as statically determinate [2]. The biomechanical systems that are statically determinate are simple and efficient because the forces and moments to be applied are easy to calculate, using simple measurements of appliance forces and distances [2].
In statically indeterminate systems the wire is engaged in the brackets of all teeth, including both the active and the reactive (anchor) units of the system. The extent of the forces and the moments developed in relation to the brackets are determined by the wire deflection. When the wire is inserted into two bracket slots, the force systems that are developed in the two units interact and consequently cannot be measured directly. A continuous arch can be considered as a long series of statically indeterminate systems [2].
Consistent and inconsistent systems
When an archwire is inserted into a series of malaligned brackets, it will produce both forces and couples at each bracket. When both the force and the moment at the bracket are in the correct direction in relation to their suitability to produce the desired tooth movement, the force system is termed consistent [1, 2]. If only some forces or moments are in the required direction, the force system is considered inconsistent [1, 2]. Consistency, therefore, usually refers to a force system where both forces and couples are needed.
Sometimes, however, either the applied force or the couple may not be required or they may produce an undesired side effect. In addition, if a side effect force or couple is present, the force system will also be considered inconsistent [1, 2]. Inconsistency is often the reason why a straight‐wire appliance may encounter a poor response [1, 2].
Appliances
Orthodontic forces are obtained by deflection or torsion of flexible wires and cantilevers, and by activation of springs and elastics.
An important characteristic of the force systems generated by a cantilever or by well‐maintained up‐and‐down elastics is their high degree of constancy over time and deactivation (qualitative constancy).
In direct contrast, the force system generated by a straight‐wire appliance is only determined by the mutual relationship between the brackets and the wire [3]. Placing straight wires into badly placed brackets may or may not result in favourable tooth movement, depending on the geometric relationships between the brackets [11].
It will become apparent that these limitations in the straight‐wire approach can unmistakably influence orthodontic outcomes [3]. Using a so‐called customized straight‐wire approach with predetermined prescription brackets and utilizing robot‐formed wires cannot replace the manual skill of the orthodontist, neither can it render the biological and mechanical basis upon which the profession is built redundant [3, 4].
Ideal orthodontic care achieves individualized, predetermined treatment objectives. The selected course of action should address the patient’s problems and meet the individualized goals. These components imply that different patients require different treatments, which means that one appliance design (brackets prescription, archwire sequence, etc.) will not be capable of solving the problems of all patients [1–3].
In a continuous arch technique, where the number of variables is unknown or not measurable, the system becomes statically indeterminate and orthodontic prediction becomes impossible.
It is therefore clear that a purely straight‐wire approach cannot replace the custom‐made appliances needed to accomplish the specific goal of aligning an ectopic tooth efficiently.
The orthodontic tooth movement can generate bone and it is important to recognize that teeth can be moved ‘with bone’ or ‘through bone’. The tissue reaction that determines whether the movement is with bone or through bone depends on the stress/strain distribution in the periodontium surrounding the loaded teeth [3]. The displacement of teeth into edentulous areas or outside the initially given envelope without loss of attachment has demonstrated that teeth can be displaced with bone if the stress/strain distribution can be controlled [3].
No standard bracket design can deliver individualized treatment objectives. Only the orthodontist can control the specific characteristics of the force system to be used in treatment. The optimal alignment of ectopic teeth can only be resolved by the application of a custom‐made appliance, using a force system generated by wire bending [3].
Treatments should be performed with individualized appliances that adapt the force system to the patient and not the patient to the force system.
The active units
There are six basic elements employed in the treatment mechanics, specifically for the alignment of ectopic teeth. They are:
The cantilever.
The torsion/ballista spring.
Elastics or closed‐coil springs.
Piggyback arch wire.
The V bend/root spring (alpha–beta spring).
Torqueing auxiliaries.
Preference depends entirely on the directional requirement of the movement needed and the proximity of the ectopic tooth to the continuous archwire.
Cantilevers
Cantilevers are useful in the delivery of a single extrusive and/or lateral force. A cantilever system is characterized by a pure force acting at its extremity (the free end) with single‐tooth contact. Its other end is engaged in a bracket, slot or tube, where it exerts an equal and opposite force and a moment [12, 13]. The cantilever system may be used in many modifications. As a rule, the cantilever should be as long as possible in order to decrease the force and increase the deflection (activation distance or range). The auxiliary tube of the first molar bands is most suited for engaging the cantilever, since it prevents excess play in the tube. It will accept a 0.016 in. × 0.022 in. cantilever wire in a 0.018 in. or a 0.017 in. × 0.025 in. cantilever wire in a 0.022 in. strap‐up.
With a statically determinate force system, where forces and moments are either known or measurable, the behaviour of the impacted tooth is mostly predictable. Impacted teeth need movement in two directions. An eruptive force is needed to bring the tooth to the level of the occlusal plane and a horizontal (buccal or mesio‐distal) force to bring the tooth into alignment in the arch. This may be achieved using a cantilever. However, it may also be achieved using a triangular elastic (1/4 in., 6 mm/70 cN) to the two opposing teeth, provided that they are engaged in a rigid continuous archwire in the opposing arch.
Cantilevers are made either of beta‐titanium (TMA) wires, Connecticut New Archwires or nickel–titanium (NiTi) wires. When using NiTi wires, bends should ideally be made with a hammerhead plier, or the Sander Memory Maker, to maintain the desired cantilever shape. Using a range of different types of wire for cantilever construction allows the orthodontist to use light forces, which can easily and usefully be measured with a gauge, in combination with long ranges of activation.
Cantilever for extrusion of buccal displaced canines
The force system is acting on the canine and first molar (see Figure 3.1a–d). The cantilever will produce forces and moments in different planes of space. In the sagittal plane (Figure 3.1c),
