Tr. Meling et J. Odegaard, THE EFFECT OF 2ND-ORDER COUPLE ON THE APPLICATION OF TORQUE, American journal of orthodontics and dentofacial orthopedics, 113(3), 1998, pp. 256-262
Complex combinations of linear forces, moments, and couples are develo
ped by the arch wire during orthodontic treatment. For instance, appli
cation of torque to a canine during distal driving may create force in
teractions 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 to
rsion simultaneous to fixed amounts of second-order couples or fixed d
egrees of second-order bracket angulation. Application of a second-ord
er couple through a bracket to a longitudinally twisted arch wire prod
uces a third order couple, since the bracket slot walls exert forces o
n the wire, tending to detwist it. This third-order couple will usuall
y be small as the distance between the two couple members is short. Ne
vertheless, it may have a restraining effect on the third-order wire-b
racket interaction. The results show that application of second-order
couples or bracket angulations lead to an increase in exerted torque f
or 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 tor
que unless it was subjected to a second-order couple. Thus, in an in v
ivo situation where farces interact, the actual torsional play may be
substantially less than predicted from theoretical models only regardi
ng third-order mechanics, The restraining effect of second-order coupl
es tapered when the torque created by longitudinal twisting became muc
h larger than the torque exerted by the second-order couple, Second-or
der couples of biologically acceptable magnitudes had little effect on
the level of torque after the third-order clearance had been eliminat
ed.