Analysis of moment/force ratios in the mechanics of tooth movement.

Orthodontic tooth movement is analyzed by means of the center of rotation model and the concept of moment/force ratios. Several equivalent force systems are considered at both the bracket and the center of resistance of the tooth. When moment/force ratios are evaluated at the bracket, the laws of physics appear to be suspended: inconsistencies occurring as single forces applied at different points claim equivalent results and pure translational movements purport to be nonzero moment/force ratios. These paradoxes can be reconciled only if the moment/force ratios are analyzed at the center of resistance of the tooth. Here, all of the moments applied to the tooth by the force system are included in the analysis. Only when the force system is evaluated around the center of resistance of the tooth is the concept of moment/force ratios consistently correct.