This document provides an overview of frictionless mechanics in orthodontics. It discusses various loop and spring configurations that can be used for space closure without tooth movement along the archwire. Advantages include control of tooth movement and known force levels. Disadvantages include more complex mechanics and potential patient discomfort. Factors like loop height and geometry determine the moment-to-force ratio and type of tooth movement achieved. The document defines key terms and principles of biomechanics relevant to frictionless orthodontic tooth movement.

1. Arun Bosco Jerald
2018 Batch
FRICTIONLESS MECHANICS

2. Contents
• Introduction
• Advantages
• Disadvantages
• Terminologies
• Biomechanics for frictionless mechanics
• Factors determining the tooth movement
• En masse space closure
• Separate canine and incisor retraction
• Six piece mechanics
• A torqued appliance
• Directional edgewise orthodontic approach
• Broussard two force system
• Bimetric arch-Tandem yoke
• Bidimensional edgewise technique
• Light force edgewise technique-bull loop
• Lingual lever arm technique
• Bite opening and space closing arch wire
• Compound loops
• Double key hole loop with Asher face bow
• Vertical loop
• T loops
• Tear drop shaped loop
• Poul Gjessing spring
• A segmental spring
• Simultaneous intrusion and space closure –utility arches
• Three piece mechanics
• K-sir appliance
• Opus loop
• Closing loop arch wire
• Computerized testing of orthodontic loops
• Conclusion
• References

3. Introduction
• In frictionless mechanics, teeth are moved without the brackets sliding
over the archwire.
• Retraction is accomplished with the help of loops or springs.
• Frictionless space closure involves bending loops of various
configurations-
• Sectionally (To deliver the desired force to an individual tooth)
OR
• In a continuous archwire (To deliver the desired force levels to several
teeth)

4. • When activated, the loop distorts from the original configuration
• As the tooth moves the loop gradually returns to its original preactivated
position – delivering energy stored at the time of activation.

5. Advantages(Kelley Carr and Jerome L. Blafer )
• Teeth can be moved long distances with control of axial inclinations
• Teeth can be depressed effectively.
• Forces of known value are used and are incorporated in spring assemblies
before they are placed in the mouth.
• Translational forces placed on some teeth can be pitted against rotational
forces on other teeth.
• The units to be moved are not inhibited by archwire friction.
• Though lighter wires are used to apply forces for movement, heavy wires
are used for anchorage stabilization.
• Auxiliary springs can be activated over long distances giving low load
deflection rates with relatively constant force.

6. Disadvantages [Julie Ann Staggers, Nicholas Germane (1991)]
• A good understanding of mechanics is required when using retraction
loops or springs, because minor errors in mechanics can result in major
errors in tooth movement.
• More wire bending skill and chair time required than with sliding
mechanics.
• Retraction loops may be uncomfortable.
• Retraction loops produce an undesirable mesial-out moment when
individual teeth are retracted, due to the force of the spring placed
facial to the center of resistance.

7. Terminologies
Force
• It is defined as “An act upon a body that changes or tends to change the state
of rest or the motion of that body”. (R.J Nikolai)
Couple
• Two forces equal in magnitude and opposite in direction but not on the same
line.
• The result of applying two forces in this way is a pure moment, because the
translatory effect of the forces cancels out.
• A couple will produce pure rotation, spinning the object around its center of
resistance; the combination of a force and a couple can change the way an
object rotates while it is being moved

8. Center of resistance - CRes
• CRes is the point on the body (tooth) where a single force
would produce translation, ie. All points in tooth moving in parallel,
straight lines.
• Depends on alveolar bone support, root length, no. of roots.
• It is at the approximate mid point of embedded portion of root.

9. Centre of resistance for different structures
Structure Centre of resistance
Single-rooted tooth One-fourth to one-third the distance from CEJ to
apex
Molars At furcation
Maxillary dentition Apical to and between the roots of premolars
(Poulton DR, 1959)
Maxilla Posterosuperior to zygomaxillary suture or slightly
inferior to Orbitale
For intrusion of maxillary
anteriors
Distal to the lateral incisor roots
Mandibular dentition Apical and between the roots of premolars

10. Center of rotation - CRot
• The point around which rotation actually occurs when an object is being
moved.
• When two forces are applied simultaneously to an object, the center of
rotation can be controlled and made to have any desired location.
• The application of a force and a couple to the crown of a tooth, in fact, is
the mechanism by which bodily movement of a tooth, or even greater
movement of the root than the crown, can be produced.

11. Types of tooth movement
CRes
CRot

12. Sign convention
• Positive sense: moments that tend to produce mesial, labial or buccal
crown movement
Force directed Anterior, lateral or extrusive
• Negative sense: moments that tend to produce distal or lingual crown
movement
Force directed posterior, medial or intrusive

13. Moment of force - MF
• Defined as the rotational tendency when force is applied away from
the center of resistance
• If a force F is acting at a perpendicular distance d from the center
of resistance, the moment of force is mathematically given as
‘M = F x d’
• The direction of the moment of a force can be determined by continuing
the line of action around the center of resistance towards the point of
origin.
• The moment about a given point or line is independent of the location
of that force on its line of action. (only the perpendicular distance ‘d’)

14. Direction of the moment of a force
Moment of force

15. Moment of a couple - MC
• In this coplanar, non-concurrent force systems, where F1=F2 =F
Considering the magnitude: F1= -F and F2= +F
Fx = F1+F2 = 0 and Fy = 0
So, ∑M=0
ie, there is no movement in this plane.
But, there is still a tendency for this tooth to rotate
This is due to moment of the couple

16. • Defined as tendency to rotate when two equal and opposite
forces ‘F’ separated by a perpendicular distance ‘d’
• Magnitude of this moment of couple is ‘F x d’
• The couples are sometimes called ‘pure moments’ since they
tend to produce rotation about the CRes of a tooth and will
produce this CRot irrespective of the location of the couple
on a tooth
• For this reason, the couples are also called as ‘free vectors’

17. • In this system, there is a negative sense since the crown is
moving lingually and the root is being moved labially
• For equilibrium, a couple can only be balanced with another
couple of same magnitude, opposite sense and the same
aspect/plane
• In the orthodontic type of non-coplanar, non-concurrent
force systems, the 3rd dimension is also to be considered: Fz
• Hence, for equilibrium the Fx , Fy and Fz should be zero
so that the ∑M=0

18. Forces, Moments, and Couples in Tooth Movement
• Consider the clinical problem posed by a
protruding maxillary central incisor.
• If a single force of 50 gm is applied against the
crown of this tooth, as might happen with a spring
on a maxillary removable appliance, a force system
will be created that includes a moment.
• The result will be that the crown will be retracted
more than the root apex, which might actually
move slightly in the opposite direction.
15 mm
M= 50×15=750gm mm

19. • If it is desired to maintain the inclination of the tooth while retracting
it, it will be necessary to overcome the moment created when the force
was applied to the crown. One way to decrease the magnitude of the
moment is to apply the force closer to the center of resistance.
• In orthodontics, it is impractical to apply the force directly to the root,
but a similar effect could be achieved by constructing a rigid attachment
that projected upward from the crown.
• Then the force could be applied to the attachment such that its line of
action passed near or through the center of resistance.

20. • If the attachment were perfectly rigid, the effect would be to reduce or
eliminate the moment arm and thereby the tipping .
• Because it is difficult to make the arms long enough to totally eliminate
tipping, this procedure is only a partial solution at best, and it creates
problems with oral hygiene.

21. • Another way to control or eliminate tipping is to create a second moment
opposite in direction to the first one.
• If a second counterbalancing moment could be created equal in
magnitude to the moment produced by the first force application, the
tooth would remain upright and move bodily.
• A moment can be created only by application of a force at a distance,
however, so this would require that a second force be applied to the
crown of the tooth.

22. ∑M= -(200×15) + (150×20)
= -3000 + 3000 = 0 gm mm
∑F= -200 +150 = -50 gm
• So the force system is equivalent to a couple with
a 50 gm net force to move the tooth lingually.
• Controlling forces of this magnitude with a
removable appliance is very difficult, almost
impossible—effective root movement is much
more feasible with a fixed appliance.
15mm
20mm
200gm
150gm
∑M= 0 gm mm
∑F= -50 gm

23. • The tendency for the incisor to tip when it was being retracted could be
controlled by applying a second force to the lingual surface of this tooth,
perhaps with a spring in a removable appliance pushing outward from
the lingual near the incisal edge.
• As a practical matter, it can be difficult to maintain removable appliances
in place against the displacing effects of a pair of springs with heavy
activation.

24. • The usual orthodontic solution is a fixed attachment on the tooth,
constructed so that forces can be applied at two points.
• With round wires in bracket slots, an auxiliary spring is needed to
produce a torquing couple.
• A rectangular archwire fitting into a rectangular bracket slot on the
tooth is most widely used because the entire force system can be
produced with a single wire.

25. (A) Auxiliary root positioning springs and auxiliary
torquing springs were used routinely with the
Begg appliance, and both can be seen in the
maxillary arch of this patient being treated with
an early (1980s) Begg-edgewise combination
appliance. The torquing spring contacts the facial
surface of the central incisors; uprighting springs
are present bilaterally on the canines. Note that the
base wires are pinned in the Begg slot, and the
edgewise slot is not used at this point in treatment.
(B) An auxiliary torquing spring in use with the Tip-
Edge appliance, the current version of a
combination Begg-edgewise appliance.
(C) Root positioning (sidewinder) springs used with
the Tip-Edge appliance to correct the axial
inclination

26. • A rectangular archwire fitting into a rectangular
slot can generate the moment of a couple (MC)
necessary to control root position.
• The wire is twisted (placed into torsion) as it is put
into the bracket slot. The two points of contact are
at the edge of the wire, where it contacts the
bracket.
• The moment arm therefore is quite small, and
forces must be large to generate the necessary MC.
• If a rectangular archwire is to be used to retract a central incisor bodily, the net
retraction force should be small, but the twisting forces on the bracket must be
large in order to generate the moment

27. • Couples are often referred to as the applied moment in orthodontics.
• Torque is a common synonym for moment (both moments of forces and of
couples).
• Torque is erroneously described in terms of degrees by many orthodontists.
• The degrees of wire bending or the angulation of bracket slot design are
methods to produce moments, i.e., they describe the shape of the wire or
bracket.
• The appropriate unit for the applied torque is gram millimeters (force ×
distance).
• It is the description of the moments that more accurately describes the
rotational components of a force system and appliance design.

28. Moment-to-force ratio (M/F)
• In the orthodontic literature, the relationship between the force and the
counterbalancing couple often has been expressed as the “moment-to-
force” ratio.
• M/F for various tooth movements (Burstone)
▪ 5 : 1 Uncontrolled tipping
▪ 8 : 1 Controlled tipping
▪ 10 : 1 Translation
▪ >10 : 1 Root movement

29. • According to Proffit, M/F of 1 to 7 would produce controlled tipping,
• Ratios of 8 to 10 (depending on the length of the root) would produce
bodily movement, and
• Ratios greater than that would produce torque.
• Because the distance from the point of force application to CRes can and
does vary, M/F must be adjusted if root length, amount of alveolar bone
support, or point of force application differs from the usual condition.

30. MC / MF Ratios and Control of Root Position
MC/MF = 0 Pure tipping (tooth rotates around center of resistance)
0 < MC/MF < 1 Controlled tipping (inclination of tooth changes but the center of rotation is
displaced away from the center of resistance, and the root and crown move in
the same direction)
MC/MF =1 Bodily movement (equal movement of crown and root)
MC/MF > 1 Torque (root apex moves further than crown)
MC / MF ratios more precisely
describe how a tooth will respond.

31. Anchorage
Definition
• “Refers to the nature and degree of resistance to displacement offered by
an anatomic unit when used for the purpose of effecting tooth
movement” ( T.M.Graber)
• “Amount of movement of the posterior teeth(molars, premolars) to close
the extraction space in order to achieve selected treatment goal”
(Ravindra Nanda)

32. Classification
Ravindra Nanda
• A anchorage : critical / severe / maximum
75 % or more of the extraction space is needed for anterior retraction.
• B anchorage : moderate
Relatively symmetric space closure (50%)
• C anchorage : non critical / minimal
75% or more of space closure by mesial movement of posterior teeth

33. Charles Burstone
• Group A: Posterior teeth contribute less than one quarter to total space
closure
• Group B: Posterior teeth contribute from one quarter to one half to total
space closure
• Group C: Posterior teeth contribute more than one half to total space
closure

35. Cortical Bone Anchorage
• T0 anchor a tooth, its roots are placed in proximity to the dense cortical bone
under a heavy force that will further squeeze out the already limited blood
supply and thus anchor the tooth by restricting the physiological activity in an
area of dense laminated bone. Because of its density and limited blood supply,
the cortical bone resists change and tooth movement is limited.
• For efficient movement the mechanical procedures should steer the roots away
from the denser cortical bone and through the less dense channels of the
vascular trabecular bone.
• Since each tooth is supported by cortical bone, an understanding of this bony
structure and support is necessary in order either to move the roots into the
cortical bone to anchor them or to avoid the cortical bone, if possible, for their
efficient movement.

36. Musculature Anchorage
• The facial type described by the cephalometric morphology reflects the
musculature which supports the occlusion.
• Where the musculature is strong as characterized by the deep bite, low
mandibular plane, brachyfacial type, the teeth demonstrate a "natural
anchorage".
• In the open bite vertical dolichofacial patterns, the musculature seems
weaker and less able to overcome the molar extruding and bite-opening
effect of our treatment mechanics.

37. Biomechanics for frictionless mechanics
• The teeth in an arch wire will invariably assumes the passive position of
the arch wire.
• When we place bend in the middle of the wire and engage into bracket
two equal and opposite moments are produced
• When offset bend is placed differential force is produced.
• This same principles apply in frictionless mechanics where instead of
bend, loop is placed in the wire.

38. • Bends placed on the mesial and distal legs of loop are called as α and β
respectively
• These bends produce α and β moments when wire is placed into bracket

39. • Activating the loops produces the forces in frictionless mechanics.
• Pulling the distal end of the arch wire through molar tube and cinching
it back does this.
• According to Charles Burstone M/F for translation is about 10:1, a
regular 10mm high vertical loop offers a M/F of only 3:1 when it is
activated by 1mm.
• To get M/F of 10:1 activation should be reduced to .2mm, but force level
is not sufficient for retraction

40. • Factors that influence m:f ratio (Burstone and Koeing /1976/ AJO)
• Height of the loop
• Horizontal loop length
• Apical length of the wire
• Placement of the loop
• Helix incorporation
• Angulations of loop legs

41. • In order to increase moment, height can be increased but it has limitation
as available space in the vestibule
• The most effective way to increase M/F is placing Pre-activation bends
or Gable Bends.
• These bends can be placed within the loops or where loop meets the
arch wire.

42. • As we try to engage the wire into bracket we pull the horizontal arm of
the loop down producing a moment called the ‘activation moment’ and
the loop is said to be in ‘Neutral position’
• Thus with this added moment, M:F ratio of loop is increased.

43. • The α MOMENT produces distal root movement of anterior teeth,while
the β MOMENT produces mesial root movement of posterior teeth.
• If α = β No vertical force
• If α ≠ β ,Vertical force

44. • If β moment is >α moment ; posterior anchorage is enhanced by the
mesial root movement of posterior teeth and net extrusive effect on
posteriors and intrusive force on anterior teeth.
• If α moment is > β anchorage of anterior segment is increased by distal
root movement and net extrusive effect on anterior teeth and intrusive
effect on posterior.
• The M:F ratio increases as spring gets deactivated
• Spring should not be activated too frequently

45. α = β α < β α > β
ᵝ ᵅ ᵝ ᵅ ᵝ ᵅ

46. Factors determining the tooth movement
required during space closure (Ravindra Nanda)
• Amount of crowding
• Extractions are usually done to relive crowding
• Anchorage control becomes very crucial
• Maintaining anchorage while creating space for decrowding is
important
• Anchorage
• Anchorage classification during treatment planning is very important
for desired results. various methods like (headgear, lip-bumper,
lingual-arch, trans palatal arch e.t.c)

47. • Axial inclination
• Inclination of canine and incisor are particularly important.
• When same force and moment applied to a tooth or a group of teeth
with different axial inclination will result in different type of tooth
movement
• Example in case of unfavorable positioned canine(root mesial crown
distal)
• Midline discrepancies and left or right asymmetries
• These problems should corrected as early as possible
• Asymmetric forces could result in unilateral vertical
• Forces causing asymmetric anchorage loss

48. • Vertical dimension
• Attention should be given to vertical forces during space closure .
• Undesirable vertical extrusive forces may result in increased lower
facial height, increased inter labial gap, excessive gingival display

49. 0.018 Vs 0.022 slot
• The use of 0.018 slot is most preferable when frictionless mechanics is
employed.
• Better anterior torque control-0.017 x 0.025” in an 0.018 slot. Hence the
play in the wire and the bracket slot would be less.
• For sliding mechanics, at least 2 mil of clearance is required between the
bracket and the arch wire. A 0.019x 0.025 SS wire would have a 3mil play
in a 0.022 slot.
• Wire would be springier and less rigid compared to those of wires in
0.022 slot. Hence the loops would have adequate flexibility when
incorporated.
• Moments and forces produces would be greater in larger dimension
wires.

50. • Besides configuring the looped arch wire to deliver proper M/F to
achieve the direction of tooth movement desired, the loop's load-
deflection rate (F/D) assumes added importance with this approach.
• If F/D is large, stress levels, traumatic to the PDL, alveolar bone, and
roots, can be delivered at very small loop activations that are difficult to
deliver precisely.
• Also, large F/D, requiring small activations, deactivate after small tooth
movements; if the M/F is not constant, the PDL stress distributions
change rapidly as the tooth cycles from controlled tipping to translation
to root movement.

51. • Most closing loop designs offered today optimize for low F/D at the
expense of M/F.
• another way to lower the F/D is by using arch wires formed from alloys
with reduced Young's Modulus

52. • The closing loops should always be fabricated in rectangular wire to
prevent rolling of the wire along the bracket slot.
• Appropriate closing loops in a continuous arch wire will produce
approximately 60:40 closure of the extraction space, if only second
premolar and first molar are included in the anchorage unit and some
uprighting of incisors is allowed.
• Greater retraction can be obtained if second molar is a part of
anchorage unit, less if incisor torque is required.

53. Retraction
Staged
En-masse
Frictionless Sliding
Simultaneous
Intrusion
And retraction
Stage 1 Stage 2
Canine
Anteriors
Frictionless Sliding
Frictionless
Sliding
Tip and upright

54. En-masse space closure
• The anchorage unit consists of the right and left posterior teeth which
are connected by a buccal stabilizing segment and a transpalatal arch in
the maxillary arch and a lingual arch in the mandibular arch.
• During space closure, conceptually (Two tooth concept) one should think
of only two teeth - an anterior tooth comprising of incisors and the
canines which have been connected and a posterior tooth which includes
molars and pre-molars.

55. • The attachment on the posterior tooth(segment) is a 0.018 by 0.025 inch
auxiliary tube on the first molar, and the one on the anterior tooth
(segment) is an auxiliary vertical tube on the canine bracket.
• Although adjustments are still possible within the individual segments
between space closure, the orthodontist should concern himself
primarily with only the force system that will be applied to the anterior
and posterior auxiliary tubes.

56. • The principle of enmasse space closure.
A. Blocks represent anterior and posterior
segments.
B. One-stage translation.
C and D, Two-stage space closure.
C. The anterior segment is initially tipped around
a center of rotation near the apices of the
incisors.
D. Root movement follows with a center of
rotation near the incisor bracket.

57. Individual Canine Retraction
• Many times, because of anterior crowding or a midline discrepancy,
space must be made available through separate canine retraction.
• The same treatment decisions with regard to retraction and anchorage
requirements must be made as are made for en-masse retraction.
• The choice of mechanics is determined by the type of movement desired
and anchorage requirements.
• Because the force applied is buccal to the center of resistance of the
canine, a moment is produced on the canine during separate canine
retraction, which will cause the canine to rotate distal-in while it retracts.

58. • There are four ways to counteract this moment
• Simultaneously applying a force from the lingual.
• Placing anti-tip and anti-rotation bends into the attraction spring.
• Placing a cuspid-to cuspid stabilizing segment.
• Using a buccal arch wire.
Force from the lingual:
• By bonding a button to the lingual of the canine and placing an elastic
which is changed daily by the patient, a force can be applied from the
lingual.
• The magnitude of the force is equal or greater than the distal force
supplied by a buccal T-spring at ½ activation (3.0mm).

59. • This will initially give a total distal force equal to the recommended
force, half delivered from the lingual and half delivered from the buccal
which prevents or reduces rotation of the cuspid.
• Drawbacks :
• Patient compliance.
• The force from the elastic decays very quickly. » enough force not being
delivered for efficient cuspid retraction.
• With buccally inclined canines, the center of resistance is too far
lingual for a lingual elastic to be effective.

60. Anti-rotation and anti-tip bend
• This removes the necessity of patient
compliance from the treatment and also
delivers a more constant anti-rotational
and anti-tip moments to the teeth
involved.

61. Cuspid-To-Cuspid Bypass (Stabilizing Segment)
• These forces are applied at the bracket and are, therefore, in most cases,
buccal to the center of resistance of the canine. An intrusive force can
create buccal movement of the canine crown while an extrusive force can
cause lingual movement. The bypass eliminates this side-effect.
• A rigid wire, preferably 0.021” × .025” or at least 0.017” × 0.025” SS is
stepped down 3 to 4mm mesial to the canines and around the incisors .
• This allows for simultaneous bracketing and alignment of the incisors as
the canines are retracted.

62. • The vertical step down also incorporates additional wire length which
allows the step to be bent lingually or labially, depending upon patient
comfort and the need to keep the anterior wire away from the incisors as
the canines retract.

63. • In some patients, no gingival step is made if the incisors are not to be
bracketed until canine retraction is completed.
• Gradual first order reverse curvature is placed to produce moments
rotating the canines distal-out .
• The arch form of the wire is made longer and wider than the initial 3-3
distance.
• The amount of increased wire length distal to the canines is determined
by the amount that the canines must be retracted to relieve the anterior
crowding.

64. • The increased length provides a means of extending the segment
anteriorly to avoid contacting the incisors during retraction.
• To avoid lip irritation and patient discomfort, the wire should only be
1.5mm labial to the incisors.
• This distance can be adjusted in each visit by advancing the wire as the
canines retract.
• The increased width allows for the intercanine width to increase as the
canines retract into a wider part of the arch.
• The arch wire width must also be widened enough to counteract any
constrictive force caused by the force of retraction.

65. Separate Incisor Retraction
• En masse retraction of six anterior teeth is preferred because of its
simplicity and control. For that reason, separate incisor retraction is
limited to those cases where only a small amount of space needs to be
closed following full or partial canine retraction.
• In extreme protrusion situations with deep or potentially deep overbite,
the incisors can be retracted and intruded simultaneously by employing a
three-piece intrusion arch.
• The intrusion force is applied posterior to the center of resistance of the
incisors and usually directed parallel to their long axes or with a slightly
greater distal direction. In any event, the line of action of the force must
not lie below the center of resistance of the posterior teeth.

66. • If space distal to the lateral is small with slightly flared incisors, a bypass
arch can be used to close the space.
• A continuous arch from the molar auxiliary tubes is fabricated of 0.017”
× 0.025” TMA .
• This bypass arch is formed by stepping the wire gingivally 6mm anterior
and 5mm posteriorly.
• Start the bend about 7mm mesial to the first molar tube and 5mm distal
to the lateral bracket.
• The bypass forms a “flat top” loop.

67. • If conditions allow, the step can be bent further gingivally reducing the
force-deflection rate.
• The bypass loop has gradual curvature incorporated (curve of spee in
the upper arch) to produce the moments that prevent unwanted tipping.
• The same principles apply as for the more sophisticated T-loop where
placing the loop distally increases the posterior (b) moment. Also, a
smaller radius of curvature increases the M/F ratio both anteriorly and
posteriorly.
• The distal activation is small (1.5 to 2.0mm) since the force-deflection
rate is much higher that the standard “T” loop.

68. • The force-deflection rate can be further lowered by fabricating a
composite. A 0.018” TMA wire with the appropriate step is welded to the
edgewise wire.
• The edgewise wire is cut off between the two steps forming a bypass
composite

69. • In some patients, a large space will exist between canine and lateral. In
this case, major retraction is indicated with a T-loop .
• As in all space closures, spring activation is dictated by the movement
desired and the anchorage requirements.
• Because no auxiliary tube is available on the incisors, modifications must
be made in the anterior segment for attachment of the spring.
• The anterior segment is left 5.0 mm long distal to the lateral incisors,
and a vertical tube is welded (soldered) to the anterior segment in which
the mesial part of the spring can be placed.
• To bypass the cuspid bracket, the spring is inserted from the gingival
into the vertical tube

71. ORTHODONTIC WIRE LOOPS
• Although the orthodontic arch wire is often activated by bending to
create facio-lingual or occluso-gingival tooth movement, routine
mesiodistal displacements through archwire deformation cannot be
accomplished directly because of the extremely high longitudinal
stiffness of wire.
• To reduce this stiffness at a specific location, a wire loop may be
incorporated in the arch, effectively providing a spring of manageable
flexibility between segments of the arch wire.

72. • In general, the orthodontic wire loop may be bent directly into the
continuous arch wire, or a loop or spring may be fabricated from a piece
of wire and activated between a pair of neighboring teeth segments
• The "legs" of a wire loop extend occluso-gingivally from the arch-form
plane into the "body" of the loop, the shape of which serves to primarily
characterize the loop.

73. • The performance of a loop is determined by
1. Spring properties.
2. Root paralleling moments.
3. Location of the loop relative to adjacent brackets.
4. Additional design considerations.
• The spring properties of loops are determined by
• Wire material
• Size of the wire
• Distance between the attachments
Wires of greater springiness or smaller cross sectional area allows
the use of simple loop designs.

74. Root paralleling moments
• While considering the extraction space closure, a loop must generate not
only closing forces, also it must produce appropriate moments to bring
the roots parallel to each other.
• But this requirement will limit the amount of wire that can be
incorporated to make the loop. When we incorporate a loop, the spring
becomes springier, and unable to produce necessary moments.
• It is shown that unacceptably tall loops would be required to generate
appropriate moments in this manner, so additional moments must be
generated by placing gable bends, when the loop is placed in mouth

75. Location of the loop
• Group A anchorage situations
• Loop is placed closer to the anterior segment.
• For maximum anchorage, the β bend should be higher than the α bend.
• Group B anchorage situations
• Gable bends in the form of α and β bends are given, α = β; in order to
achieve a 50:50 or 60:40 ratio of anterior retraction and posterior
protraction.
• Loop should be located at the centre of the extraction space.

76. • Group C anchorage situations
• Anterior anchorage is to be reinforced. The various methods to
reinforce the anchorage in the anteriors include:
• Involve as many teeth in the anterior segment as possible.
• 2nd premolar extractions preferred.
• Active lingual root torque in the incisal segment.
• Break down posterior anchorage.
• α bend is increased compared to the β bend.
• Loop is shifted closer to the posterior segment

77. Additional design considerations
• The design of the spring should be as simple as possible, because more
complex designs will be uncomfortable for the patient, more difficult to
fabricate and more prone to fracture or breakage.
• The more wire gingival to the bracket, the more favorable the activation
moment and therefore better the overall M/F ratio
• The force of the retraction spring is applied by pulling the distal end
through the molar tube and cinching it back.

78. • A loop is more effective, when it is closed rather than opened during
activation.
• Moreover a loop is designed to opened to activate, can be made, so that
when it closes completely ,the vertical legs come in contact, preventing
further movement, producing a ‘fail safe effect’.
• A loop made in wire with a low modulus of elasticity like TMA, will
have a lower load deflection rate than one made in stainless steel wire.
• But M/F is not depended on wire material.

79. • A closed loop has low load deflection rate due to reduced length of the
wire. It is having more range of activation than an open loop due to the
additional wire and the Bauschinger effect (range of activation is always
greatest in the direction of last bend).
• The M/F of both the loops having same design are same .
• The main differences between the both are the activation. Open loop is
activated by pulling the legs apart, hence unbending the loop, whereas
the closed loop is activated by bringing the legs together, in the direction
of last bend

81. Open vertical loop
• Originated by Dr. Robert W Strang
(1933)
• Used for retraction of anterior teeth.
• 5mm height and 2mm width
• Activation by 1mm
Open vertical loop with helix
• Includes the addition of a single apical
loop, with a radius of 1.0 mm, or two
lateral helices at the base, each with a
radius of 0.5 mm

82. Closed vertical loop
• Only being difference is horizontal overlapping.
Closed vertical loop with helix
• Morris Stoner (1975)

83. • Dr. Harry Bull (1951) introduced a variation of standard vertical loop
• Loops legs were tightly abutting each other
• Fabricated from 0.021 x 0.025 SS.
Omega loop
• Introduced by Morris Stoner in the year 1975.
• Stresses are distributed more evenly through the curvature instead of
concentrating them at the apex.
Bull loop

84. • The technique is modifying the distal leg of the closing loop with a
small loop, allows simple and accurate multiple activations.
• A step-in bend is required distal to the loop to maintain continuous
archform.
Modified omega loop

85. • Once the archwire is in place, the teeth distal to the space are ligated
together.
• The end of the ligature wire is then threaded through the small loop and
tightened to activate the closing loop.
• The tail of the ligature wire is tucked in, and the end of the archwire is
cut flush to the distal of the terminal molar band. After space closure,
the loop becomes passive.

86. • A similar design uses a U-bend instead of a small loop, allowing
activation of the wire without a step-in bend.
• A three-pronged plier is used to bend this closing loop.
• The archwire is inserted, and the first molars, second premolars, and
canines were ligated together. The ligature wire was brought through
the U-bend and activated with a hemostat.

87. Snail Loop (JCO, 2008)
• 0.017" ×0.025" SS wire by bending a simple omega
loop into a spiral shape, which provides the forces and
moments.
• Has the potential for twice as much activation as a
stainless steel omega loop before undergoing
permanent deformation.
• The outer portion of the snail loop is 8mm high and
6mm wide, and the inner portion is 6mm high and
3mm wide.

88. • Preactivation alpha and beta bends incorporated into
the wire (α= 25°,
• β= 35°; total = 60°) are greater than those used for the
conventional omega loop.
• The anterior and posterior moments produced by these
preactivation bends will counteract the tipping
moments created by the retraction force of the
appliance, and are reinforced by the activation moment
produced by the loop’s spiral design

89. • If an extrusive or intrusive force against the anterior and posterior
segments is not desired, the loop must be centered between them.
• Miniscrews may be used with the snail loop for additional anchorage.
• Advantages
• Potential for greater, more efficient vertical movement of the anterior
segment, due to the flexibility in the vertical plane provided by the spiral
design.
• Lower load-deflection rate from using a longer wire.
• More control of the moment-to-force ratio, allowing bodily movement,
controlled tipping, or uncontrolled tipping as desired.
• Reduced number of activations and patient visits.
• Easier fabrication and placement.
• Improved hygiene and patient comfort, with less cheek impinge ment

90. Delta loop
• Described by William Proffit.
• Advocates using 0.016x0.022” wire in 0.018 slot and
0.018x0.025” wire in 0.022 slot.
• Opening type of loop.

91. Rickett’s Maxillary Cuspid Retraction Spring
• It is a double vertical helical extended crossed T closing loop spring
which contains 70 mm of 0.016’’ × 0.022’’ SS wire.
• It produces only 30-50 gm per mm of activation, because of the
additional wire used in its design and all loops are being contracted
during its activation.
• 3–4 mm of activation is sufficient for upper cuspid retraction

92. Rickett’s Mandibular Cuspid Retraction spring
• It is a compound spring, a double vertical helical closing loop.
• It contains 60 mm of 0.016 × 0.016 blue Elgiloy and produces
approximately 75 gm of force per mm of activation.
• A range of variation exists due to loop size and character of wire.
Therefore, 2–3 mm of activation is required to produce the desired force

93. Tear Drop Loop
• In 1983, R.G.Alexander used these Tear drop shaped loops in his vari-
simplex discipline.
• The loops are placed distal to the maxillary lateral incisor or canine
bracket for enmasse retraction.
• The closing loop archwire extends through the first molar tube. Before
placing the archwire in the mouth, the portion of the archwire distal to
the closing loops is reduced approximately .001” in the anodic polisher,
so that part of the wire can slide through the brackets easily during
activation.
• It is activated by pulling it distally 1 to 2mm to open the closing loop,
and bending the end 45 degrees gingivally to produce a stop.
• Activated every four to five weeks by 1mm.

94. • The ideal force applied to achieve movement of the mandibular incisors is
approximately 2.60 N.
• The springs that best approached this value were the teardrop springs of
6mm height activated 0.5 mm, which provided 2.51 N force, and
• The teardrop loop of 8 mm height activated 1.0 mm, provided 2.77 N force.

95. Poul Gjessing Canine Retraction Spring
• Designed by Poul Gjessing in 1985
• The spring consists of :
• A double ovoid helix of 10 mm height gingivally having 5.5mm width
• A smaller occlusally placed helix of 2 mm diameter
• Available commercially in the preformed version, constructed in 0.016 ×
0.022 inch SS wire
• Only one helix if TMA wire used

96. • Anti-rotation bend of 35° in
the distal extension
• Anti-tip bend of 15° on the
anterior leg and
• Beta bend 12˚ for 2nd
premolar
• 30° (12° bend + sweep) in the
distal leg for 1st molar
Anti rotation bend
Beta bend
Occlusal loop
Anti tip bend
Apical loop
35º
5.5 mm
15º
2 mm
30º
12º

97. • To prevent jiggling in the 0.022 inch
brackets, a 90° twist of the anterior
leg is recommended, so that the 0.022
inch dimension is vertical and
corresponds to the vertical dimension
of the bracket.

98. • Activated by pulling distal to the molar tube until sections of double
helix separate by 1 – 2 mm.
• Produces 140 – 160 gm of force for every 1 mm of activation
• Moment initially 10, increases to 12.5
• 1.2 mm of space closure in 4 weeks
• Reactivation every 4 to 6 weeks

99. Poul Gjessing retraction arch (1992) for controlled incisor retraction

100. K-SIR Loop
• The Kalra Simultaneous Intrusion and Retraction (K-SIR)
archwire is a modifi cation of the segmented loop mechanics
of Burstone and Nanda.
• It is a continuous 0.019 × 0.025 inch TMA archwire with
closed 7 × 2 mm U-loops at the extraction sites.
• 90° V-bend at U-loop to produce centered V bend
• 60° V-bend posterior to loop to increase beta moment
• 20° anti-rotation bend distal to U-loop to prevent buccal
segments from rolling mesiolingually

101. • A trial activation of the archwire is performed outside the mouth. This
trial activation releases the stress built up from bending the wire and
thus reduces the severity of the V-bends.

102. • After the trial activation, the neutral position of the each loop is
determined with the legs extended horizontally.
• In neutral position, the U-loop will be about 3.5 mm wide.
• The archwire is inserted into the auxiliary tubes of the first molars and
engaged in the six anterior brackets.

103. • It is activated about 3 mm, so that the mesial and distal legs of the loops
are barely apart.
• The second premolars are bypassed to increase the interbracket distance
between the two ends of attachment.
• This allows the clinician to utilize the mechanics of the off-centre V-
bend.

104. • The K-SIR archwire exerts about 125 gm of intrusive force on the
anterior segment.
• There will initially cause controlled tipping of the teeth into the
extraction sites.
• As the loops deactivate and the force decreases, the moment-to-force
ratio will increase to cause first bodily and then root movement of the
teeth.
• The archwire should therefore not be reactivated at short intervals, but
only every six to eight weeks until all space has been closed.
• It is to be noted that activation in the mouth is 3 mm every 6–8 weeks.

105. T-Loop Spring
• The T-loop was first introduced by Charles H. Burstone at the
University of Connecticut in 1982.
• Can be fabricated from 0.017” × 0.025” TMA or 0.16” × 0.022” SS wires.
• Specially designed for canine retraction in segmented arch technique and
enmasse or separate incisor retraction.
• Burstone describes this segmental T-loop as one of the most versatile
space closure devices available

106. Design
• Has a horizontal loop of 10 mm length and 2 mm diameter.
• Mesial leg is of 5 mm height and distal leg is of 4 mm height. (Distal
section inserted into auxiliary slot of molar tube)
α β

107. • Preactivated at 6 points

109. • For individual canine retraction, anti-rotation bends of 120° is given
between the legs during pre-activation.

110. • and trial activated before use
• The total preactivation is 190˚ which becomes 180˚ after trial activation

112. Group B (symmetric space closure) using a T-loop
• T-loop spring centered between the anterior and posterior attachments
produces this force system.
• The center position can be found by
Length=
interbracket distance −activation
2
• With the use of a vertical tube at the canine, a 90° gingival bend at the
calculated distance eases placement and monitoring throughout space
closure.

113. • If the canine bracket doesn’t have a vertical tube, crimpable ‘cross tubes’
may be attached to the anterior segment.
• To insert the T-loop, the spring is placed in the auxiliary molar tube.
Then, the 90° bend is inserted into the canine tube.
• The distal end is pulled back until the distal arm is the desired length
which results in desired activation.

114. Length=
interbracket distance −activation
2

115. • The tooth movement is expected to follow three phases – Tipping,
translation and root movement.
• The progress of space closure is assessed by observing the amount of
remaining space, the axial inclinations of the anterior and posterior
segments and the occlusal relationship.
• During the tipping phase, the anterior and posterior occlusal planes
angle towards one another due to segment’s tipped axial inclinations.
This angulation corrects during root movement.
• When the occlusal planes regain parallelism, spring reactivation is
indicated and the amount of reactivation should be based on the space
closure requirements at that time.

116. Group A space closure
• The biomechanical paradigm for this space closure problem is to increase
the β: M/F relative to the α: M/F ratio.
• Utilizing the V-bend principle, the T-loop is positioned closer to the
posterior attachment or the molar tube. It is not necessary to be far off-
center to obtain an adequate moment differential, with most cases
requiring only 1-2mm off-centering.
• Because the beta moment is greater than the alpha moment, a vertical
intrusive force may exaggerate the tipping tendency and steepening the
anterior occlusal plane.

117. • Likewise, the increased beta moment may steepen the posterior occlusal
plane.
• Maintaining an adequate horizontal force helps reduce these effects.
• The posterior occlusal plane can also be controlled with the use of a high
pull head gear.
• It is likely that a root correction stage will be required following group A
space closure.
• The nature of root correction needed will depend on the specific needs
of the case.

118. Group C space closure
• The biomechanical principle reverses the approach to Group A space
closure.
• The alpha(anterior) moment is increased compared to beta moment.
• The T loop is positioned closer to the anterior segment.
• It is important that the anterior wire segment achieves full bracket
engagement. Otherwise, the play within the brackets reduces the
effectiveness of the moment differential .
• One or two millimeters close to the anterior teeth is all that is necessary.

121. Asymmetrical ‘T’ Archwire (Hilgers ,JCO,1992)
• It is a new loop system made of .016” X .022” TMA(for .018” brackets)
or .019” X .025” TMA(for .022” brackets).
• TMA wire is ideal because of its inherent metallurgical qualities.
• It has sufficient stiffness, for optimum stability, and working range, to
minimize reactivations.

122. • Furthermore, because of the moderate forces, they are active over a long
span.
• On the other hand, stainless steel is too stiff, its working range too
narrow, to move teeth effectively over a long span.
• Nickel titanium has a wide working range, but its stiffness is too low to
provide the stability needed for the loop.
• The alloy also has a high recovery rate within its working range, making
it more valuable as a continuous archwire without loops.

123. • The shorter, mesial portion of the loop can be closed and the longer,
distal portion opened to create a step between anterior and posterior
segments that allows simultaneous bite opening and space closure.

124. • The loop can also be activated intraorally to advance the
upper incisors during the initial phase of treatment, or to
increase torque during retraction.
• To bend the loop into a preformed TMA archwire, the
rounded tip of either a small, Capcud bird beak plier or a
small optical plier is used.
• The vertical portion of the loop should be 5mm, the
anterior loop 2mm and the posterior loop 5mm.
• The loop is bent slightly inward to prevent irritation of
cheek, and the distal ends of the archwire allow easy
insertion into a pre-rotated molar tube.

125. Modified ‘T’ Loop Arch Wire
• Was devised by Barton H.Tayer in 1981.
• In some cases,there is a need for additional maxillary intrusion (bite
opening), space closure and torque toward the end of active treatment.
Typically the mandibular arch is completed. It may require a small
amount of space closure; but leveling, alignment and rotations have been
corrected.
• The maxillary arch should be in class I relationship from cuspid to molar,
but final space closure of the anterior section is prevented by
interference of mandibular anterior brackets. The maxillary anterior
teeth still require lingual root torque, and depression to gain additional
bite opening to permit space closure and overjet reduction.
• The modified T-loop archwire achieves all these corrections.

126. Design
• With ‘018’ slots – 16cm of 0.016×0.022 Blue elgiloy wire is used.
• With ‘022’ slots – 16cm of 0.019×0.025’ Blue elgiloy wire is used.
• Here, it is Edgewise appliance where brackets are not pretorqued or
inouted but are angulated to individual choice.
• Arch form is produced using a turret with lingual root torque in the
anterior section.
• A helix of 2mm diameter is made 1mm distal to the lateral incisor
bracket. The posterior leg is positioned bucally. 1mm should remain
between the medial of the helix and the lateral bracket.
• The distal end of the helix is placed at 90° to the occlusal plane.

127. • Place the round end of 139 plier in contact with and superior to the helix
bending the wire mesially 60°
• Place the round beak above this bend, with the sharp beak contacting the
mesial leg of the loop. The archwire is bent around the round beak until
it is inclined 45° toward the occlusal plane.
• The round beak is moved down the arch wire and the wire is recurved
around the beak to form a modified ‘T’ measuring approximately 7mm.
• The distal leg of the T-loop is formed parallel to and passively
contacting the mesial leg.

129. • The anterior section of the archwire is bent gingivally approximately
3mm. When this is done at both the helix, anterior postion of the
archwire will have 30° of lingual root torque. The posterior part of the
archwire should be detorqued by manipulating the modified T-loops.
• The archwire is inserted, clinched posterior to the buccal tubes.
Activation of modified T-loop is done.
• Augmentation forces for space closure are by placing class I elastics
around the loop.

130. • For bite opening & lingual root torque, class II elastics are passed
between vertical legs of the T-loop and engaged in the distal leg. Head
gears are also employed for bite opening and lingual root torque.
• Thus, the modified T-loop archwire with optional augmentation forces
will accomplish maxillary anterior depression, lingual root torque
besides and closing of extraction space. Barton H. Tayer has
accomplished these 3 goals in 3 to 5 months.

131. T Loops For Adult Patients
• In 1989, Clemens Manhartsberger et al used the segmented arch
technique for space closure in adult patients.
• T-loops of 0.016inch × 0.022 and 0.017 × 0.025 TMA, with angulations
incorporated via concentrated bends and graduated curvature were used.
• In adult patients, the average M/F ratio advised are not applicable due to
variation of the center of resistance.
• This is due to differing levels of bony support and periodontal loss.
• Thus, with a change in center of resistance, the M/F ratio must be
modified.

132. • In a T-loop, the amount or wire placed gingivally at the top of the loop
increases the M/F ratio and reduces the load deflection rate.
• In adult patients, the force magnitude must be reduced and M/F ratio
must be increased.
• The necessity of producing a lower load deflection rate in such cases
suggests the use of wire with a lower stiffness.
• Force magnitude can be lowered by reducing the cross section and / or
the amount of activation of the spring.
• The M/F ration can be increased by augmenting the angulation of the
T-loop.

133. • In 1997, Raymond L. Siatkowski put forth a design process using
Castigliano’s theorem to derive equations for M/F ration in terms of
loop geometry.
• The equations are used to optimize designs by optimizing M/F to
produce tooth movement via translation.
• The predicted results are verified experimentally.
• The result of this process is a new design, the OPUS loop, which is
capable of delivering a non-varying target M/F within the range of 8.0
to 9.1mm inherently, without adding residual moments via twists or
bends(commonly Gable bends) anywhere in the archwire or loop before
insertion.
Opus Loop

134. SPRING DESIGN
• 10 mm high, 10 mm long, and 0.5 mm radius in 0.016 ´ 0.022 inch S.S.
wire, 0.018 ´ 0.025 inch S.S. wire, and 0.017 ´ 0.025 inch TMA.

136. Three-Piece Intrusion Arch
• A segmented approach to simultaneous intrusion and space closure was
done by Bhavna Shroff et al.
• One couple, asymmetrical v-bend system

137. • Anterior segment - 0.021" x 0.025" SS, stepped gingivally by 3 mm
distal to the laterals and extends till distal of canine
• Intrusion cantilevers - 0.017" x 0.025" TMA or SS (with helix)
• Intrusion cantilever hooked onto the stepped portion distal to CRes of
incisor segment.
• Note that the hooking has to be clear of the gingival step of anterior
segment to allow sliding and retraction of incisors.
• A light class I elastic chain to redirect the force along incisor long axis.
• Caution – Do not include canine in anterior segment. Canine intrusion is
better done separately using cantilever from the auxiliary tube of the
molar

138. • An intrusive force perpendicular to the distal extension of the anterior
segment and applied through the center of resistance of the anterior
teeth will intrude the incisor segment.
• It is possible to change the direction of the net intrusive force by
applying a small distal force.
• The line of action of the resultant force will be lingual to the center of
resistance and a combination of intrusion and tip back of anterior teeth
will occur.

139. • This line of action of the resultant force can be made parallel to the long
axis of the anterior teeth if an appropriate distal force is combined with
a given intrusive force.
• Then, the point of force application must be more anterior and as close
to the distal of the lateral incisor bracket as possible.
• The distal force used in this intrusion retraction system is of very low
magnitude and is used to redirect the line of action of the intrusive
force.
• One advantage of this system is the low magnitude of force applied on
the reactive or anchorage unit.

140. Utility arch
• This was reviewed by Graber and Swain
• Fabricated from 16 x 16 or 16 x 22 SS / Blue Elgiloy wire
• Anterior section in the incisor slots
• Anterior vertical step height - 5 to 8 mm in maxilla and 4 to 5 mm in
mandible
• Buccal Bridge - contoured to prevent trauma to gingiva, may be enclosed
in archwire sleeve
• Posterior vertical step height - 4 to 5 mm in maxilla and 3 to 4 mm in
mandible

141. Molar segment
• Into main / auxiliary slot
• 45 degrees of molar tipback
• 45 degrees of buccal root torque (for cortical anchorage)
• 30 degrees of anti-rotation (to avoid mesio-lingual molar rotation during
retraction)
• Adequate expansion at molars

142. Anteriorly wire lifted and engaged in incisor brackets to produce
• Intrusive force (equilibrium for extrusive force at molar)
• Moment of force created due intrusive force acting labial to CRes – tends
to procline
• Moment of couple created by engagement of wire in slot (III order
bracket – wire angulation, also I and II order if brackets not aligned and
levelled)

143. • The vertical forces created by the III order couple in the incisor bracket
may alter the intrusive force depending on the type and magnitude of
torque.
• When anterior segment has lingual root torque, the intrusive force on
anteriors can be diminished, equaled or even overpowered.
• With labial root torque, the intrusive force on anteriors is augmented.
• Use of round wire avoids the effects of third order couple on the
incisors.

145. Mc Namara’s modification (JCO,1986)
Retraction utility arch
• Helix anterior to anterior step
• Posterior step away from molar tube
• Pulled distally and cinched to activate
Protraction utility arch
• Helix posterior to anterior step
• Posterior step abutting molar tube
• Activated by ligating the anterior section into slot and opening the helix
Tip back may be distributed in molar and buccal bridge sections.

147. Conclusion
A good understanding of mechanics is required when using retraction loops
or springs, because minor errors in mechanics can result in major errors in
tooth movement. Today's orthodontist requires a working knowledge of
both friction and frictionless mechanics. There are indications for both and
hence a practitioner should always have an open mind when it comes to
choosing the right mechanics.