Original Article

Biomechanics of Torque from Twisted Rectangular

Archwires
A Finite Element Investigation

Vijay Jayadea; Satish Annigerib; Chetan Jayadec; Punit Thawanid

ABSTRACT
Objective: To evaluate the magnitudes of initial and subsequent sequential deactivational third-
order moments generated in rectangular twisted archwires (either when the archwires are actually
twisted before insertion in the standard edgewise bracket slots or when they are indirectly twisted
in the preadjusted slots of the modern edgewise brackets) in order to judge their biologic ac-
ceptability.
Materials and Methods: A finite element study was carried out with the MSC Patran/Nastran
interface. Three-dimensional models were constructed with 170 nodes of upper 0.017- 0.025-
inch and 0.019- 0.025-inch archwire segments extending bilaterally from the maxillary central
incisors to the first premolars. Required twists were applied at the appropriate locations to derive
the applied and reactionary moments both initially and during the time needed for complete de-
activation.
Results: The results indicated that a round-tripping possibility does exist in certain clinical pro-
cedures. Furthermore, the moments produced could be quite high, thereby enhancing the pos-
sibility of root resorption.
Conclusions: Twists in rectangular archwires may be used only when reciprocal torque is needed
on adjacent teeth. In other situations, alternative torquing methods should be considered.
KEY WORDS: Torque; Archwire twist; Biomechanics

INTRODUCTION roots. This archwirebracket slot relationship is altered

in either of two ways: the operator may actually twist
Faciolingual control over root positions of all the
the archwire when using standard edgewise brackets,
teeth is of vital importance for optimal esthetic, func-
or the archwire may be indirectly twisted by the built-
tional, and health outcomes of orthodontic treatment
in torque in preadjusted edgewise (PAE) brackets.
and for the stability of results. The third-order relation-
Strangely enough, the reciprocal effects on the adja-
ship of a rectangular archwire in the rectangular brack-
cent teeth from these twists are rarely considered. Al-
et slots is expected to provide such control over the
though the empirical clinical practice appears to be ef-
fective in controlling root positions, a sequence of
a
Professor and Department Chair, SDM College of Dental
Sciences, Department of Orthodontics, Dhavalgiri, Sattur, Dhar-
teeth movements from the time the torque is applied
wad, Karnataka, India. until the archwires are deactivated needs to be eval-
b
Professor and Department Chair, BVB College of Engi- uated in order to detect if any round-trip root move-
neering and Technology, Department of Civil Engineering, Hubli, ments occur during these clinical procedures.
Karnataka, India. Over the years, many authors13 have acknowledged
c
Reader, SDM College of Dental Sciences, Department of
Orthodontics, Dharwad, Karnataka, India. that the torquing mechanism is not well understood. Re-
d
Former Postgraduate, SDM College of Dental Sciences, ciprocal torque in the opposite direction on the adjacent
Department of Orthodontics, Dharwad, Karnataka, India. Cur- teeth was mentioned as early as 1933 by Brodie1 and
rently in private practice of orthodontics, Mumbai, Maharashtra, later by others, such as Thurow.4 However, the com-
India.
plexity that arose on account of this reactive effect was
Corresponding author: Dr Vijay Jayade, MDS, FDSRCPS
(Glasgow), Eureka Towers, Traffic Island, Hubli, 580029, Kar- not considered seriously until Isaacson et al5 focused
nataka, India (e-mail: jayadechetan@hotmail.com) attention on it in 1993. They hypothesized that if four
Accepted: June 2006. Submitted: March 2006. teeth in a row, with the brackets placed at equal distance
2007 by The EH Angle Education and Research Foundation, from one another, are connected with a straight piece of
Inc. rectangular wire, and if progressive incremental torque

Angle Orthodontist, Vol 77, No 2, 2007 214 DOI: 10.2319/030106-83

BIOMECHANICS OF TORQUE USING FEM 215

placement, the applied torquing moments on them

would gradually diminish, as would the corresponding
reactionary moments on the middle teeth (lateral inci-
sor in this case). The twists in the archwire may then
start acting on the middle teeth, and ultimately these
teeth might be torqued. However, a step-by-step con-
struction needs to be worked out to detect if any
round-trip movement takes place during this whole
process. Other situations such as twists in the arch-
wire for torquing two teeth in the same direction or
torquing a single tooth and the effects of a straight
archwire in the pretorqued brackets need to be simi-
larly studied.
These considerations are related not only to the me-
chanical efficiency of the appliances we use routinely,
but also to their biologic effects that could be harmful,
Figure 1. Interplay of applied and reactive moments in progressive because round-trip root movement has been implicat-
incremental torque (reprinted from Isaacson et al,5 reproduced with ed in root resorption.7 Furthermore, the magnitudes of
permission from American Association of Orthodontists). torquing moments generated by archwires in various
dimensions and of various materials need to be esti-
mated, because it is also postulated that excess torqu-
is built in the archwire for moving the roots of three con- ing moments may be responsible for damage to the
secutive teeth in the same direction, only the roots of the roots or the cortical plates.
first and last teeth will experience torquing moments in Therefore, we believe there is a need to investigate
opposite directions. The middle teeth will experience no the above issues related to torsional behavior of the
moments at all because of neutralization of the applied edgewise rectangular archwires. Thus, the present
moments by reactive moments (Figure 1). study was undertaken with the following aims and ob-
If this hypothesis is correct, it would apply to any jectives:
group of three or more teeth. A common clinical prac-
a. To verify the hypothesis of Isaacson et al5 regard-
tice that is analogous to the above situation is where
ing the effects of progressive root torque on a
incremental torquing bends are placed for torquing the
group of four teeth from a straight length of wire as
roots of maxillary central and lateral incisors in the lin-
well as from the curved portion of an archwire ini-
gual direction.6 The incremental twists for attaining
tially and after some tooth movement.
such torque are placed on both sides between the up-
b. To determine the actions and reactions in an edge-
per lateral incisor and cuspid and between the central
wise archwire when twisted for producing torque in
and lateral incisors. Applying the above reasoning to
different situations and how the effects might alter
this group of three teeth (central incisor, lateral incisor,
over time in order to ascertain if there is any round-
and cuspid) on either side, the central incisor and the
trip movement involved.
cuspid roots should experience torque in lingual and
c. To explore the effects of built-in torque on upper
labial directions, respectively, whereas the lateral in-
anterior teeth in one of the PAE appliances.
cisor root should experience no moment at all. In clin-
d. To estimate the moments generated by archwires
ical practice, however, both the lateral and central in-
of different sizes and materials when twisted for the
cisors undergo lingual root torque over a period of
above torquing actions in order to judge their bio-
time. Even allowing for some differences between this
logic suitability.
situation and the above hypothetical one (namely, that
in the clinical situation a curved segment of archwire
MATERIALS AND METHODS
connects the teeth and not a straight length and that
the brackets are not equidistantly placed), an expla- The finite element method (FEM) is an excellent en-
nation to bridge the gap between the theory and prac- gineering tool to study problems of this nature. Its ac-
tice is needed. curacy in analyzing the stresses and strains in objects
The probable explanation is that the effects men- such as an archwire is very high when it is provided
tioned by Isaacson et al5 are the initial effects of a with correct material properties, structural configura-
torqued archwire on the teeth. As the torque starts to tion, and loads. We used the Patran/Nastran FEM soft-
express on the end teeth in the group (central incisor ware for our study.
and cuspid in this case), thereby causing their dis- Three-dimensional (3D) models of an edgewise

Angle Orthodontist, Vol 77, No 2, 2007

216 JAYADE, ANNIGERI, JAYADE, THAWANI

Table 1. Comparison of moments generated by twisting 0.018-

0.025-inch stainless steel wire by 1 in laboratory and FEM studiesa
Moment
Experiment Mean value generated
range of of moment in FEM
Range of Mean moments experi- study,
play play produced mental, Nmm Nmm
2.986.31 4.6 3.244.79 3.86 3.39
a
FEM indicates finite element method.

plied as a rotational displacement, with the axis of ro-

tation coinciding with the plane of the wire. This sim-
ulated twisting of the wire was performed as if torque
were introduced into it. Because the software did not
permit application of boundary conditions in directions
other than along the global coordinate axes (ie, the
x-, y-, and z-axes), the twists had to be resolved along
the x- and y-axes. This is shown in Figure 2a. The last
tooth in the group was restrained from all movements
including rotations. In some cases this tooth was the
first premolar, whereas in others it was the canine or
even the lateral incisor. This was performed to simu-
late a cinch-back.
The accuracy of this approach was validated by sim-
ulating the classic laboratory study of Meling et al8 in
the same software and comparing the findings with the
Figure 2. (a) Global co-ordinate system showing the twist (resolved)
along global x- and y-axes according to the right-hand thumb rule.
original study. A twist of 1 was applied to a straight-
(The rule implies that when the thumb points in the axis of direction length 0.018- 0.025-inch SS wire, engaged in three
of rotation, the direction in which the remaining fingers curl indicates brackets spaced at 4 mm, in order to compute the mo-
the sense of direction of twist or moment). (b) Finite element model ments generated. The values obtained by the FEM
depicting moments generated. closely matched those in the experimental study (Ta-
ble 1).
After completing this step, torquing moments in
archwire were created both as a straight length and
0.017- 0.025-inch and 0.019- 0.025-inch arch-
as the anterior segment of an upper archwire (Figure
wires were studied. The desired torquing displace-
2). The archwire span included four teeth bilaterally
ments, to simulate applied twists in the archwire or
from the central incisor to the first premolar and was
those from built-in torque in the brackets, were applied
made with 170 nodes. The length of the archwire was
at the correct locations on the archwire models for
6.06 cm according to the average crown sizes. Known
computing applied moments.
material properties of stainless steel viz Youngs mod-
The reactive moments (both initial and also over
ulus (1.79 105 Nmm2) and Poissons ratio (0.3) were
time from wire relaxation as a result of tooth move-
assigned. As per the experts (author SA) advice, it
ments) arising in the archwire at other locations were
was not necessary to model the brackets because ap-
then derived by the FEM (Figure 2b).
plication of appropriate boundary conditions at the
The procedure for deriving the sequence of altering
bracket locations replicates the precise archwire-
moments consequent to tooth displacements was as
bracket interface. The analysis made use of the 3D
follows:
beam element from the Nastran element library. This
element is capable of accurately modeling axial, flex- a. Initial twisting bends of 10 each were applied at
ural, and shear deformations. An elastic analysis was the desired locations, and the reactionary moments
carried out iteratively to account for geometric nonlin- at various other locations were obtained by FEM
earity and large deformations. computations. (One tooth outside the group of teeth
The archwire was modeled in the xy-plane of the under consideration was included as the anchor
global coordinate system. All torquing forces were ap- tooth, which provided the resistance for applied and
plied along the plane of the archwire as forced rota- reactionary moments to become effective.)
tional displacements. The torsion of the wire was ap- b. To simulate gradual tooth movement and conse-

Angle Orthodontist, Vol 77, No 2, 2007

BIOMECHANICS OF TORQUE USING FEM 217

quent deactivation of the archwire, the teeth sub- Table 2. Initial moments produced by progressive incremental
torque in a straight length of wire, and the subsequent alteration in
jected to the above moments were permitted root
the moments from 2 of root displacement at either end
displacements (by altering displacement boundary
conditions) in small steps of 1.5 to 2, which is the Torquing moments on each tooth, Nmm
average root displacement per month seen in clin- Activation, Tooth 1 Tooth 2 Tooth 3 Tooth 4
ical experience. The resulting changes in the ap- Tooth 1: 0
plied and reactionary moments were derived by the Tooth 2: 10
FEM. Tooth 3: 20
c. The teeth continuing to experience sizeable mo- Tooth 4: 30 19.5 0 0 19.5
Tooth 1: 2
ments were further permitted root displacements of Tooth 2: 10
1.5 to 2, and the change in applied and reaction- Tooth 3: 20
ary moments was again computed. Tooth 4: 28 15.3 3.8 4 15.1
d. The process was continued in the same step-by-
step fashion until the moments on all teeth were
Table 3. Initial moments from progressive incremental torque in a
reduced to approximately 5 Nmm, which was con- curved segment of archwire
sidered the threshold moment needed for causing
Torquing moments on each tooth, Nmm
root displacement. At this point, the archwire was
deemed to have been effectively deactivated by the Right Right Left Left
displacement of roots of all teeth. Activation, lateral central central lateral
Right-lateral: 0
However, certain simplifications and assumptions Right-central: 10
had to be accepted as dictated by the nature of the Left-central: 20
study: Left-lateral: 30 19.46 8.97 1.68 33.1

a. The software assumes that the archwire fits pre-

cisely in the bracket slot without any play (eg, it archwire was to be considered. This was not displayed
assumes a slot height of 0.019 inches for the arch- in the pictorial output and had to be read from the text
wire having the dimension 0.019 0.025 inches). output file. The torque moment at each bracket (in
Although this is not the clinical reality, it does not Nmm) was calculated from the torque developed in the
affect the applicability of findings to the clinical mesial and distal elements. This was then tabulated
practice; what is depicted here is the clinically ef- for each bracket.
fective torque that acts on the teeth after the arch- Because the teeth were not modeled, the amount of
wire-bracket play has been overcome. Thus, as- tooth displacement was not determined in this study.
suming that in a given clinical situation the arch- However, tooth displacement was assumed to be in
wire-bracket play is 10 and that a tooth is subject- the direction of the torque developed in the wire.
ed to a torque of 10, it would actually mean that a The results are presented in the following groups of
twist of 20 has been given in the archwire to over- tables (positive values indicate lingual root torque, and
come the 10 play. Because this play generally is negative values indicate labial root torque):
uniform in all the brackets for any given archwire,
the assumption of no play is fully justified. Verification of Isaacsons Hypothesis
b. The facts that the slot sizes in reality are slightly (Tables 2 and 3)
larger and the wire sizes are slightly smaller than Table 2 confirms the veracity of Isaacsons hypoth-
the ones stated by the manufacturers and that the esis for a straight length of archwire. As can be in-
archwire edges are beveled were disregarded. ferred, only the end teeth experienced equal and op-
c. It was also assumed that all the brackets were per- posite torquing moments in spite of giving incremental
fectly leveled and aligned. torque. Thereafter, when the end teeth moved by 2,
the middle teeth started experiencing moments. The
RESULTS results differed slightly when a curved section of the
The results were obtained as resultant of twisting archwire was studied (Table 3).
force (torquing) and bending of the archwire. This was
Initial and Subsequent Altered Moments in the
displayed as arrows pointing in the direction around
Actively Twisted Archwires in Nontorqued
which the resultant moment was generated. Because
Brackets (Tables 4 to 6)
the bending of the archwire has to be negated before
insertion into the brackets, it was not taken into ac- The results of application of progressive torque to
count. Hence, only the moment along the plane of the the maxillary lateral and central incisors are given in

Angle Orthodontist, Vol 77, No 2, 2007

218 JAYADE, ANNIGERI, JAYADE, THAWANI

Table 4. Initial and subsequent altered moments during progressive Table 7. Initial and altered moments in the use of MBT brackets
incremental torque applied to lateral and central incisors (cuspid bracket 7)
Torquing moments on each tooth, Nmm Torquing moments on each tooth, Nmm
Amount of Amount of
torque, Central Lateral Canine torque, Central Lateral Canine Premolar
Central: 20 Central: 17 23.42 13.4 42.56 (13.93)
Lateral: 10 30.74 6.53 13.76 Lateral: 10
Central: 18 Canine: 7
Lateral: 12a Central: 15 22.12 6.89 31.79 (10.4)
Canine: 2 22.53 0.23 8.11 Lateral: 8
Central: 16 Canine: 5
Lateral: 12
Canine: 4 17.62 0.14 0.08
Central: 14 and reached a value close to zero. Thereafter, it
Lateral: 12
Canine: 4 12.91 3.69 0.06 changed into a positive moment that gradually in-
Central: 12 creased and then reduced.
Lateral: 12 The moments generated during torquing of two central
Canine: 4 8.11 7.58 0.08 incisors for lingual root torque (with twists placed be-
Central: 10 tween the central and lateral incisors on either side) are
Lateral: 10
Canine: 4 6.8 4.97 2.64
given in Table 5. Although the moments generated on
the central incisors were close to the optimum recom-
a
It is assumed that the root of the lateral incisor will move labially
mended value (23.94 Nmm) and in the lingual direction
owing to the moment generated. This will increase the archwire-
bracket angle, and hence the resultant torque will be 12. as intended, the lateral incisors experienced a labial root
torquing effect of slightly lesser magnitude (19.46 Nmm)
that may or may not be desirable. During deactivation,
Table 5. Initial and subsequent altered moments during lingual root the labial root torque on the lateral incisors reduced
torquing of two central incisors
sharply and then changed to lingual root torque. The
Torquing moments on each tooth, Nmm cuspids, which were resisting the displacement of the
Amount of
torque, Central Lateral Canine lateral incisors, experienced a labial root torque that
10 23.94 19.46 gradually increased and then reduced slightly.
8 15.8 9.15 2.76 The moments generated during torquing of a single
6.5 9.49 1.22 4.8 tooth (Table 6) by both 0.019- 0.025-inch and 0.017-
5 3.4 6.43 6.9 0.025-inch SS archwires on the right central incisor
Central: 5 5.8 1.71 4.84
were very high initially (39.19 Nmm and 30.21/Nmm).
Lateral: 3.5
Although the moments on the left central and right lat-
eral incisors were not very high to begin with, these
dropped sharply when some relaxation in the wire was
Table 4. Although the initial moment on the central in-
permitted to simulate small amount of root movement.
cisor was quite high (30.74 Nmm) and that the cuspid
experienced a negative moment of much lesser mag-
Moments Generated in a PAE Setup
nitude (6.53 Nmm), the lateral incisor experienced a
(MBT Prescription and 0.019- 0.025-inch
negative moment (13.76 Nmm) and not a zero mo-
SS Archwires)
ment. With deactivation, the moment on the central
incisor gradually reduced whereas the moment on the The moments differed considerably in the lateral in-
cuspid dropped sharply and continued to be close to cisor and cuspid area, depending on whether the up-
zero. The interesting observation was that when the per cuspid brackets had a positive torque, negative
root of lateral incisor moved labially because of the torque, or zero torque (Tables 7 and 8). With 7 of
initial negative moment, the moment soon reduced torque in the cuspid brackets, the negative moments

Table 6. Initial and subsequent altered moments during single-root torquing (in this case, the right central incisor)
Torquing moments on each tooth, Nmm
SS archwire
size, inches Activation Right canine Right lateral Right central Left central Left lateral
0.019 0.025 10 19.29 39.19 15.37
0.019 0.025 8 2.82 9.14 24.68 4.1 3.81
0.017 0.025 10 14.96 30.21 11.97
0.017 0.025 8 2.2 7.11 19 3.24 2.96

Angle Orthodontist, Vol 77, No 2, 2007

BIOMECHANICS OF TORQUE USING FEM 219

Table 8. Initial moments in the use of MBT brackets (cuspid bracket DISCUSSION
0 or 7)
Effects of Curvature in Modifying the Archwire
Torquing moments on each tooth, Nmm
Amount of Behavior
torque, Central Lateral Canine Premolar
In recent years, it has been realized that the me-
Central: 17
Lateral: 10 chanics enunciated for two-dimensional models of
Canine: 0 23.42 0.58 13.76 straight length of wires need to be cautiously applied
Central: 17 to the archwires, for the latter are 3D entities and their
Lateral: 10 curvature is likely to affect the bending and torsional
Canine: 7 23.42 10.22 15.05 (13.93)
behavior. Isaacson et al9 reported this in a subsequent
article in connection with the V bend mechanics. Our
study also noted this while assessing the veracity of
Table 9. Initial moments generated with the use of inverted upper Isaacsons hypothesis. It was validated in relation to a
lateral incisor bracket and cuspid bracket having 7, 0, or 7 torque straight length of wire. However, when applied to the
curved segment of the archwire, though the end teeth
Torquing moments on each tooth, Nmm
Amount of experienced moments in opposite directions their
torque, Central Lateral Canine Premolar magnitudes were not the same. Furthermore, one of
Central: 17 the two middle teeth experienced a moment close to
Lateral: 10 zero, but the other middle tooth experienced a sizable
Canine: 7 57.67 79.35 42.56 (13.93)
amount of moment.
Central: 17
Lateral: 10
Canine: 0 57.67 65.37 13.76 Possibility of Round-trip Movements in Certain
Central: 17 Torquing Procedures
Lateral: 10
Canine: 7 57.67 51.39 15.05 (13.93) Our suggested explanation for the movement of
middle teeth consequent to displacement of end teeth
and gradual deactivation of archwires proved to be
correct, as did our suspicion that some round tripping
on the cuspids were very high (42.56 Nmm) but may occur during certain applications of torque.
dropped suddenly with small amount of relaxation in Progressive incremental torque was introduced by
the archwire. Another interesting observation was that the standard edgewise technique to overcome the re-
though the upper cuspid with 0 built-in torque was ciprocal effects on the adjacent teeth from the wire
expected to experience no torquing moment, it did ex- twists. However, as was noted in the results, the root
perience a negative moment of sufficient magnitude to of lateral incisor in the simulated setup initially expe-
be clinically effective (13.76 Nmm). rienced a labial root torquing moment, which gradually
As can be seen in Table 9, the moments generated reduced to zero and then changed to a lingual root
on the central incisor when the lateral incisor bracket torquing moment. This would mean that the lateral in-
was inverted were very high in all three situations cisor is likely to experience some round tripping and
(57.67 Nmm), and the negative moments on the lateral that its total lingual root torque is much less than the
incisor were extremely high (79.35 Nmm) when the torque undergone by the central incisor.
cuspid bracket had built-in torque of 7. Although they In the other situation simulating lingual root torque
were of lesser magnitude when the cuspid had 0 or only on the maxillary central incisors (as in the treat-
7 torque, they were still quite high (65.37 Nmm and ment of a Class II division 2 situation), the roots of
51.39 Nmm). The moment on the cuspid with its brack- maxillary lateral incisors initially experienced an almost
et having built-in torque of 7 was also very high (42.56 equal labial moment, which reduced sharply and then
Nmm). changed to a positive moment as the archwire deac-
tivated. This again indicates a possibility of round-trip
movement of the lateral incisors.
Torquing Moments from Various Wires

The moments mentioned in all the above tables are Torque Considerations in the PAE Appliances
for the SS archwires. As can be seen, they are often The setup simulated in our study was the currently
quite high. A rough estimation of the moments gen- popular MBT prescription.10 Other prescriptions have dif-
erated by the TMA and NiTi archwires of equivalent fering built-in torque values, but the trends noted here
sizes for similar situations can be made from their tor- (in the specific case of MBT with upper cuspid brackets
sional stiffness ratio, which is SS:TMA:NiTi 10:3:1. having negative torque) would apply to them also.

Angle Orthodontist, Vol 77, No 2, 2007

220 JAYADE, ANNIGERI, JAYADE, THAWANI

The high magnitudes of some of the moments ob- plications, for high moments are often produced
served in this study will not apply in clinical practice that drop suddenly when tooth movements start.
when untorqued archwires are used. This is because Also, round tripping could occur in many instances.
the largest archwire normally used is 0.019 0.025 c. The use of TMA archwires in preference to SS
inches, which has about 10 to 12 of archwire-slot archwires may reduce these adverse effects but
play that will reduce the moments substantially. How- may not eliminate them completely. Alternative
ever, additional torque (up to 20) is often needed in methods proposed by authors such as Thurow4
the 0.019- 0.025-inch SS archwire during treatment, (torquing spurs in round-base archwire), DeAngelis
as per the recommendation of the proponents of the and Davidovitch7 (use of Warren springs), and
technique.10 This added torque would overcome the Isaacson and Rebellato12 (torquing arches) deserve
archwire-slot play, and then the FEM values would be serious attention because the reciprocal reactions
close to the moments that are likely to be generated from these are spread on many (often distant) teeth
in the clinical practice, when SS archwires are used. and are controlled more easily.
Inversion of the maxillary lateral incisor bracket is d. The moments generated by the NiTi archwires,
often recommended10 in cases where the lateral inci- even those that are 0.019 0.025 inches, may be
sors are in-standing to begin with. One should keep in too low to bring about active torquing of teeth over
mind the possibility of developing extremely high mo- long periods. However, they may prove beneficial
ments in the SS archwires when following this prac- when reciprocal torque is needed on adjacent
tice. teeth, especially when using preadjusted brackets,
Another observation worth noting is that the recip- more so with some brackets inverted.
rocal effects on adjacent teeth might override the built-
in torque, and the tooth may experience a moment REFERENCES
quite different from the intended one. 1. Brodie AG. A discussion of torque force. Angle Orthod.
1933;3:263265.
2. Rauch ED. Torque and its application to orthodontics. Am
Estimation of the Moments Generated by J Orthod. 1959;45:817830.
Archwires of Different Sizes and Alloys 3. Nikolai RJ. Bioengineering Analysis of Orthodontic Mechan-
ics. Philadelphia, Pa: Lea & Febiger; 1985:272321.
The optimal values recommended by various authors 4. Thurow RC. Edgewise Orthodontics. 4th ed. St Louis, Mo:
such as Burstone,11 Nikolai,3 and Meling et al8 for rect- CV Mosby Co; 1982:171, 275.
angular wire torque range from 20 Nmm to 10 Nmm for 5. Isaacson RJ, Lindauer SJ, Rubenstein LK. Moments with
root movement and bodily translation. In general, torqu- the edgewise appliance. Incisor torque control. Am J Orthod
Dentofacial Orthop. 1993;103:428438.
ing moments from heavy SS archwires are high and of- 6. Tweed CH. Clinical Orthodontics. St Louis, Mo: CV Mosby
ten above the physiologic limit, those from TMA archwi- Co; 1969:148153.
res are generally within the physiologic limit, and those 7. DeAngelis V, Davidovitch Z. Optimal orthodontics: an
from NiTi archwires are below the physiologic limit. How- achievable target. In: Davidovitch Z, Mah J, eds. Biological
ever, NiTi archwires would be the obvious choice in sit- Mechanisms of Tooth Movement and Craniofacial Adapta-
tion. Boston, Mass: Harvard Society for the Advancement
uations where very high moments are expected to be of Orthodontics; 2004:116.
generated from SS archwires. 8. Meling TR, Odegaard J, Meling EO. On mechanical prop-
erties of square and rectangular stainless steel wires tested
CONCLUSIONS in torsion. Am J Orthod Dentofacial Orthop. 1997;111:310
320.
a. Twists in rectangular archwires seem to be appro- 9. Isaacson RJ, Lindauer SJ, Conley P. Responses of 3-di-
mensional arch wires to vertical V-bends: comparisons with
priate only when reciprocal torque is required on existing 2-dimensional data in the lateral view. Semin Or-
the adjacent teeth, but one should be aware of high thod. 1995;1:5763.
moments arising in full-sized or nearly full-sized SS 10. McLaughlin RP, Bennett JC, Trevisi HJ. Systemized Ortho-
archwires. The recommendation of Thurow4 to use dontic Treatment Planning. St Louis, Mo: CV Mosby Co;
undersize archwires for this purpose is worth re- 2001:41, 284.
11. Burstone CJ. The mechanics of the segmented arch tech-
membering. nique. Angle Orthod. 1966;36:99120.
b. This method to cause active root torque appears 12. Isaacson RJ, Rebellato J. Two-couple orthodontic appliance
mechanically and biologically unsound for other ap- systems: torquing arches. Semin Orthod. 1995;1:3136.

Angle Orthodontist, Vol 77, No 2, 2007