The effect of second-order couple on the application of torque

Complex combinations of linear forces, moments, and couples are developed by the arch wire during orthodontic treatment. For instance, application of torque to a canine during distal driving may create force interactions if the tooth tips distally toward the extraction site. This investigation studied the effect of second-order couples and bracket angulations on the application of torque to a single tooth. By using a test apparatus to simulate application of torque to a single tooth, 0.016 x 0.022 inch stainless steel wires were tested in longitudinal torsion simultaneous to fixed amounts of second-order couples or fixed degrees of second-order bracket angulation. Application of a second-order couple through a bracket to a longitudinally twisted arch wire produces a third-order couple, since the bracket slot walls exert forces on the wire, tending to detwist it. This third-order couple will usually be small as the distance between the two couple members is short. Nevertheless, it may have a restraining effect on the third-order wire-bracket interaction. The results show that application of second-order couples or bracket angulations lead to an increase in exerted torque for angles of twist below 22 degrees. Because of torsional play, a wire twisted 18 degrees in a 0.018-inch bracket slot did not exert any torque unless it was subjected to a second-order couple. Thus, in an in vivo situation where forces interact, the actual torsional play may be substantially less than predicted from theoretical models only regarding third-order mechanics. The restraining effect of second-order couples tapered when the torque created by longitudinal twisting became much larger than the torque exerted by the second-order couple. Second-order couples of biologically acceptable magnitudes had little effect on the level of torque after the third-order clearance had been eliminated.