ORIGINAL ARTICLE
Resistance to sliding with 3 types of elastomeric modules Helen Sylvia Griffiths,a Martyn Sherriff,b and Anthony John Irelandc London and Bristol, United Kingdom Introduction: Super Slick (TP Orthodontics, LaPorte, Ind), a polymeric-coated ligature, has recently been introduced to the orthodontic market. The manufacturer claims it will significantly reduce friction. The purposes of this study were to determine whether Super Slick modules show lower friction than round and rectangular modules and to put the frictional forces into perspective with a self-ligating bracket. Methods: Maxillary premolar, stainless steel, self-ligating, and monocrystalline brackets with .022-in slots were used with straight lengths of .018-in and .019 ⫻ .025-in stainless steel wires. Buccal segment models were set up with 1 molar band and 2 premolar brackets for each test group: self-ligating brackets with the slide closed, self-ligating brackets with the slide open, and monocrystalline brackets. The latter 2 groups were tested with all 3 types of elastomeric module. Each setup was tested both under dry conditions and after soaking in a water bath for 1 hour. Results: The self-ligating brackets demonstrated virtually zero friction with each combination of wire and environmental condition. When the different bracket and elastomeric module combinations were compared, significant differences were observed. In all but 2 combinations, round modules provided the least resistance to sliding and rectangular modules the greatest, with Super Slick modules in between the 2. The self-ligating bracket provided the least resistance to sliding of all the bracket/ligation combinations and almost entirely eliminated friction under the conditions of this experiment. Conclusions: Super Slick modules demonstrated greater resistance to sliding than conventional round modules, but not rectangular. Self-ligating brackets provided the least resistance to sliding of all bracket/ ligation combinations and were the only method that almost entirely eliminated friction. The .018-in and .019 ⫻ .025-in wires exhibited similar friction in the dry state, but, when wet, the .018-in wire produced less friction. Ceramic brackets demonstrated greater resistance to sliding than stainless steel brackets. Lubrication reduced the friction with .018-in wires and increased it for .019 ⫻ .025-in wires. (Am J Orthod Dentofacial Orthop 2005;127:670-5)
T
he straightwire appliance relies on the ability of orthodontic wires to slide through brackets and tubes during space closure, unless friction-free mechanics with looped archwires are used. When sliding mechanics are used, friction is a major consideration;1 it is estimated that 50% of the orthodontic force applied is used purely to overcome the friction in the system.2 Many factors have been implicated in influencing friction in orthodontic systems, including: wire alloy composition,3-13 wire deflection,5,6,8,14,15 wire size,3,5-9,11,12,15-20 bracket slot material,4,6,7,11,13,14,16 bracket width,3-5,8,9,21 lubrication,6,10,11,13-16,19,21,22 and method of ligation.1,5,11,16-18,20-24 a
Fixed-term training appointment in orthodontics, Bristol Dental Hospital and School. b Senior lecturer in biomaterials science, GKT Dental Institute, London. c Consultant/senior lecturer in orthodontics, Bristol Dental Hospital and School. Reprint requests to: Dr A. J. Ireland, Department of Child Dental Health, Bristol Dental Hospital and School, Lower Maudlin Street, Bristol BS1 2LY, United Kingdom; e-mail,
[email protected]. Submitted, October 2003; revised and accepted, January 2004. 0889-5406/$30.00 Copyright © 2005 by the American Association of Orthodontists. doi:10.1016/j.ajodo.2004.01.025
670
There is general agreement that stainless steel wires demonstrate the least resistance to sliding, -titanium the greatest, and nickel-titanium alloy somewhere between the 2.3-7,9,11-13 Friction tends to increase with the angulation of the archwire to the bracket slot.5, 6,8,14,15 The size of the archwire,3,5-7,12,15-18,20 specifically an increased vertical dimension, appears to be an important factor in friction in some studies. 3,5,6 However, other studies have found increasing archwire dimension not to be significant8,9; some have found that smallerdimension archwires produce the highest friction.11,19 Stainless steel brackets show less frictional resistance to sliding than ceramic brackets,6,7,11,13,14,16 although this would appear to be more marked with smaller-dimension archwires.11 There is some controversy regarding the effect of bracket size on friction,3-5,8,9,21 with some studies finding that wider brackets demonstrate higher friction than narrow brackets5,21 and vice versa.3,9 Similar conflicting reports exist for lubrication6,10,11,13-16,19,21,22 and its effects on resistance to sliding. Some investigations have found that some form of lubrication reduces friction,6,14,22,19,24 whereas oth-
Griffiths, Sherriff, and Ireland 671
American Journal of Orthodontics and Dentofacial Orthopedics Volume 127, Number 6
ers have found no such relationship.11,15 There are also reports that lubrication might even increase observed friction.10,13,16 The problem in comparing these studies is the difference in lubricants used, with some using human saliva22 and others artificial saliva.10,13 Finally, the method of ligation can highly influence friction,1,5,11,16-18,20-24 with conventional polyurethane ligatures increasing friction significantly when compared with stainless steel ties.11 In an effort to reduce the effect of metal and elastomeric ties on the resistance to sliding, manufacturers in recent years have produced self-ligating brackets, which have been shown to generate negligible friction.5,17,18,22-24 In 2000, a polymeric-coated ligature, Super Slick, was introduced to the orthodontic market with claims that it significantly reduced friction1,22 compared with conventional ties. The aim of this study was to determine whether Super Slick modules show a lower resistance to sliding when compared with standard round and rectangular cross-section modules and to put this into perspective with a self-ligating bracket. MATERIAL AND METHODS
The brackets used in this study were maxillary first premolar Damon 2 (Ormco, Orange, Calif) and Inspire (Ormco) brackets with .022-in slots. The Damon 2 bracket is a stainless steel, self-ligating, passive-clip bracket, and the Inspire bracket is a monocrystalline sapphire bracket. The size of the wires used in this experiment to simulate sliding mechanics were .018-in round and .019 ⫻ .025-in rectangular stainless steel. The testing machine was the LR5K (Lloyd Instruments, Segensworth, Fareham, England) with a 100 N load cell that was set to pull the wire through the brackets at 5 mm per minute11; each test was run for 2 minutes. The brackets were attached to acrylic teeth with cold-cure acrylic, and molar bands were attached to acrylic molars in the same way. A buccal segment was then set up with 1 molar and 2 premolars engaged on a straight section of .021 ⫻ .025-in stainless steel wire so as to achieve good alignment of the slots. The buccal segments were then cast in stone so that they could be held firmly in alignment (Fig 1), but also allowed them to be attached to the testing machine and for the test wire to run freely. Ten setups were made for each test group: 1. Damon 2 brackets with the slide closed 2. Damon 2 brackets with the slide open 3. Inspire brackets Groups 2 and 3 were tested with all 3 types of unstretched, gray, elastomeric modules. The 3 types of modules were Super Slick (TP Orthodontics, LaPorte, Ind), Dispens-A-Stix (round edged; TP Orthodontics)
Fig. Buccal segment test rig consisting of 1 molar band and 2 premolar brackets (Damon 2 with slider open) and Dispense-A-Stix modules in place, engaging straight section of .019 ⫻ .025-in stainless steel wire. Table I.
Bracket/ligation combination codes
Code number
Bracket/ligation combination
1 2 3 4
Ceramic bracket with standard polyurethane ring Ceramic with Super Slick polyurethane ring Ceramic with square profile polyurethane ring Damon 2 with standard polyurethane ring without clip Damon 2 with Super Slick polyurethane ring without clip Damon 2 with square profile polyurethane ring without clip Damon 2 with clip
5 6 7
and Lig-A-Ties (square edged; TP Orthodontics). The reason for using the Damon 2 bracket with the slide left open was to eliminate the need to compare 2 sets of data with different interbracket spans. However, this was a problem with the Inspire brackets, because they were wider than the Damon 2 bracket (by 0.44 mm), but no commercially available ceramic bracket could be found having the same mesiodistal width as the Damon 2 bracket (2.67 mm). Each setup was tested in both dry conditions and after having been soaked in a water bath at 37°C for 1 hour. New modules were placed before starting each dry test and before immersion in the water bath. The Shapiro-Wilk W test was used to test the data for normality. The data were found to be nonparametric, so the Kruskal-Wallis 1-way analysis of variance was used to compare the 3 elastomeric modules in each of the bracket/wire/wet/dry combinations. Summary statistics and confidence intervals of the differences of the means were also calculated for these groupings.
672 Griffiths, Sherriff, and Ireland
Table II.
Summary for .018-in stainless steel
Bracket/ligation Dry state 1 2 3 4 5 6 7 Wet state 1 2 3 4 5 6 7
Table III.
American Journal of Orthodontics and Dentofacial Orthopedics June 2005
Max
Mean
Median
SD
Interquartile range
1.67 3.27 3.63 1.51 2.53 2.8 0.01
4.68 8.79 6.85 2.76 4.17 4.0 0.01
3.38 4.94 4.86 2.17 3.30 3.36 0.01
3.32 4.61 4.71 2.36 3.20 3.32 0.01
0.88 1.52 0.96 0.42 0.59 0.33 0.01
2.95-3.97 4.16-5.21 4.22-5.29 1.91-2.43 2.85-3.86 3.24-3.46 0.0-0.01
2.75-4.01 3.85-6.03 4.18-5.55 1.87-2.47 2.88-3.73 3.12-3.59 0.01-0.01
.746 .017 .683 .185 .322 .531 —
1.68 0.85 2.86 1.04 1.00 1.00 ⫺0.02
3.48 2.23 3.75 1.83 1.87 4.39 0.02
2.44 1.51 3.21 1.40 1.44 2.20 0.003
2.45 1.51 3.19 1.40 1.41 2.12 0.00
0.51 0.37 0.25 0.26 0.31 0.84 0.01
1.98-2.69 1.29-1.65 3.08-3.36 1.19-1.61 1.21-1.72 1.64-2.44 0.0-0.01
2.09-2.78 1.26-1.75 3.04-3.38 1.22-1.57 1.23-1.65 1.63-2.76 ⫺0.004-0.01
.466 .982 .603 .269 .364 .029 .044
Min
95% CI
Shapiro-Wilk P
Summary for .019 ⫻ .025-in stainless steel
Bracket/ligation Dry state 1 2 3 4 5 6 7 Wet state 1 2 3 4 5 6 7
Min
Max
Mean
Median
SD
Interquartile range
95% CI
Shapiro-Wilk P
3.40 2.29 3.64 1.43 2.28 2.67 ⫺0.01
6.05 7.86 6.41 2.88 3.33 3.70 0.85
4.18 4.42 4.80 2.31 2.86 3.29 0.15
3.72 3.80 4.59 2.34 2.91 3.42 0.03
0.98 1.59 0.86 0.46 0.33 0.35 0.27
3.49-4.38 3.61-5.05 4.36-5.41 2.20-2.67 2.73-2.96 3.12-3.54 0.0-0.14
3.48-4.89 3.28-5.56 4.18-5.41 1.98-2.64 2.62-3.09 3.04-3.54 ⫺0.05-0.35
.007 .228 .558 .465 .652 .255 .003
2.33 2.24 4.04 2.13 1.55 2.67 0.03
5.19 5.40 8.61 5.75 4.90 6.76 1.27
3.42 3.70 5.80 3.26 3.76 4.77 0.43
3.22 3.35 5.42 3.07 3.99 4.86 0.13
0.96 1.20 1.30 1.01 1.06 1.70 0.52
2.69-3.90 2.89-4.73 5.01-6.54 2.78-3.47 3.61-4.51 3.33-6.35 0.07-0.80
2.74-4.10 2.84-4.55 4.87-6.73 2.53-3.98 3.00-4.52 3.56-5.98 0.06-0.80
.390 .244 .363 .038 .099 .045 .002
RESULTS
There were no obvious differences between the values obtained with the .018-in and .019 ⫻ .025-in wires in the dry state, but a difference was found when wet, with the .018-in wires exhibiting less resistance to sliding than the rectangular archwires (Tables I-III). The whole sample exhibited greater friction with ceramic brackets than with metal brackets, except the Super Slick modules on .019 ⫻ .025-in wires in the wet state, which demonstrated very little difference between the 2 brackets (Tables I-III). We found significant differences in resistance to sliding between the Damon 2 brackets with the slide closed and all other combinations of bracket and
module. The Damon 2 brackets demonstrated virtually zero friction with each combination of wire and environmental condition (Tables I-III). When the different bracket and elastomeric module combinations were compared, significant differences were also demonstrated (Tables IV-IX). In all but 2 combinations, the round cross-section modules provided the least resistance to sliding and the rectangular cross-section modules the greatest, with the Super Slick modules between the 2. The only 2 exceptions to this were the ceramic brackets with .018-in stainless steel wires: in dry conditions the Super Slick ties produced the highest frictional force yet when wet, they demonstrated the lowest force (Tables II, IX).
Griffiths, Sherriff, and Ireland 673
American Journal of Orthodontics and Dentofacial Orthopedics Volume 127, Number 6
Table IV. Kruskal-Wallis rank sum test for ceramic brackets with 3 modules (standard, Super Slick, and square-edged) and .018-in stainless steel wire Ligation Dry state Standard Super Slick Square-edged Wet state Standard Super Slick Square-edged
Observations
Observed statistic
P ⬎ 2
10 10 10
11.41
.003
10 10 10
22.10
.001
Table V.
Kruskal-Wallis rank sum test for ceramic brackets with 3 elastomeric modules (standard, Super Slick, and square-edged) and .019 ⫻ .025-in stainless steel wire, dry and wet states
Ligation Dry state Standard Super Slick Square-edged Wet state Standard Super Slick Square-edged
Observations
Observed statistic
P ⬎ 2
10 10 10
3.75
.15
10 10 10
14.44
.001
Significant differences between all 3 types of elastomeric modules were demonstrated by the KruskalWallis test (Tables IV-VII) with the exception of 2 nonsignificant results found when comparing the 3 modules in dry conditions on ceramic brackets with .019 ⫻ .025-in stainless steel wires (Table V) and on Damon 2 brackets with the clip open in wet conditions with .019 ⫻ .025-in stainless steel wires (Table VII). When this test was repeated to compare each module against each other, no distinct pattern emerged (Table VIII). The results indicated that, with the .018-in stainless steel archwires, friction was less in wet conditions, but, for the .019 ⫻ .025-in stainless steel archwires, the reverse was true, with higher friction in wet conditions. DISCUSSION
Contrary to previous studies that showed that Super Slick modules significantly reduce friction with sliding mechanics,1,22 our results indicate that they do not confer any advantage over conventional, round, crosssection modules, and, in fact, their resistance was greater (Tables I-III, IX). The only exception to this
Table VI.
Kruskal-Wallis rank sum test for metal brackets with 3 elastomeric modules (standard, Super Slick, and square-edged) and .018-in stainless steel wire
Ligation Dry state Standard Super Slick Square-edged Wet state Standard Super Slick Square-edged
Observed statistic
P ⬎ 2
10 10 10
18.74
.001
10 10 10
9.43
.009
Observations
Table VII.
Kruskal-Wallis rank sum test for metal brackets with 3 elastomeric modules (standard, Super Slick, and square-edged) and .019 ⫻ 0.025-in stainless steel wire Ligation Dry state Standard Super-slick Square edged Wet state Standard Super Slick Square-edged
Observed statistic
P ⬎ 2
10 10 10
16.24
.001
10 10 10
4.60
Observations
.1
was when they were used with ceramic brackets in wet conditions on .018-in stainless steel wire (Tables III, IX). The reason for this could be that the modules were slightly more stretched on the wider Inspire bracket than on the Damon 2 bracket, but the module did not show a reduction in friction with the same bracket using .019 ⫻ .025-in stainless steel wire, which would be expected if this were the reason for the reduction in friction. The rectangular cross-section modules showed the highest resistance to sliding. The internal diameter of these modules was the smallest of all 3 modules (1.21 mm), with the Super Slick ties slightly wider (1.27 mm) and the round cross-section modules wider still (1.36 mm). It is possible that this accounts for the difference in friction. When comparing the methodology of previous studies of Super Slick ties,1,22 we noted that 1 article1 was similar to our own in that 3 brackets were aligned on the wire (compared with 1 molar band and 2 brackets in the current study), but the second article22 involved only 1 bracket, and this could have contributed to the differences in results.11 The other difference in these studies was the choice of lubricant. In this
674 Griffiths, Sherriff, and Ireland
Table VIII.
American Journal of Orthodontics and Dentofacial Orthopedics June 2005
Kruskal-Wallis test showing significant differences Factors
Module comparisons
Wire
Bracket
Environment
.018 .018 .019 .019 .018 .018 .019 .019
Ceramic Ceramic Ceramic Ceramic SS SS SS SS
Dry Wet Dry Wet Dry Wet Dry Wet
⫻ .025 ⫻ .025 ⫻ .025 ⫻ .025
Standard vs Super Slick
Standard vs square-edged
Super Slick vs square-edged
* *
* **
** *
** * ** ** **
* * * * **
* ** * ** **
*Significant pairwise comparisons. **Nonsignificant pairwise comparisons. Table IX.
Ranking of data by frictional force (1 ⫽ lowest; 3 ⫽ highest)
Wire
Bracket
Environment
Standard
Super Slick
Square
.018 .018 .019 ⫻ .025 .019 ⫻ .025 .018 .018 .019 ⫻ .025 .019 ⫻ .025
Ceramic Ceramic Ceramic Ceramic SS SS SS SS
Dry Wet Dry Wet Dry Wet Dry Wet
1 2 1 1 1 1 1 1
3 1 2 2 2 2 2 2
2 3 3 3 3 3 3 3
study, the test modules were soaked in a water bath for 1 hour at 37°C, whereas Devanathan1 presoaked and irrigated the modules with water throughout the experiment, and Main et al22 soaked the modules in human saliva for 1 hour before testing. Negligible frictional forces were produced by the Damon 2 brackets. This concurs with results of other studies with self-ligating brackets.5,17,18,22-24 Thus, it would seem that a self-ligating system is the most appropriate way to eliminate resistance to sliding by ligatures. The effect of archwire dimension on frictional forces appeared to be insignificant in the dry state, with both the .018-in and .019 ⫻ .025-in stainless steel wires producing similar results, whereas in the wet state, the .018-in wires had lower friction. Most current literature suggests that larger-diameter archwires produce greater friction,3,5-7,12,15-18,20 but some studies have found that the smaller the wire, the larger the resistance to sliding,11,19 which is probably explained by the ability of teeth to tip more on smaller wires. Only 1 study9 was found that produced nonsignificant results between wire sizes in dry conditions and agreed with the results of our study. Most results indicated higher resistance to sliding with ceramic brackets compared with metal brackets.
This finding is supported in the literature by numerous studies6,7,13,14 having similar results. In our study, we were unable to find a ceramic bracket that matched the mesiodistal width of the Damon 2 bracket, so we used Inspire brackets, which were 0.44 mm wider. This could have affected the results, because bracket dimension has been shown to affect friction,3,5,9,21 although there is disagreement in this area, with some investigators finding that wider brackets cause an increase in friction,5,21 while others have found the reverse.3,9 It is, therefore, difficult to draw any conclusions about the difference in bracket width. The only way to do this would be to use brackets with the same mesiodistal dimension. The effect of lubrication is debatable,6,10,11,13-16,19,21,22 and the results from this study were inconclusive in that lower friction occurred in wet conditions as opposed to dry with the .018-in stainless steel archwire, and higher friction values resulted from the .019 ⫻ .025-in archwire in wet conditions when compared with dry. A difficulty of comparing the results of this study with the previous studies1,22 of Super Slick ties is the difference in methodologies. In 1 study,1 some aspects of its design are unclear, such as which type of archwires were used and their precise dimensions. In the other study,22 the use of human saliva as a lubricant
American Journal of Orthodontics and Dentofacial Orthopedics Volume 127, Number 6
might have influenced the result, as well as the use of a single bracket in the test unit. However, there appear to be widely differing results between the current study and the others,1,22 suggesting the need for further studies of Super Slick ties. The in vivo environment differs markedly from ex vivo conditions because of variables such as masticatory forces and temperature. These findings are only a guide to expected clinical performance; actual clinical behavior might be somewhat different. CONCLUSIONS
1. Super Slick modules demonstrated a higher resistance to sliding when compared with conventional round cross-section modules but provided an advantage over the rectangular cross-section modules. 2. The Damon 2 self-ligating bracket provided the least resistance to sliding of all bracket/ligation combinations and was the only method that almost entirely eliminated friction. 3. The .018-in and .019 ⫻ .025-in wires exhibited similar friction in the dry state, but, in the wet state, the .018-inch wire produced less friction than the .019 ⫻ .025-in wire. 4. Ceramic brackets demonstrated greater resistance to sliding than stainless steel brackets. 5. Lubrication reduced the friction with .018-in wires and increased it with .019 ⫻ .025-in wires. We thank Prof Alan Harrison for the use of the testing apparatus and Mr R. Vowles for his help with the same apparatus. REFERENCES 1. Devanathan D. Performance study of a low friction ligature. LaPorte, Ind: Research Laboratory of TP Orthodontics; 2000. 2. Proffit WR. Contemporary orthodontics. Saint Louis: C. V. Mosby; 2000. 3. Drescher D, Bourauel C, Schumacher HA. Frictional forces between bracket and archwire. Am J Orthod Dentofacial Orthop 1989;96:397-404. 4. Kusy RP, Whitley JQ. Coefficients of friction for arch wires in stainless steel and polycrystalline alumina bracket slots: I. The dry state. Am J Orthod Dentofacial Orthop 1990;98:300-12. 5. Frank CA, Nikolai RJ. A comparative study of frictional resistances between orthodontic bracket and archwire. Am J Orthod 1980;78:593-609. 6. Ho KS, West VC. Friction resistance between edgewise brackets and archwires. Aust Orthod J 1991;12:95-9.
Griffiths, Sherriff, and Ireland 675
7. Angolkar PV, Kapila S, Duncanson MG, Nanda RS. Evaluation of friction between ceramic brackets and orthodontic wires of four alloys. Am J Orthod Dentofacial Orthop 1990;98:499-506. 8. Peterson L, Spencer R, Andreasen G. A comparison of friction resistance for nitinol and stainless steel wire in edgewise brackets. Quint Int 1982;13:563-71. 9. Tidy DC. Frictional forces in fixed appliances. Am J Orthod Dentofacial Orthop 1989;96:249-54. 10. Stannard JG, Gau JM, Hanna MA. Comparative friction of orthodontic wires under dry and wet conditions. Am J Orthod 1986;89:485-91. 11. Ireland AJ, Sherriff M, McDonald F. Effect of bracket and wire composition on frictional forces. Eur J Orthod 1991;13:322-8. 12. Garner LD, Allai WW, Moore BK. A comparison of frictional forces during simulated canine retraction of a continuous edgewise arch wire. Am J Orthod Dentofacial Orthop 1986;90:199203. 13. Pratten DH, Popli K, Germane N, Gunsolley JC. Frictional resistance of ceramic and stainless steel orthodontic brackets. Am J Orthod Dentofacial Orthop 1990;98:398-403. 14. Tselepis M, Brockhurst P, West VC. The dynamic frictional resistance between orthodontic brackets and archwires. Am J Orthod Dentofacial Orthop 1994;106:131-8. 15. Andreasen GF, Quevedo FR. Evaluation of friction forces in the 0.022 ⫻ 0.028 edgewise bracket in vitro. J Biomech 1970;3:151-60. 16. Riley JL, Garrett SG, Moon PC. Frictional forces of ligated plastic and metal edgewise brackets [abstract]. J Dent Res 1979;58:98. 17. Sims APT, Waters NE, Birnie DJ, Pethybridge RJ. A comparison of the forces required to produce tooth movement in vitro using two self-ligating brackets and a pre-adjusted bracket employing two types of ligation. Eur J Orthod 1993;15:377-85. 18. Thomas S, Sherriff M, Birnie D. A comparative in vitro study of the frictional characteristics of two types of self-ligating brackets and two types of pre-adjusted edgewise brackets tied with elastomeric ligatures. Eur J Orthod 1998;20:589-96. 19. Baker KL, Nieberg LG, Weimer AD, Hanna M. Frictional changes in force values caused by saliva substitution. Am J Orthod Dentofacial Orthop 1987;91:316-20. 20. Echols PM. Elastic ligatures: binding forces and anchorage taxation. Am J Orthod 1975;67:219-20. 21. Nicolls J. Frictional forces in fixed orthodontic appliances. Dent Pract 1968;18:362-6. 22. Hain M, Dhopatkar A, Rock P. The effect of ligation method on friction in sliding mechanics. Am J Orthod Dentofacial Orthop 2003;123:416-22. 23. Berger JL. The influence of the SPEED bracket’s self-ligating design on the force levels in tooth movement: a comparative in vitro study. Am J Orthod Dentofacial Orthop 1990;97:219-28. 24. Shivapuja PK, Berger J. A comparative study of conventional ligation and self-ligation bracket systems. Am J Orthod Dentofacial Orthop 1994;106:472-80.