The Effects of First-and Second-Order Gable Bend Angles on Forces and Moments Generated by Triangular Loops

Abstract

Many orthodontic spring designs have been used to close extraction spaces. The triangular loop is an often-used spring in the Graduate Orthodontic Clinic at the Indiana University School of Dentistry. Previous studies of the triangular loop have focused on its geometry and dimensions with various in-plan (second-order) gable bend angles. To date, no investigator has studied the effect of out-of-plane (first-order) gable angle on the in-plane forces and moments generated by the triangular loop. Thus, the purposes of this study are: (1) to determine the effect of first-order gable bend angles on the forces and moments produced by triangular loops and (2) to show that the effects of first- and second-order gable bends are independent of each other. Three hundred sixty triangular loops were divided equally into 36 groups with combinations of 0°, 15°, and 30° first- and second-order gable bend angles. Force and moment components along three mutually perpendicular axes (x, y, and z) were measured. The x, y, and z axes are the mesiodistal, occlusogingival, and buccolingual axes respectively. Separate statistical analyses were performed for Fx, Fy, Fz, Mx, My, Mz, Mz/Fx and My/Fx. Comparisons were made between the 36 groups and between activation distances. The Sidak multiple comparison adjustment method was used to control the overall confidence level at 95%. The hypotheses are (1) the first-order gable bends do not affect the forces and moments generated by triangular loops, and (2) the first and second-order behaviors are independent of each other. The results support the first hypothesis partially. It was shown that the magnitude of Fx and Mz/Fx increased significantly with second-order gable bends but did not change with first-order bends. The magnitude of My/Fx increased significantly with increasing first-order gable bend angles but did not change significantly with second-order gable bends. The second hypothesis is also accepted. The effects of first- and second-order gable angles are independent of each other. Both first- and second-order gable angles are needed to have an appropriate force/moment system for tooth translation.