Burçak K, Cetinşahin A, Arman A, Uçkan S. Success of zygomatic plate‐screw anchorage system. J Oral Maxillofac Surg 2010; 68: 602–605.23 23. Vardimon AD, Graber TM, Voss LR. Hygienic magnetic technique to align impacted teeth. Presented at the 87th annual session of the American Association of Orthodontists, Montreal, Canada, 1987.
24 24. Sandler PJ, Meghji S, Murray AM et al. Magnets and orthodontics. Br J Orthod 1989; 16: 243–249.
25 25. Darendeliler MA, Friedli JM. Treatment of an impacted canine with magnets. J Clin Orthod 1994; 28: 639–643.
26 26. Vardimon AD, Graber TM, Drescher D, Bourauel C. Rare earth magnets and impaction. Am J Orthod Dentofacial Orthop 1991; 100: 494–512.
27 27. Mancini GP, Noar JH, Evans RD. Neodymium iron boron magnets for tooth extrusion. Eur J Orthod 1999; 21: 541–550.
28 28. Noar JH, Wahab A, Evans RD, Wojcik AG. The durability of parylene coatings on neodymium iron boron magnets. Eur J Orthod 1999; 21: 685–693.
29 29. Noar JH, Shell N, Hunt NP. The performance of bonded magnets used in the treatment of anterior open bite. Am J Orthod Dentofacial Orthop 1996; 109: 549–557.
30 30. Sandler JP. An attractive solution to unerupted teeth. Am J Orthod Dentofacial Orthop 1991; 100: 489–493.
31 31. Ingervall B. The use of magnets in orthodontic therapy: panel discussion. Eur J Orthod 1993; 15: 421–424.
32 32. Gianelly A. The use of magnets in orthodontic therapy: panel discussion. Eur J Orthod 1993; 15: 421–424.
33 33. Rygh P. The use of magnets in orthodontic therapy: panel discussion. Eur J Orthod 1993; 15: 421–424.
34 34. Vardimon AD. The use of magnets in orthodontic therapy: panel discussion. Eur J Orthod 1993; 15: 421–424.
3 Biomechanics for Aligning Ectopic Teeth
Ulrich Kritzler and Katja Chromy
Statically determinate and statically indeterminate systems
Consistent and inconsistent systems
Appendix: Colour code convention for moments and forces
Basic principles
In orthodontics the application of appropriate forces and moments is necessary for full control during tooth movement. The chosen appliance will influence the rates of tooth movement, potential tissue damage and pain response [1, 2]. However, this is only one side of the equation, because there is a consequential and equivalent opposite reaction to these forces and moments, which will act on the anchor teeth and must be resisted [1, 2].
An understanding of applied biomechanics guides the orthodontist to determine how to maximize the former (the application of appropriate forces) and control the latter (the opposite reaction). When the clinician has determined the treatment goals and has established a sequence of treatment, the force systems needed for reaching those goals can be developed by optimally selecting and combining forces [1–3].
In order to succeed, the orthodontist must have a clear strategy to promote the desired tooth movement. Well‐defined treatment goals described in all three planes of space, followed by the application of a goal‐oriented appliance, are key to the solution of most problems encountered when aligning impacted teeth. Only an appropriate application of force can efficiently generate this displacement [4].
We are often presented with facile solutions to our mechanical problems utilizing brackets and wires, but these are mostly inappropriate. While they represent efficient marketing, and serve the interests of the supply company, they are not a panacea for all biomechanical obstacles.
So long as biological and mechanical principles and experience in manual skills are ignored, the orthodontist will inevitably encounter the same problems with every kind of appliance. These principles and skills are the very foundations upon which the profession is built and must be employed if the ectopic tooth is to be moved into the arch and aligned efficiently [3].
In order to achieve this, the first step is to determine the exact 3D location of the ectopic tooth to be moved, its shape and its proximity to the adjacent teeth.
In the nature of things, the individual tooth will likely be displaced at a distance from and essentially outside its normal location area, where all methods of movement may be conveniently applied. Accordingly, initial single‐point forces will be generally employed for the purpose of bringing these teeth into a more convenient and accessible location, from where sophisticated orthodontic 3D control of movement will be feasible, referred to elsewhere in this volume as the ‘orthodontic ballpark’. A single‐point force has both magnitude and direction. When a force does not act through the centre of resistance (CR) of a tooth, the tooth will rotate, the CR will move in the direction of the line of that force, and the tooth will simultaneously rotate around the CR [5].
It is important that the point of force application on the ectopic tooth be as near as possible to the tip of its cusp, thus enabling the formation of a mental picture of the tooth in relation to its immediate vicinity and assisting in planning its projected movement.
Force application to a single point of contact is restricted to producing extrusive and tipping forces and should be used for as long as the ectopic tooth has not been brought close to its desired place in the arch.
Current literature supplies no evidence regarding the relation between force magnitude and rate of tooth movement and there is no evidence‐based force level that can be recommended for the optimal efficiency in clinical orthodontics [6]. However, the available evidence from animal experimental studies indicates that the optimal range is 25–35 cN [7, 8]. It is these light forces that should be used to bring the tooth into the arch [1, 2, 8].
Forces act in a straight line [4, 9]. Accordingly, if there is an obstacle in the direct path to the target site, the tooth must initially be moved in a different direction, in order to avoid the obstacle and bring it to a location from where a straight line may then be achieved.
If resorption of the roots of adjacent teeth is evident or appears likely to occur, it will be essential to undertake treatment at the earliest opportunity in order to distance the offending tooth from those roots [10].
Statically determinate and statically indeterminate systems
When a force is acting on a single‐point contact on the ectopic tooth, i.e. there is no wire
