Korean J Orthod.  2025 May;55(3):212-223. 10.4041/kjod24.114.

Force and moment analysis of clear aligners: Impact of material properties and design on premolar rotation

• Kim DW
• Lee HJ
• Kim KB
• Kim SH
• Kim SS
• Park SB
• Choi YK
• Kim YI

• KMID: 2568344
• DOI: http://doi.org/10.4041/kjod24.114

Abstract

Objective
To quantitatively analyze and compare the forces and moments generated by thermoformed polyethylene terephthalate glycol (PETG) and direct-printed TC-85 clear aligners (CAs), with various margin designs, during premolar rotation.
Methods
In total, 132 CAs were fabricated and divided into four groups (n = 33 per group). Group C consisted of thermoformed PETG aligners with a 2 mm gingival margin. Group E comprised direct-printed TC-85 aligners with equi-gingival margin, whereas Group G utilized direct-printed TC-85 aligners with 2 mm gingival margins. Finally, Group T featured direct-printed TC-85 aligners with an additional 1 mm thickness at the mesial embrasure. The forces and moments were measured using a 6-axis force/moment transducer at 2°, 3°, and 4° of rotation. All measurements were conducted at 37°C to simulate intraoral conditions. Forces were measured in the buccolingual, anteroposterior, and vertical directions, while moments were measured in the mesiodistal, buccolingual, and rotational planes.
Results
The PETG aligners (Group C) showed significantly increased buccal and posterior force across the rotation angles (P < 0.05), whereas the intrusive force remained consistent. In contrast, the TC-85 aligners maintained consistent forces across all rotation angles. Direct-printed aligners demonstrated significantly lower intrusive forces than PETG aligners (P < 0.001). Group T exhibited reduced unwanted forces while maintaining effective rotational moments. Furthermore, all direct-printed aligners showed more predictable force delivery patterns than thermoformed aligners.
Conclusions
Direct-printed TC-85 aligners demonstrated superior force consistency and reduced unwanted side effects compared with traditional PETG aligners. Although marginal design modifications did not significantly improve rotational efficiency, they effectively reduced unwanted intrusive forces.

Keyword

Aligners; Rotation; Forces; Moments

Figure

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  Figure 1 Experimental apparatus design. The second premolar was separated and connected to a 6-axis miniature force/torque sensor. A rotation zig was installed on the lower side of the second premolar.

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  Figure 2 Designs of clear aligners. A, D, Group E; B, E, Group T; C, F, Groups C and G. Group E, equi-gingival margin; Group T, mesial thickness; Group C, control-polyethylene terephthalate glycol; Group G, 2 mm gingival margin.

• 

  Figure 3 Forces generated by four groups at each of the rotation degrees. A, Rotation degree of 2°; B, Rotation degree of 3°; C, Rotation degree of 4°. Red dot indicates the mean value, and diamond-shaped symbols (◇) represent outliers beyond 1.5 times the interquartile range. Group C, control-polyethylene terephthalate glycol; Group E, equi-gingival margin; Group T, mesial thickness; Group G, 2 mm gingival margin.

• 

  Figure 4 Moments generated by four groups at each of the rotation degrees. A, Rotation degree of 2°; B, Rotation degree of 3°; C, Rotation degree of 4°. Red dot indicates the mean value, and diamond-shaped symbols (◇) represent outliers beyond 1.5 times the interquartile range. Group C, control-polyethylene terephthalate glycol; Group E, equi-gingival margin; Group T, mesial thickness; Group G, 2 mm gingival margin.

• 

  Figure 5 Conventional type (PETG material) and direct-printing type (TC-85 material) clear aligners fitting in the embrasure area. PETG, polyethylene terephthalate glycol.

Reference

1. Jeremiah HG, Bister D, Newton JT. 2011; Social perceptions of adults wearing orthodontic appliances: a cross-sectional study. Eur J Orthod. 33:476–82. https://doi.org/10.1093/ejo/cjq069. DOI: 10.1093/ejo/cjq069. PMID: 20651044.

2. Djeu G, Shelton C, Maganzini A. 2005; Outcome assessment of Invisalign and traditional orthodontic treatment compared with the American Board of Orthodontics objective grading system. Am J Orthod Dentofacial Orthop. 128:292–8. discussion 298https://doi.org/10.1016/j.ajodo.2005.06.002. DOI: 10.1016/j.ajodo.2005.06.002. PMID: 16168325.

3. Gu J, Tang JS, Skulski B, Fields HW Jr, Beck FM, Firestone AR, et al. 2017; Evaluation of Invisalign treatment effectiveness and efficiency compared with conventional fixed appliances using the Peer Assessment Rating index. Am J Orthod Dentofacial Orthop. 151:259–66. https://doi.org/10.1016/j.ajodo.2016.06.041. DOI: 10.1016/j.ajodo.2016.06.041. PMID: 28153154.

4. Galan-Lopez L, Barcia-Gonzalez J, Plasencia E. 2019; A systematic review of the accuracy and efficiency of dental movements with Invisalign®. Korean J Orthod. 49:140–9. https://doi.org/10.4041/kjod.2019.49.3.140. DOI: 10.4041/kjod.2019.49.3.140. PMID: 31149604. PMCID: PMC6533182.

5. Rossini G, Parrini S, Castroflorio T, Deregibus A, Debernardi CL. 2015; Efficacy of clear aligners in controlling orthodontic tooth movement: a systematic review. Angle Orthod. 85:881–9. https://doi.org/10.2319/061614-436.1. DOI: 10.2319/061614-436.1. PMID: 25412265. PMCID: PMC8610387.

6. Robertson L, Kaur H, Fagundes NCF, Romanyk D, Major P, Flores Mir C. 2020; Effectiveness of clear aligner therapy for orthodontic treatment: a systematic review. Orthod Craniofac Res. 23:133–42. https://doi.org/10.1111/ocr.12353. DOI: 10.1111/ocr.12353. PMID: 31651082.

7. Simon M, Keilig L, Schwarze J, Jung BA, Bourauel C. 2014; Treatment outcome and efficacy of an aligner technique--regarding incisor torque, premolar derotation and molar distalization. BMC Oral Health. 14:68. https://doi.org/10.1186/1472-6831-14-68. DOI: 10.1186/1472-6831-14-68. PMID: 24923279. PMCID: PMC4068978.

8. Charalampakis O, Iliadi A, Ueno H, Oliver DR, Kim KB. 2018; Accuracy of clear aligners: a retrospective study of patients who needed refinement. Am J Orthod Dentofacial Orthop. 154:47–54. https://doi.org/10.1016/j.ajodo.2017.11.028. DOI: 10.1016/j.ajodo.2017.11.028. PMID: 29957318.

9. Cervinara F, Cianci C, De Cillis F, Pappalettera G, Pappalettere C, Siciliani G, et al. 2019; Experimental study of the pressures and points of application of the forces exerted between aligner and tooth. Nanomaterials (Basel). 9:1010. https://doi.org/10.3390/nano9071010. DOI: 10.3390/nano9071010. PMID: 31336979. PMCID: PMC6669747. PMID: 24315cd63aa54dbeaf43e58f85f769e3.

10. Jiang T, Wu RY, Wang JK, Wang HH, Tang GH. 2020; Clear aligners for maxillary anterior en masse retraction: a 3D finite element study. Sci Rep. 10:10156. https://doi.org/10.1038/s41598-020-67273-2. DOI: 10.1038/s41598-020-67273-2. PMID: 32576935. PMCID: PMC7311544.

11. Gomez JP, Peña FM, Martínez V, Giraldo DC, Cardona CI. 2015; Initial force systems during bodily tooth movement with plastic aligners and composite attachments: a three-dimensional finite element analysis. Angle Orthod. 85:454–60. https://doi.org/10.2319/050714-330.1. DOI: 10.2319/050714-330.1. PMID: 25181252. PMCID: PMC8612436.

12. Cortona A, Rossini G, Parrini S, Deregibus A, Castroflorio T. 2020; Clear aligner orthodontic therapy of rotated mandibular round-shaped teeth: a finite element study. Angle Orthod. 90:247–54. https://doi.org/10.2319/020719-86.1. DOI: 10.2319/020719-86.1. PMID: 31469592. PMCID: PMC8051248.

13. Hong K, Kim WH, Eghan-Acquah E, Lee JH, Lee BK, Kim B. 2021; Efficient design of a clear aligner attachment to induce bodily tooth movement in orthodontic treatment using finite element analysis. Materials (Basel). 14:4926. https://doi.org/10.3390/ma14174926. DOI: 10.3390/ma14174926. PMID: 34501017. PMCID: PMC8433704.

14. Seo JH, Eghan-Acquah E, Kim MS, Lee JH, Jeong YH, Jung TG, et al. 2021; Comparative analysis of stress in the periodontal ligament and center of rotation in the tooth after orthodontic treatment depending on clear aligner thickness-finite element analysis study. Materials (Basel). 14:324. https://doi.org/10.3390/ma14020324. DOI: 10.3390/ma14020324. PMID: 33435457. PMCID: PMC7826543.

15. Yokoi Y, Arai A, Kawamura J, Uozumi T, Usui Y, Okafuji N. 2019; Effects of attachment of plastic aligner in closing of diastema of maxillary dentition by finite element method. J Healthc Eng. 2019:1075097. https://doi.org/10.1155/2019/1075097. DOI: 10.1155/2019/1075097. PMID: 30944717. PMCID: PMC6421825.

16. Grant J, Foley P, Bankhead B, Miranda G, Adel SM, Kim KB. 2023; Forces and moments generated by 3D direct printed clear aligners of varying labial and lingual thicknesses during lingual movement of maxillary central incisor: an in vitro study. Prog Orthod. 24:23. https://doi.org/10.1186/s40510-023-00475-2. DOI: 10.1186/s40510-023-00475-2. PMID: 37423974. PMCID: PMC10329968. PMID: dde3a9dad6254735b63e88aa717b05b0.

17. Grünheid T, Loh C, Larson BE. 2017; How accurate is Invisalign in nonextraction cases? Are predicted tooth positions achieved? Angle Orthod. 87:809–15. https://doi.org/10.2319/022717-147.1. DOI: 10.2319/022717-147.1. PMID: 28686090. PMCID: PMC8317555.

18. Lombardo L, Arreghini A, Ramina F, Huanca Ghislanzoni LT, Siciliani G. 2017; Predictability of orthodontic movement with orthodontic aligners: a retrospective study. Prog Orthod. 18:35. https://doi.org/10.1186/s40510-017-0190-0. DOI: 10.1186/s40510-017-0190-0. PMID: 29130127. PMCID: PMC5682257. PMID: 6a742898868040d58c7b55aee2d8b42c.

19. Haouili N, Kravitz ND, Vaid NR, Ferguson DJ, Makki L. 2020; Has Invisalign improved? A prospective follow-up study on the efficacy of tooth movement with Invisalign. Am J Orthod Dentofacial Orthop. 158:420–5. https://doi.org/10.1016/j.ajodo.2019.12.015. DOI: 10.1016/j.ajodo.2019.12.015. PMID: 32620479.

20. Hahn W, Engelke B, Jung K, Dathe H, Fialka-Fricke J, Kubein-Meesenburg D, et al. 2010; Initial forces and moments delivered by removable thermoplastic appliances during rotation of an upper central incisor. Angle Orthod. 80:239–46. https://doi.org/10.2319/033009-181.1. DOI: 10.2319/033009-181.1. PMID: 19905847. PMCID: PMC8973237.

21. Kravitz ND, Kusnoto B, Agran B, Viana G. 2008; Influence of attachments and interproximal reduction on the accuracy of canine rotation with Invisalign. A prospective clinical study. Angle Orthod. 78:682–7. https://doi.org/10.2319/0003-3219(2008)078[0682:Ioaair]2.0.Co;2. DOI: 10.2319/0003-3219(2008)078[0682:IOAAIR]2.0.CO;2. PMID: 18302468.

22. Liu CL, Sun WT, Liao W, Lu WX, Li QW, Jeong Y, et al. 2016; Colour stabilities of three types of orthodontic clear aligners exposed to staining agents. Int J Oral Sci. 8:246–53. https://doi.org/10.1038/ijos.2016.25. DOI: 10.1038/ijos.2016.25. PMID: 27660048. PMCID: PMC5168413.

23. Condo R, Pazzini L, Cerroni L, Pasquantonio G, Lagana G, Pecora A, et al. 2018; Mechanical properties of "two generations" of teeth aligners: change analysis during oral permanence. Dent Mater J. 37:835–42. https://doi.org/10.4012/dmj.2017-323. DOI: 10.4012/dmj.2017-323. PMID: 29998941.

24. Bendler JT. 1999. Handbook of polycarbonate science and technology. CRC Press;Boca Raton: https://search.worldcat.org/ko/title/1027759168. DOI: 10.1201/9781482273694.

25. Lu QW, Macosko CW. 2004; Comparing the compatibility of various functionalized polypropylenes with thermoplastic polyurethane (TPU). Polymer (Guildf). 45:1981–91. https://doi.org/10.1016/j.polymer.2003.12.077. DOI: 10.1016/j.polymer.2003.12.077.

26. Johal A, Sharma NR, McLaughlin K, Zou LF. 2015; The reliability of thermoform retainers: a laboratory-based comparative study. Eur J Orthod. 37:503–7. https://doi.org/10.1093/ejo/cju075. DOI: 10.1093/ejo/cju075. PMID: 25431104.

27. Min S, Hwang CJ, Yu HS, Lee SB, Cha JY. 2010; The effect of thickness and deflection of orthodontic thermoplastic materials on its mechanical properties. Korean J Orthod. 40:16–26. https://doi.org/10.4041/kjod.2010.40.1.16. DOI: 10.4041/kjod.2010.40.1.16.

28. Ryokawa H, Miyazaki Y, Fujishima A, Miyazaki T, Maki K. 2006; The mechanical properties of dental thermoplastic materials in a simulated intraoral environment. Orthod Waves. 65:64–72. https://doi.org/https://doi.org/10.1016/j.odw.2006.03.003. DOI: 10.1016/j.odw.2006.03.003.

29. Ryu JH, Kwon JS, Jiang HB, Cha JY, Kim KM. 2018; Effects of thermoforming on the physical and mechanical properties of thermoplastic materials for transparent orthodontic aligners. Korean J Orthod. 48:316–25. https://doi.org/10.4041/kjod.2018.48.5.316. DOI: 10.4041/kjod.2018.48.5.316. PMID: 30206530. PMCID: PMC6123073.

30. Lee SY, Kim H, Kim HJ, Chung CJ, Choi YJ, Kim SJ, et al. 2022; Thermo-mechanical properties of 3D printed photocurable shape memory resin for clear aligners. Sci Rep. 12:6246. https://doi.org/10.1038/s41598-022-09831-4. DOI: 10.1038/s41598-022-09831-4. PMID: 35428796. PMCID: PMC9012852. PMID: 916cae2b1906469492ffad0957859600.

31. Masella RS, Meister M. 2006; Current concepts in the biology of orthodontic tooth movement. Am J Orthod Dentofacial Orthop. 129:458–68. https://doi.org/10.1016/j.ajodo.2005.12.013. DOI: 10.1016/j.ajodo.2005.12.013. PMID: 16627170.

32. Proffit WR, Fields HW, Larson B, Sarver DM. 2018. Contemporary orthodontics. 6th ed. Mosby;Philadelphia: https://search.worldcat.org/ko/title/1053796533. DOI: 10.1053/j.sodo.2018.10.005.

33. Elkholy F, Mikhaiel B, Repky S, Schmidt F, Lapatki BG. 2019; Effect of different attachment geometries on the mechanical load exerted by PET-G aligners during derotation of mandibular canines: an in vitro study. J Orofac Orthop. 80:315–26. https://doi.org/10.1007/s00056-019-00193-7. DOI: 10.1007/s00056-019-00193-7. PMID: 31595320.

34. Ferlias N, Dalstra M, Cornelis MA, Cattaneo PM. 2022; In vitro comparison of different Invisalign^® and 3Shape^® attachment shapes to control premolar rotation. Front Bioeng Biotechnol. 10:840622. https://doi.org/10.3389/fbioe.2022.840622. DOI: 10.3389/fbioe.2022.840622. PMID: 35372304. PMCID: PMC8966893. PMID: f5ac4683d4e649fab5a415605e6e3fc3.

35. Brezniak N. 2008; The clear plastic appliance: a biomechanical point of view. Angle Orthod. 78:381–2. https://doi.org/10.2319/0003-3219(2008)078[0381:Tcpa]2.0.Co;2. DOI: 10.2319/0003-3219(2008)078[0381:TCPA]2.0.CO;2. PMID: 18251593.

36. Hahn W, Zapf A, Dathe H, Fialka-Fricke J, Fricke-Zech S, Gruber R, et al. 2010; Torquing an upper central incisor with aligners--acting forces and biomechanical principles. Eur J Orthod. 32:607–13. https://doi.org/10.1093/ejo/cjq007. DOI: 10.1093/ejo/cjq007. PMID: 20462912.

37. Bowman SJ. 2017; Improving the predictability of clear aligners. Semin Orthod. 23:65–75. https://doi.org/10.1053/j.sodo.2016.10.005. DOI: 10.1053/j.sodo.2016.10.005.

38. Savignano R, Valentino R, Razionale AV, Michelotti A, Barone S, D'Antò V. 2019; Biomechanical effects of different auxiliary-aligner designs for the extrusion of an upper central incisor: a finite element analysis. J Healthc Eng. 2019:9687127. https://doi.org/10.1155/2019/9687127. DOI: 10.1155/2019/9687127. PMID: 31485303. PMCID: PMC6702849.

39. Meier B, Wiemer KB, Miethke RR. 2003; Invisalign--patient profiling. Analysis of a prospective survey. J Orofac Orthop. 64:352–8. https://doi.org/10.1007/s00056-003-0301-z. DOI: 10.1007/s00056-003-0301-z. PMID: 14692049.

40. Simon M, Keilig L, Schwarze J, Jung BA, Bourauel C. 2014; Forces and moments generated by removable thermoplastic aligners: incisor torque, premolar derotation, and molar distalization. Am J Orthod Dentofacial Orthop. 145:728–36. https://doi.org/10.1016/j.ajodo.2014.03.015. DOI: 10.1016/j.ajodo.2014.03.015. PMID: 24880843.