Influence of archwire and bracket dimensions on sliding mechanics: derivations and determinations of the critical contact angles for binding

There is every indication that classical friction controls sliding mechanic s below some critical contact angle, theta(c). Once that angle is exceeded, however, binding and notching phenomena increasingly restrict sliding mech anics. Using geometric archwire and bracket parameters, the theta(c) is cal culated as the boundary between classical frictional behaviour and binding- related phenomena. What these equations predict is independent of practitio ner or technique. From these derivations two dimensionless numbers are also identified as the bracket and the engagement index. The first shows how th e width of a bracket compares to its Slot; the second indicates how complet ely the wire fills the Slot. When nominal wire and bracket dimensions are c alculated for both standard Slots, the maximum theta(c) theoretical ly equa ls 3.7 degrees. Thus, knowledge of the archwire or bracket alone is insuffi cient; knowledge of the archwire-bracket combination is necessary for theta (c) to be calculated. Once calculated, sliding mechanics should be initiate d only after the contact angle, theta, approaches the characteristic value of theta(c) for the particular archwire-bracket combination of choice-that is, when theta approximate to theta(c).