We investigated “Forces and Moments” and “Forces and Deflections” in ligual orthodontics to distinguish from biomechanics of labial appliance, resulting in making the differences clear between them. In lingual orthodontics, it is not easy to construct and place an properly shaped continuous archwire with loops and springs for maxillary anterior retraction. Nevertheless, frictionless mechanics seems most appropriate for this purpose when a lingual appliance is used. This is due to the reduced interbracket distance resulting in increased friction. In addition, the same amount of distal root torque is thought to generate a greater force on the incisors with a lingual appliance because of the higher load/deflection rate caused by the short interbracket distance. Assuming that the distance between incisor and canine brackets is twice as short with a lingual appliance as with a labial applianece, relationship of the force level required to achieve the the same amount of deflection (m) between the two appliances can be expressed as F=F'X(2I/I)3=8F' (F: lingual appliance, F': labial appliance).
By the same token, the amount of deflection for the same torque requirement is twice as small with a lingual appliance (F'') as with a labial one (F'), which can be represented as F''=FX1/2=8F'X1/2=4F'. According to the cantilever principle, the larger the load/deflection rate, the greater the force derived from the deflection. When a continuous archwire is activated for distal root movement of the incisors the alpha moment exceeds the beta moment to generate a net extrusive force on the incisors. This extrusive force, which is greater with a lingual appliance, does not cause the bite to deepen if the appliance (7th generation Kurz lingual appliance) has bite planes built into the maxillary incisor brackets for the mandibular incisors to occlude against. However, the line of extrusive force passing labial to the center of resistance (CR) of the four maxillary incisors, the extrusive force produces a large amount of mesial root movement of the incisors with the mandibular incisal edges acting as a fulcrum. The M/F ratio decreases along with the mesial root movement, potentially causing uncontrolled tipping of the incisors. We applied an acrylic cap in combination with a high pull J-hook headgear to resist the extrusive force, resulting in a good result.

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