Influence of force systems on archwire-bracket combinations.

Orthodontic forces and couples are presented for the 3 principal directions and planes by using simplified free-body diagrams, equilibrium principles, and equivalent force systems. These simplified free-body diagrams show only the forces and couples applied by the practitioner to a single tooth or a group of teeth-minus any frictional effects associated with appliances. By using equilibrium principles, these forces and couples are resisted by each root in an equal but opposite manner. When an equivalent force system is produced at the center of resistance, the simplified free-body diagram requires only 1 force and 1 couple at the center of resistance of a tooth or a group of teeth because the reactions are the same but opposite in magnitude. This approach not only is much easier to comprehend but also facilitates the conceptualization of tooth mechanics with regard to centers of rotation. Specific examples of this approach include cases in which a tooth is labially or lingually displaced, intruded or extruded, bodily translated, or bodily rotated, as well as the combined effects of translation and rotation with and without auxiliary appliances or friction.