 # Forces and moments generated by removable thermoplastic aligners

There are some mistakes in the article “Forces and moments generated by removable thermoplastic aligners: Incisor torque, premolar derotation, and molar distalization” (Simon M, Keilig L, Schwarze J, Jung BA, Bourauel C. Am J Orthod Dentofacial Orthop 2014;145:728-36). Mistake 1 is the labeling of the coordinate system, and mistake 2 is the unit of force.

Mistake 1 (p. 730 and 732). As published, the article states that the “coordinate system was set up: the positive x-axis describes extrusive forces…parallel to the long axis of the tooth…For a molar, the positive y-axis describes buccal movements,…the positive z-axis describes mesial movements…For a maxillary incisor, the positive y-axis describes distal movements,…the positive z-axis describes buccal movements…(Fig 3).” On Figure 3, the z-axis is labeled correctly, but the y-axis is incorrect. Viewing Figure 3, we see the following: the positive x-axis (+x) is coming out of the page, the positive y-axis (+y) is horizontal and points to the right, and the positive z-axis (+z) is vertical and points upward. The coordinate system obeys the right-hand rule correctly. Just the labeling of the y-axis is wrong in Figure 3.

Mistake 2 (p. 732). The equation was published as “1 N = 1/9.81 kg = 102 g.” It should be written as “1 N = 1/9.81 kgf = 102 gf.”

In MKS (meter-kg-second) of the metric system, “kg” is the unit of mass, and “N” is the unit of force. In Newtonian mechanics, force = mass × acceleration and weight = mass × gravity. On earth’s surface, gravity is 9.81 m/s 2 . If the mass m is 1 kg, its weight W is

W = m × g = 1 kg × 9.81 m / s 2 = 9.81 N .