A FORMULA FOR THE DISPLACEMENT OF AN ARCH WIRE WHEN SUBJECTED TO A 2ND-ORDER COUPLE

A new formula, expressing the local angular displacement of an orthodo ntic beam when subjected to a second-order couple applied at midspan, has been developed and analyzed. The computed displacements were compa red with the results of ex vivo testing. There was good agreement betw een the results from the theoretical evaluation and the bench testing. Second-order activation of an orthodontic beam can be described in fo ur sequential phases. The initial displacement is influenced by the se cond-order clearance between bracket-slot and wire as well as the rela tionship between the bracket-slot width and interbracket distance. Dur ing phase II there is a nonlinear relationship between applied couple and rotational displacement. Within phases three and four displacement is linearly related to the interbracket distance, provided the relati onship between the bracket-slot width and interbracket distance remain s constant. For a given tooth size, the second-order beam stiffness is exponentially related to bracket width. The experiments also show tha t even small deflections of thin stainless steel wires can lead to sec ond-order couples of large magnitudes when using a clinically relevant interbracket distance. Consequently, it is important that the orthodo ntist evaluates his or her choice of bracket width and arch wire stiff ness in each clinical case in order to avoid supra-physiologic force l evels.