The effects of first- and second-order gable bends on forces and moments generated by triangular loops

Introduction: Triangular loops are frequently used for space closure. Studies of this loop have focused on dimensional and in-plane (second-order) gable-bend influences on the generated forces and moments, but there have been no investigations into the effects of out-of-plane (first-order) gable bends. Both bends are generally needed to accomplish tooth translation. The primary purpose of this project was to ascertain whether first- and second-order bend effects were uncoupled. Methods: Ninety triangular loops were divided into 9 groups with combinations of 0° and 30° first- and second-order gable bends in the anterior and posterior positions. Forces (Fx, Fy, Fz) and moments (Mx, My, Mz) generated along 3 mutually perpendicular axes—x (mesiodistal), y (occlusogingival), and z (buccolingual)—were measured, and moment/force ratios (Mz/Fx, My/Fx) were calculated. Statistical comparisons were made between the 9 groups and between activation distances. The Sidak multiple-comparison adjustment method was used to control the overall confidence level at 95%. Results: It was shown that the magnitude of Mz/Fx increased significantly with second-order gable bends but did not change with first-order bends. The opposite was found for My/Fx. Conclusions: Thus, in triangular springs, first- and second-order gable bends produce the desired effects without interfering with each other.