Influence on binding of third-order torque to second-order angulation

Using an earlier model, which described the critical contact angle for binding from second-order angulation alone, a more generalized model is derived that combines the effects of angulation and torque. From this vantage point, the onset of binding is evaluated for 3 scenarios: second-order angulation alone, third-order torque only, and a combination of second-order angulation and third-order torque. These scenarios are detailed by plotting the critical contact angle for binding against the torque angle as a function of 10 wire dimensions (16 x 16, 16 x 22, 17 x 17, 17 x 22, 17 x 25, 18 x 18, 18 x 22, 18 x 25, 19 x 25, and 21 x 25 mil), 4 bracket widths (70, 100, 130, and 160 mil), and 4 bracket slots (18, 20.5, 22, and 24.5 mil). From these plots, we learn that each wire base dimension (eg, an 18-mil base as found in 18 x 18-mil, 18 x 22-mil and 18 x 25-mil archwires) has a common maximum critical contact angle for binding. Moreover, each wire-slot combination has a common maximum torque angle, which is independent of bracket width. Finally, we learn that archwire-bracket combinations that use a metric 0.5-mm slot might have some advantages with regard to torquing--given the current philosophy that light, continuous forces are more favorable.