Responses of 3-dimensional arch wires to vertical v-bends: comparisons with existing 2-dimensional data in the lateral view.

The mechanics of V-bends in orthodontic arch wires have been described almost exclusively in terms of bending forces in two-dimensional (2-D) single plane terms. When a rectangular arch wire enters a third dimension, a more complex wire deformation pattern develops from both torsion and bending during the activation of the V-bends. The necessity for a rectangular three-dimensional (3-D) arch wire to undergo torsion during activation results in a greater resistance to deformation at those points in the wire where the torsion is greatest. This is especially apparent with 2 x 2 long span arch wires. This study used finite element analysis to model the force systems produced by activation of V-bends in 3-D arch wires. In both 2-D and 3-D data, greater moments are present as any V-bend is moved toward either adjacent bracket. In 3-D systems, however, a V-bend at the molar produces significantly less moment and associated equilibrium forces than the same V-bend located the same distance from the incisor. Moreover, the reversal of the direction of the moments at either bracket does not occur when the V-bend location is two thirds of the distance toward that tooth as reported with 2-D studies.