Three-dimensional relationship between the critical contact angle and the torque angle.

The purpose of this study was to analyze the relationship between the critical contact angle and the torque angle in an orthodontic bracket and archwire assembly in 3 dimensions. Three-dimensional mathematical models were created with geometric bracket-archwire parameters that included 2 slot sizes, 3 bracket widths, and 3 to 4 wire sizes. From this, 3-dimensional mathematical equations (3DMEs) for the critical contact angle and the maximum torque that result in critical contact angles of 0 were derived and calculated. To evaluate the effects of archwire-bracket parameters on critical contact angles, analysis of variance (ANOVA) was performed at the significance level of P < or = .05. For all bracket-archwire combinations, the critical contact angle decreased as bracket width, torque angle, and wire size increased. Therefore, all bracket-archwire parameters except slot height had an effect on the critical contact angle. Results of the critical contact angle produced from our 3DMEs were the same as those produced by 3D computer-aided design (SolidWorks Corp, Concord, Mass), thus confirming the validity of our derived equations. In addition, the effect of a beveled edge was investigated in some archwires. Furthermore, torsional play angles were calculated and found to be similar to those in previous reports. The results of this study provide theoretic and experimental bases for clinical orthodontic practice and indicate that torque angles should be included in the evaluation of the critical contact angle.