced a larger mean frictional 

force at +10 degrees of torque than at -10 degrees. One 

possible explanation could be the occlusogingival asymmetry 

of the tie-wings of the Victory bracket design (Figure 3- 

9); when viewed from a mesiodistal perspective, the 

occlusal tie-wing apparently extends farther facially than 

the gingival tie-wing, suggesting that the elastomeric 

module could have been lying across the wire with more 

66

tension on one edge of the wire and/or the direction of the 

net normal force from the tie was skewed. 

Only the SmartClip set showed a significant increase 

in friction with every five-degree increase in torque (in 

either twist-direction). Because 5 degrees of third-order 

rotation from 0 degrees does not eliminate the wire-slot 

clearance with this bracket-wire combination, a possible 

reason for the observed increase in friction could be the 

contact of the nickel-titanium-alloy “C-clips” with the 

wire during testing. Any contact of the wire with the 

clips during sliding could have produced a notable 

contribution to frictional resistance; a previous 

orthodontic-materials study found nickel-titanium-alloy 

wire to have a relatively large kinetic frictional 

coefficient when paired with a stainless steel bracket. 18 

Effect of Bracket Design 

At zero degrees of torque, the results of this study 

were similar to those from a previous research-effort 46 that 

evaluated friction in both self-ligating and traditionally 

ligated brackets. In the present study, with no torque 

imposed, mean frictional resistance was found to be 

significantly less from each of the four self-ligation sets 

when compared to that from the Victory set (brackets tied 

67

with elastomeric ligatures). Friction values obtained from 

both passive self-ligating sets at ±5 degrees remained 

significantly smaller than the friction produced by the 

Victory set, likely due to the absence of any other than 

incidental contact from ligation within these self-ligating 

bracket-slots. 

With the exception of the In-Ovation R set and 

positive angles, increasing the torque from ± 5 to ±10 

degrees brought the frictional resistances from the self- 

ligating attachment-sets to magnitudes similar to those 

from the Victory sets. This finding contrasted outcomes 

from a previous study 44 that found self-ligating brackets to 

produce smaller frictional forces than traditionally 

ligated brackets with torque placed. In the present 

research, interaction of the wire with the slot walls, as 

well as with the ligating mechanism, would be expected to 

occur when approaching ±10 degrees of torque, possibly 

tempering the alleged advantage of smaller frictional 

resistance that is commonly associated with self-ligating 

brackets. The marked increase in friction found in the 

self-ligating (but not in the Victory) sets when increasing 

the torque from ±5 degrees to ±10 degrees suggest that 

there were faciolingual force additions from substantial 

contacts with the ligating mechanisms. The In-Ovation R 

68

set, when the torque angle was increased from +5 to +10 

degrees, displayed substantially higher frictional 

resistance, possibly a result of increased normal forces 

due to its “active” self-ligation and the asymmetrical clip 

design. 

When the torque was increased beyond the third-order 

clearance values to ±15 degrees, the friction associated 

with the SmartClip and the In-Ovation R sets grew to 

significantly larger magnitudes than the values displayed 

by the other three sets. This finding may be related to 

properties of the individual ligating mechanisms of these 

brackets. Interactions of the archwires with the clips in 

both brackets were likely because of the faciolingual 

dimensions of the ligated slots. Bunkall 58 attributed 

larger frictional forces from SmartClip brackets with 

first-order wire-slot discrepancies to flexure of the 

nickel-titanium-alloy clips contributing to normal forces 

as well as the relative roughnesses of the nickel-titanium- 

alloy surfaces. The clip integral to the In-Ovation R 

bracket is made of a cobalt-chromium alloy which has been 

reported to have a greater frictional potential related to 

surface-roughness than stainless steel, 13 and it may also 

have contributed to the relatively greater resistance 

displayed in this study. 

69

The design of this study does not entirely represent 

what might occur in clinical situations. Because teeth 

tend to tip and rotate during tooth movement, 6 the effects 

of first- and second-order angulations on slot-wire 

friction should not be ignored when selecting a set of 

crown-attachments. The research design and execution did, 

however, help to highlight and evaluate factors associated 

with friction in attachment-designs. Observations from 

this study lead to the recommendation that measures should 

be taken to reduce the amount of torque in the buccal 

segments before beginning en masse retraction of the 

anterior teeth. Future studies evaluating the collective 

contributions of tip, rotation and torque in a multiple 

crown-attachment setup could be helpful in determining 

optimal treatment-mechanics in certain clinical situations. 

Conclusions 

The results of this study confirmed that the presence 

of third-order torque can contribute to kinetic frictional 

resistance in the buccal segments during anterior 

retraction using sliding mechanics with crown-attachment 

sets including self-ligating brackets. At small torque 

angles, friction will tend to be less with passive than 

70

with active, self-ligating sets. The findings suggest that 

a noticeable effect from friction will be seen when the 

torque reaches and exceeds the third-order clearance-angle 

of the wire-slot combinations. Furthermore, variations in 

bracket-ligation design can influence the amount of 

friction produced, particularly at torque-values beyond the 

clearance-angle. When there is no torque present in the 

second premolar slot, attachment-sets with either passive 

or active self-ligating brackets will generate less 

friction than sets that include elastomerically ligated 

brackets. As torque increases toward the clearance-angle, 

however, differences in frictional resistances across 

crown-attachment sets generally lessen. Beyond this torque 

value, the differences in frictional resistance may not 

depend upon the category of ligation, but, instead, upon 

the basic design of the ligation mechanism. 

71

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79

Tables 

Table 3-1: Frictional-force means and standard deviations in grams at 

seven torque angles at the second premolar from five sets of crownattachments. 

Torque (degrees) 

-15 -10 -5 0 +5 +10 +15 

Victory 551 ± 36 329 ± 84 339 ± 52 303 ± 63 363 ± 84 471 ± 32 549 ± 59 

In-Ovation R 752 ± 128 440 ± 34 205 ± 8 221 ± 14 236 ± 35 623 ± 32 757 ± 79 

Time2 562 ± 103 407 ± 74 186 ± 50 196 ± 17 335 ± 22 517 ± 50 529 ± 79 

Damon 3MX 498 ± 110 358 ± 113 120 ± 17 149 ± 31 165 ± 89 440 ± 81 496 ± 69 

SmartClip 736 ± 26 433 ± 73 149 ± 44 55 ± 24 151 ± 47 427 ± 87 744 ± 38 

80

Table 3-2: Significance levels (α = 0.05) of differences in mean 

frictional forces across pairs of cells, each cell defined by a 

torque-angle, from five sets of crown-attachments. 

Bracket 

Victory In-Ovation R Time2 Damon 3MX SmartClip 

Torque (degrees) Significance 

-15 -10 .004 .004 .025 NS .004 

-5 .004 .004 .004 .004 .004 

0 .004 .004 .004 .004 .004 

+5 .006 .004 .004 .004 .004 

+10 .006 NS NS NS .004 

+15 NS* NS NS NS NS 

-10 -15 .004 .004 .025 NS .004 

-5 NS .004 .004 .004 .004 

0 NS .004 .004 .006 .004 

+5 NS .004 NS .016 .004 

+10 .025 .004 .025 NS NS 

+15 .004 .004 .025 NS .004 

-5 -15 .004 .004 .000 .004 .004 

-10 NS .004 .004 .004 .004 

0 NS NS NS NS .006 

+5 NS NS .004 NS NS 

+10 .004 .004 .004 .004 .004 

+15 .004 .004 .004 .004 .004 

0 -15 .004 .004 .004 .004 .004 

-10 NS .004 .004 .006 .004 

-5 NS NS NS NS .006 

+5 NS NS .004 NS .006 

+10 .004 .004 .004 .004 .004 

+15 .004 .004 .004 .004 .004 

+5 -15 .000 .004 .004 .004 .004 

-10 NS .004 NS .016 .004 

-5 NS NS .004 NS NS 

0 NS NS .004 NS .006 

+10 NS .004 .004 .004 .004 

+15 .025 .004 .004 .004 .004 

+10 -15 .006 NS NS NS .004 

-10 .005 .004 .025 NS NS 

-5 .011 .004 .004 .004 .004 

0 .001 .004 .004 .004 .004 

+5 NS .004 .004 .004 .004 

+15 NS .006 NS NS .004 

+15 -15 NS NS NS NS NS 

-10 .004 .004 .025 NS .004 

-5 .004 .004 .004 .004 .004 

0 .004 .004 .004 .004 .004 

+5 .025 .004 .004 .004 .004 

+10 .020 .006 NS NS .004 

*Not Significant (NS) 

81

Table 3-3: Summary from Kruskal-Wallis analyses of variance 

of frictional forces for seven torque-angles across five 

sets of crown-attachments. 


-15 -10 -5 0 +5 +10 +15 

Chi-square 17.957 7.920 22.774 24.951 22.249 17.044 21.174 

df 4 4 4 4 4 4 4 

Asymp. Sig. .001 NS* .000 .000 .000 .002 .000 


82

Table 3-4: Mean differences in frictional resistances in grams and significance levels (α = 0.05) between 

crown-attachment sets at each of seven torque-angles. 


-15 -10 -5 0 +5 +10 +15 

(a) (b) (a-b) † Sig. (a-b) Sig. (a-b) Sig. (a-b) Sig. (a-b) Sig. (a-b) Sig. (a-b) Sig. 

Victory In-Ovation R -201 .006 -111 NS 134 .000 82 .003 127 .011 -152 .002 -208 .000 

Time2 -11 NS* -78 NS 153 .000 107 .000 28 NS -46 NS 20 . NS 

Damon 3MX 53 NS -29 NS 219 .000 154 .000 198 .000 31 NS 53 NS 

SmartClip -185 .013 -104 NS 190 .000 247 .000 213 .000 44 NS -195 .000 

In-Ovation R Victory 201 .006 111 NS -134 .000 -82 .003 -127 .011 152 .002 208 .000 

Time2 190 .010 33 NS 19 NS 25 NS -99 NS 106 .043 228 .000 

Damon 3MX 254 .000 82 NS 85 .006 72 .010 71 NS 183 .000 261 .000 

SmartClip 16 NS 7 NS 56 NS 166 .000 86 NS 196 .000 13 NS 

Time2 Victory 11 NS 78 NS -153 .000 -107 .000 -28 NS 46 NS -20 NS 

In-Ovation R -190 .010 -33 NS -19 NS -25 NS 99 NS -106 .043 -228 .000 

Damon 3MX 64 . NS 49 NS 66 .045 47 NS 170 .001 77 NS -33 NS 

SmartClip -174 .022 -26 NS 37 NS 141* .000 185 .000 90 NS -215 .000 

83 

Damon 3MX Victory -53 NS 29 NS -219 .000 -154 .000 -198 .000 -31 NS -53 NS 

In-Ovation R -254 .000 -82 NS -85 .006 -72 .010 -71 NS -183 .000 -261 .000 

Time2 -64 NS -49 NS -66 .045 -47 NS -170 .001 -77 NS 33 NS 

SmartClip -238 .001 -75 NS -29 NS 94 .001 14 NS 13 NS -248 .000 

SmartClip Victory 185 .013 104 NS -190 .000 -247 .000 -213 .000 -44 NS 195 .000 

In-Ovation R -16 NS -7 NS -56 NS -166 .000 -86 NS -196 .000 -13 NS 

Time2 174 .022 26 NS -37 NS -141 .000 -185 .000 -90 NS 215 .000 

Damon 3MX 238 .001 75 NS 29 NS -94 .001 -14 NS -13 NS 248 .000 


† 

Mean difference in frictional resistance between a and b in grams.

Figures 

Figure 3-1: Four cylinders mounted in aluminum base 

plate of the friction testing device. 

Figure 3-2: Bracket-slot positioning 

template. 

84

Figure 3-3: Control of the third-order position of the 

second premolar bracket-slot. 

Figure 3-4: SLBUCCAL tube 

Figure 3-5: Damon 3MX bracket 

85

Figure 3-6: SmartClip bracket 

Figure 3-7: In-Ovation R bracket 

Figure 3-8: Time2 bracket 

86

Figure 3-9: Victory bracket 

Figure 3-10: Friction testing setup 

mounted to the Instron Universal Testing 

Machine. 

87

Friction (grams) 

800 

700 

600 

500 

400 

300 

200 

100 

0 

-15 -10 -5 0 


+5 +10 +15 

Figure 3-11: Plots of mean kinetic frictional force within the dental segment vs. torque 

angle at the second premolar from five sets of crown-attachments. 

88 

Victory 

In-Ovation R 

Time2 

Damon 3MX 

SmartClip

Figure 3-12: Cross-section diagrams of a 0.019- x 0.025-inch wire. The 

buccolingual dimension of the wire when rotated 10 degrees (line BD) is 

calculated by multiplying cos Φ2 by the hypotenuse AB. 

89

VITA AUCTORIS 

Michael Ji Hoon Chung was born on December 23, 1975 in 

Hollis, New York to Ye Hyun and Eun Soon Chung. In 1994, 

he received his high school diploma from the Horace Mann 

School in Riverdale, New York. From there he went to New 

York University and received a Bachelor of Arts degree in 

Psychology in May, 1998. From 1999 to 2003, he attended 

dental school at Columbia University in New York. He was 

awarded a Doctor of Dental Surgery degree in 2003. The 

following year, Dr. Chung studied as a resident in the 

Advanced Education in General Dentistry program at Columbia 

University. In 2004, he began his graduate studies in 

orthodontics at the Center for Advanced Dental Education at 

Saint Louis University in Saint Louis, Missouri, where he 

is currently a candidate for the degree of Master of 

Science in Dentistry. He expects to graduate in January of 

2007. 

Dr. Chung was married to Sahrip Kim in July, 2002. 

After graduation, they plan to return to the New York 

metropolitan area. 

90

The effects of third-order torque and self - Saint Louis University

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