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Cantilever Springs: Force System and Clinical Applications Andrew J. Kuhlberg

Cantilever springs are simple and efficient orthodontic appliances with a wide variety of clinical uses. Biomechanically, cantilevers are able to produce statically determinant force systems, giving the clinician the opportu- nity to deliver qualitatively and quantitatively precise forces. Cantilever springs have a large range of clinical applications. They can be used in first-, second-, and third-order problems. The basic design of cantilever springs and their various clinical applications are discussed. (Semin Orthod 2001;7: 150-159.) Copyright © 2001 by W,B. Saunders Company

A S the field of or thodontics has evolved, the options and techniques of mechano the rapy

have expanded significantly. Advances in bracket design, wire alloys, and even bonding techniques have increased clinical options. Al- though bracket designs and proprietary treat- men t protocols are broadly useful for many clinical circumstances, achieving predictable and efficient or thodont ic tooth m ovem en t requires more than simply selecting a particular bracket style or arch wire sequence. The f u n d a m e n t a l basis of o r thodon t i c the rapy remains the appl icat ion of mechan ica l forces to p roduce tooth m o v e m e n t . Force-driven appl iance designs are the u l t imate a p p r o a c h in d i rec t ing t r e a t m e n t t echn iques toward sound b iome- chanical foundat ions . ~,2 Across the wide array of o r thodon t i c devices, it is i m p o r t a n t to rec- ognize the similarities be tween various mech- anisms. 3 One of the c o m m o n designs is the cant i lever spring.

Cantilevers are beams suppor ted at one end. A schematic d iagram of a cantilever is shown in Figure 1. The key feature of the cantilever spring is that the free end only may generate a single

From the Department of Orthodontics, University of Connecticut, School of Dental Medicine, Farmington CT.

Address correspondence to Andrew J. Kuhlberg, DMD, MDS, Assistant Professor, Department of Orthodontics, University of Connecticut, School of Dental Medidne, 263 Farmington Ave, MC1725, Farmington CT 06030.

Copyright © 2001 by W.B. Saunders Company l 073-8746/01/0703-0002535. 00/0 doi: l O. 1053/sodo. 2001.26689

force (ie, there is no appl ied couple) . Equilib- r ium requires that the force act ing at the free end mus t be ba lanced by an equal and opposite force at the s u p p o r t e d end. These two equal and opposi te forces are a couple, in this case p r o d u c i n g clockwise rotat ion. The re fo re , an addi t ional m o m e n t mus t be act ing on the spr ing at the suppor t ed end in the counter- clockwise direct ion. Thus, the condi t ions of static equi l ibr ium are fully satisfied and the comple t e force system acting on the spr ing is shown in Figure lB. 4-6

For o r thodon t i c applicat ions, the fixed end of the cant i lever is the end of the spr ing in- ser ted into a b racke t or a tube (Fig 2A). The free end applies a po in t contact; it does not engage a b racke t slot or tube. The spring is activated by applying a force to this end; the force is r ep re sen t ed by the weight suspended f rom the wire in Figure 2B. The b r a c k e t / t u b e exerts an oppos ing force on the o the r end of the spring. These forces const i tute a couple, therefore , it mus t be c o u n t e r e d by a n o t h e r couple. This couple is p r o d u c e d by the bracke t ( tube) . Thus, the force system on the wire includes the two couples, the forces act ing at each end of the wire and the in t rabracke t forces. The force system act ing on the teeth is s imply the reverse of this force system (Fig 2C). The expec ted clinical m o v e m e n t s follow the forces act ing on the tee th and are dia- g r a m e d in Figure 2D. The two couples are of equal magn i tude but oppos i te in direct ion. The magn i tude of the m o m e n t (couple) is the

150 Seminars in Orthodontics, Vol 7, No 3 (September), 2001: pp 150-159

Cantilever Springs 151

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Figure 1. The general force system from cantilever springs. A point force acts on the free end of the spring (A). The equilibrium force system includes an opposing force and a concurrent moment acting at the fixed end (B). The arrows represent the forces and moments acting on the spring.

p r o d u c t o f the fo rce m a g n i t u d e mul t ip l i ed by the d is tance be tween the forces o f e i t he r couple .

Because a canti lever is a s imple two-tooth appliance, its force system is statically de te rminan t . The forces and the m o m e n t s can be readily mea- sured, thus, no u n k n o w n forces are act ing on the teeth. By working with measurab le forces and moment s , use o f this type o f appl iance per- mits greater cont ro l by the o r thodon t i s t a nd improves the predictabil i ty o f movemen t . This minimizes the potent ia l for u n e x p e c t e d too th m o v e m e n t du r ing o r t hodon t i c t rea tment .

Two extremely impor t an t and distinct advan- tages character ize the canti lever design. First, the ancho rage o r reactive teeth can be rigidly secured to ad jacent tee th with heavy arch wires or segments, thus, r educ ing their potent ia l movement . Second, the cantilever can be fabricated f rom r e d u c e d m odu lus wires relative to the wire (s) suppor t ing the a n c h o r units. This, in combina t ion with the in t roduc t ion o f a helix at the fixed end, will p r o d u c e a m o r e cons tan t

force act ing on the teeth ( tooth) be ing moved. Reactivations can thus be e l iminated o r significantly r educed .

First-Order Cantilevers

With respect to the occlusal plane, the possibilities o f a canti lever force system are shown in Figures 3A-D. The canti lever can be fixed posteriorly or anteriorly. In this plane, a cantilever p roduces transverse forces with the rotat ional m o m e n t s at the fixed end.

Midline cor rec t ion with a canti lever provides a m e t h o d o f incisor m o v e m e n t with minimal side effects. 7,8 This t echn ique may be used when e i ther a t ipping m o v e m e n t o r t ranslat ion is the requ i red movement . W h e n the incisors are t ipped (Fig 4A), f requent ly associated with ec- topic e rup t ions or the p r ema tu re loss o f pr imary teeth, a s imple force is n e e d e d to upr igh t the incisors and establish midl ine co inc idence . In contrast , the use o f an arch wire for a l ignment may result in fu ture p rob lems that would require addi t ional cor rec t ion procedures . First, indis- c r iminan t leveling may create a cant to the anterior occlusal plane. Also, this a p p r o a c h re-

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Figure 2. A cantilever inserted into an orthodontic bracket. Passive spring (A). Force system on the wire (B). Force system acting on the teeth (C). The ex- pected movements from a cantilever (D). The shadowed bracket/wire reveals the previous position. The force system on the wire includes the two couples, the forces acting at each end of the wire (large arrows), and the intrabracket forces (small arrows) Note: ar- row size is not representative of the force magnitudes.

152 Andrew J. Kuhlberg

Figure 3. Applications of the cantilever force system to first-order orthodontic problems. A cantilever inserted into the molar tube may be activated to apply a force toward the midline (A) or away from the midline (B). The total force system acting on the teeth is shown. A cantilever inserted into a tube at the canine or in the anterior region. The cantilever can be activated to produce either an expansion (C) or constriction force (D). The arrows represent the forces/moments applied to the teeth.

quires sliding brackets ( teeth) a long the a rch wire. The force o f fr ict ion acts in the opposi te d i rect ion o f the i n t e n d e d movemen t , resisting m o v e m e n t o f the denta l midl ine in the desired direct ion. T he tee th may up r igh t wi thout obtain- ing the midl ine correc t ion. T he canti lever pro- r ides an alternative m e c h a n i s m that avoids these potent ia l difficulties. T he po in t force may be

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~ = Center of Resistance

Figure 4. A midline discrepancy caused by tipping of the lower incisors. A simple force at the crowns of the teeth (without an arch wire) will upright the incisors and achieve midline coincidence (A). Midline correction by tipping (B).

appl ied to the an te r ior teeth before placing an al igning wire. The canti lever can provide a pull- ing force to shift the midline. Each incisor needs to be i n d e p e n d e n t l y t ipped to cor rec t the midline. By tying the brackets toge the r in a "Figure 8" and a t taching the canti lever at the level o f the brackets, this s imple t ipping m o v e m e n t easily corrects the midl ine d iscrepancy (Fig 4B).

An addi t ional p r o b l e m in midl ine cor rec t ion occurs when translat ion m o v e m e n t is r equ i red (Fig 5A). Canti lever mechan ics allows the po in t o f force appl icat ion to be varied as needed . Bodily m o v e m e n t occurs when a force is appl ied t h r o u g h the cen te r o f resistance o f the body (Fig 5B). By ex tend ing a passive loop apically toward the cen te r o f resistance o f the an te r ior teeth, the spr ing can be a t tached to p r o d u c e the force at the desired level.

Transverse discrepancies in the pos ter ior den- tition can also be addressed with cantilevers. Th e clinical opt ions can be ascer ta ined by reviewing the possibilities shown in Figure 3. W h e n attached to the molar buccal tube, the cantilever spring can be activated for simultaneous molar expansion and mesiobuccal rotation. The cantilever can be inserted into a vertical tube at the canine or f rom an auxiliary tube at tached to a base arch wire. Emanat ing f rom the anterior, the cantilever provides an expansion force at the molar useful for the COlTection of single-tooth dental cross-bites.

kal in terest ing appl icat ion o f the canti lever

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Figure 5. Midline correction by translation. An anterior wire with a loop extended apically to approximate the center of resistance of the incisor teeth to provide a contact point for the force (A). A force applied through the center of resistance will produce translation (B).


force system is in the expansion for unilateral cleft palate/alveolus correction. C o m m o n orthodontic problems in the unilateral cleft include poster ior cross-bite with rotat ion of the lesser segment, resulting in a more severe cross-bite in the pr imary canine region compared with the molar region. Also, the greater segment and the anter ior teeth are t ipped toward the cleft. The objectives of or thodont ic t rea tment include poster ior expansion with concur ren t mesiobuccal rotat ion of the lesser segment whereas the greater s egmen t /mid l ine often requires transverse movemen t away f rom the cleft to facilitate surgical alveolar repair. Figure 6A shows these c o m m o n problems. Figure 6B shows the movements needed to correct these problems and mee t the objectives of this stage of or thodont ic t reatment. Figure 6C is a schematic of the repo- sitioned dental segments. The movements required are effectively p roduced by the force system of cantilever springs.

Figures 7A-H is an example of a cantilever spring used for the presurgical or thodont ic t rea tment of a unilateral cleft lip and palate. Figures 7A and 7B show the c o m m o n clinical problems described earlier. The molar attachments include an auxiliary tube and the posterior segment is splinted rigidly with fiber-

Figure 6. Common problems associated with unilateral cleft lip and palate. Maxillary constriction, mesiolingual rotation of the lesser segment, and rotation of greater segment toward cleft area with maxillmy incisor midline toward cleft (A). The force system produced by a cantilever provides a means of correction for these problems. The movements required for correction of these problems (B). Idealized objective of orthodontic treatment of unilateral cleft palate (C).

re inforced composite. 9 The anter ior teeth are bracketed and a passive heavy (0.017 × 0.025- inch stainless steel) arch wire is inserted (Fig 7C). The cantilever spring (0.017 × 0.025-inch stainless steel [SS]) is designed to rotate the anter ior segment to the pat ient 's right, and to expand and rotate the poster ior segment. Figure 7D shows the passive cantilever, Figure 7E shows the active cantilever and its force system. At initial insertion, the cantilever tips the incisors// greater segment to the pat ient 's right, expand- ing the maxillary arch (Figure 7F). Subsequently, a second cantilever was fabricated that extended far- ther anteriorly to improve the range of activation. Figures 7G and 7H show the outcome of the expansion and maxillary arch formation along with the midline correction. This approach to appliance design can be especially beneficial when the placement and adjustment of palatal appliances stimulates powerful gag reflexes, not uncommon in cleft patients. This spring provides an alternative to the use of Qua&helices and other palatal appliances. The primary difficulty with a cantilever design for expansion is generation of sufficient expansion forces.

Second-Order Cantilevers From the second-order perspective, the cantilever spring force system provides vertical forces and t ip-forward/t ip-back rotational momen t s (Figs 8A-D). Cantilever springs are useful for the application of vertical forces (intrusion, extrusion) or adjustments of the axial inclination of teeth (tip-back, r o o t c o r r e c t i o n ) . 1°-13

Perhaps the most c o m m o n cantilever spring design is the anter ior intrusion arch. Intrusion arches are characterized by the point force application on the incisors. The force system f rom intrusion arches includes anter ior intrusion, poster ior extrusion, and molar tip-back (crown- distal rotation). The basic design is shown in Figure 9. The elegance of the intrusion arch design is revealed by the variety of clinical solutions it provides. Classically, the intrusion arch has been used for anter ior deep overbite correction while permit t ing the simultaneous correction of Class II molar relationships by the molar tip-back.

One of the nuances of intrusion mechanics is the ability to select the point of force application. 1° Selecting the location of the point of


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Figure 7. Maxillary expansion for a left unilateral cleft lip and palate. Pretreatment maxillary view (A), pretreatment left buccal view (B), diagram of the initial appliance set-up (C). The molars are banded, the incisors bracketed, a stiff SS segment secures the greater segment; the primary teeth in the less segment are splinted to the molar (represented in gray). Diagram of the passive cantilever spring (D). Diagram of the activated cantilever spring and the force system acting on the teeth (E). Initial placement, frontal view (F). The anterior/greater segment wire is passive 0.017 × 0.025-inch SS. The cantilever pushes on the distal aspect of the maxillary left central incisor bracket. Note that the upper midline is the full width of a lower incisor to the left. Maxillary arch after expansion and alveolar bone graft (G). Anterior view after expansion and bone graft (H). The cantilever had been replaced to increase its length and range of activation; it pushed laterally on the mesial aspect of the right central incisor bracket; note the midline correction.

force application greatly increases the clinical possibilities. Properly positioning and directing the force relative to the center of resistance of the teeth capitalizes on the effect of moments of forces. This allows increased control of changes to the axial inclination of the teeth during intrusion (Figs 10A-D). Conversely, a lack of awareness of the effect of moments of forces may result in unexpected problems; for example, the point of force application anterior to the center of resistance of the incisors for the midline correction options described previously (Figs 4 and 5) would tend to rotate the anterior teeth in the plane of occlusion. Frequently, this momen t is

small because the distance between the force application and the center of resistance is small. Recognition of these effects allows the clinician to plan accordingly.

Extrusion springs are the reverse of intrusion mechanics. Cantilevers have been used for extrusive tooth movements for high or impacted canines and anterior open-bite correction (Figs l l A and l lB) . ~,14,15 The force system on the molar tube tends to produce mesial tip-forward movement and intrusion of the molar. These reactive teeth can be appropriately supported by a relatively stiff arch wire, thus, eliminating or reducing this side effect.

Cantilever Sprb~gs 155

Figure 9. The intrusion arch is a common cantilever.

Although intrusion and extrusion springs rely on the vertical force (s) of cantilevers to achieve the treatment goals, the momen t produced by cantilever springs can also be exploited for ef- fective tooth movement. Canine root axial correction may be necessary after extraction space closure (Fig 12A).16 A cantilever spring inserted into the bracket slot of the canine is a means of achieving distal root correction (Fig 12B). Ex- tending the spring distally generates a greater momen t on the canine without heavy vertical forces. Extrusion of the canine can be prevented by stepping a stiff by-pass wire incisal to the bracket and the space closure can be retained by a "Figure 8" tie-back to the posterior teeth.

Third-Order Cantilevers

Third-order tooth movements are those that change the buccolingual axial inclination of teeth. The edgewise bracket, with the rectangular slot combined with rectangular arch wires, is a commonly recognized approach to generating torque and third-order tooth movement. Canti- lever springs are also capable of producing these buccal-lingual axial inclination corrections, of-

Figure 8. Second-order cantilever applications. In- serting the cantilever into the molar tube allows either anterior intrusion, posterior extrusion, and molar tip- back (A), or anterior extrusion, posterior intrusion, and molar tip-forward (B). An anteriorly placed cantilever that extends posteriorly allows either anterior extrusion, anterior distal root movement, and posterior intrusion (C), or anterior intrusion, anterior mesial root movement, and posterior extrusion (D).


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Figure 10. The location of the point of force application affects the type of tooth movement. The rotational movement produced by the force is dependent on the moment of the force. The moment of the force is a function of the point of force application and the distance to the center of resistance. A force at the bracket of a flared incisor (A). A force slightly distal to the bracket (B). A force positioned further distally to pass through the center of resistance (C). A force posterior to the center of resistance (D). The shadowed teeth show the previous tooth position.

ten wi thout the n e e d to resort to heavy rectangular wires engaged in to all teeth.

Excessively u p r i g h t incisors may occur after re t rac t ion a n d overjet r educ t ion , especially

A

B

when teeth are re t rac ted on r o u n d arch wires or with a d i f f e ren t i a l -momen t a nc ho r a ge strategy. 16 An an te r io r roo t cor rec t ion spr ing is a var ia t ion of a cant i lever des igned to improve the incisor axial i nc l i na t i on (Figs 13A a n d 13B). An te r io r

roo t springs are fabr icated f rom rec tangu la r

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Figure 11. A cantilever for extrusion of an impacted or high canine. Force system and appliance design (A). Treatment objective of canine extrusion (B).

Figure 12. Separate canine root correction with a cantilever. Force system and appliance design (A). Treatment objective of canine root correction (B).


Figure 13. Third-order tooth movement with a cantilever anterior root correction. Force system and appliance design (A). The cantilever is fabricated with a full-bracket sized rectangular wire. Treatment objective of anterior root correction (B).

Fabricating Cantilevers Cantilever springs can be fabricated from ahnost any orthodontic wire. Stainless steel and beta- titanium wires are popular choices because of their formability. Because of the relatively high stiffness of stainless steel, helices aid in reducing the force levels of SS springs while also increas- ing the springs' range of activation. Nickel-titanium wires have also been used in cantilever applications; however, these springs must be pre- fabricated by the manufacturer? 7 Rectangular wires are generally preferred for making cantilever springs because they resist rolling within the bracket or tube, thus, ensuring accurate control of the direction of force application.

The force generated by the spring can be mea- sured with a force gauge. The moment magnitude is the product of the force multiplied by the distance between the attachments. The moment magnitude can be increased or decreased by changing the length of the cantilever spring. This allows qualitative and quantitative control of the applied force systems. The direction of the force vector is determined by the activation of the spring.

wires that fully engage the bracket slot. The spring is activated to apply an intrusive force in the posterior region. As with the canine root correction spring, a base arch wire should pass incisal to the anterior brackets to prevent the extrusive side effect.

Rectangular orthodontic wires afford another means of cantilever activation. Placing a perma- nent twist in a curved section of wire is an alternative approach to cantilever activation (Fig 14). Torsional forces from full-sized wires within edgewise tubes or brackets generate a third-order couple acting on the bracket/slot tube.

One of the challenges of vertical tooth movements is prevention of unwanted side effects. For instance, in the treatment of an anterior open bite with an extrusion arch, the side effect on the molar /poster ior teeth may be a tip-forward moment . Tip-forward movements of the posterior teeth tend to increase occlusal plane problems associated with open bites. The use of a twist or third-order activation to an extrusion cantilever can be a means of reducing this side effect. Figures 15A-I show an anterior open bite cor- rected by extrusion with twist-activated cantilevers.

1 Figure 14. Placing a twist about the long axis of a crowed section of a rectangular arch wire. The twist creates a third-order activation that can be used for cantilever force generation. To flatten the wire (the force system on the wire) would require a downward force at one end opposed by an upward and torsional force on the opposite end.


Figure 15. Anterior open-bite correction with third-order activation of a cantilever. Pretreatment right (A), frontal (B), and left views (C). The cantilever springs passively inserted into auxilim T tubes on molars and twist activations into curved wire segments. Hooks are bent into the anterior end of the springs to engage the anterior segment (D). Buccal view of activated spring; the spring exerts an extrusive force on the incisor segment (E). Occlusal view with springs inserted. A passive transpalatal arch is placed to prevent third-order movement of the molars (F). Posttreatment right (G), frontal (H), and left views (I).

Managing Side Effects and the Reactive Forces

Because the force system of cantilever springs can be accurately de termined, the potential o r thodont ic side effects (unwanted tooth movement) can also be predicted. Recogniz- ing the possible side effects allows one to pre- pare for them at the onset of t rea tment ra ther than discovering perplexing midcourse problems. Palatal and lingual arches are beneficial in mainta in ing arch widths as well as third- order side effects on the molars. ~ Headgear and intermaxillary elastics can be useful in control l ing occlusal plane effects. Undesirable vertical movements can be restrained by heavy by-pass wires s tepped incisal to the brackets to

prevent eruptive side effects. 16 Solidly jo in ing many teeth into the anchor units with either rigid wires or splinting helps minimize unwanted effects.

Summary

Cantilever springs generate a predictable force system that is applicable to a wide variety of orthodontic problems. Especially in situations in which a point force is required, cantilever springs offer a simple option that is easily tai- lored to an individual patient 's needs. With their simple design, these springs may be used in many creative orthodontic solutions.

Cantilev~ Springs 15 9

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3. Lindauer SJ, Isaacson RJ. One-couple orthodontic appliance systems. Semin Orthod 1995;1:12-24.

4. Mulligan TF. Common sense mechanics. 1. J Clin Orthod 1979;13:588-594.



7. Nanda R, Margolis MJ. Treatment strategies for midline discrepancies. Semin Orthod 1996;2:84-89.

8. van Steenbergen E, Nanda R. Biomechanics of orthodontic correction of dental asymmetries. Am J Orthod Dentofacial Orthop 1995;107:618-624.

9. Burstone C, Kuhlberg A. Fiber-reinforced composites in orthodontics. J Clin Orthod 2000;34:271-279.

10. Burstone CR. Deep overbite correction by intrusion. AmJ Orthod 1977;72:1-22.

11. Nanda R. Correction of deep overbite in adults. Dent Clin North Am 1997;41:67-87.

12. Roberts WWD, Chacker FM, Bnrstone CJ. A segmental approach to mandibular molar uprighting. AmJ Orthod 1982;81:177-184.

13. Shroff B, Yoon WM, Lindauer SJ, et al. Simultaneous intrusion and retraction using a three-piece base arch. Angle Orthod 1997;67:455-461.

14. Fischer T, Ziegler F, Lundberg C. Cantilever mechanics for treatment of impacted canines. J Clin Orthod 2000; 34:647-650.

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16. Burstone C, van Steenbergen E, Hanley IC Modern Edgewise Mechanics and the Segmented Arch Tech- nique. Glendora, CA: Ormco Corp, 1995.

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