Fig. 1. Configurations and dimensions of three closing loops, where a is the distance from left-end to loop center, and b = 14-mm is the loop length (distance from left to right-end). (A) Vertical loop; (B) T-loop; (C) L-loop; and (D) definitions for vertical forces and moments. Positive vertical forces move tooth in the direction opposite of loop (extrusion), negative forces move tooth in the loop direction (intrusion). Positive moments rotate tooth clockwise, negative moments rotate tooth counterclockwise.
Fig. 2. Vertical loop deflection and properties at 2-mm activation when loop is centered (a/b = 0.50) or right off-center (a/b = 0.79). Gray dashed line is the unactivated loop shape.
Fig. 3. T-loop deflection and properties at 2-mm activation when loop is centered (a/b = 0.50) or right off-center (a/b = 0.79). Gray dashed line is the unactivated loop shape.
Fig. 4. L-loop deflection and properties at 2-mm activation when loop is placed left off-center (a/b = 0.21), centered (a/b = 0.50), or placed right off-center (a/b = 0.79). Gray dashed line is the unactivated loop shape.
All loop properties depended on the loop shape, position and activation. It was shown that no loop generated an inherent M/F ratio higher than its height. For symmetrical vertical and T-loops, the M/F-ratio could be increased at one end by moving the loops closer to that end, up to 1/5 of the loop length; moving the loop closer than 1/5 caused a drop in M/F-ratio. The asymmetrical L-loop gave its maximum M/F-value when centered. Directional change in the M/F-ratio happened when the loop was about 2/3 away (vertical loop) or 4/5 (T-loop), while for the L-loop the direction of the M/F ratio only changed at the opposite end of the L-loop direction, and occurred at the centered loop position. Achieving maximum M/F ratio on one end caused minimum M/F-ratio (approximately zero) at the other end, which can cause a tipping movement. The analysis also showed that vertical forces generated by vertical and T-loops switched direction at the center. The short leg end had an extrusion force (opposite direction of the loop), the long leg end was intrusion (same direction as loop). For L-loops facing right, the vertical force at the right-end was mostly extrusion (a/b > 0.14). Vertical and T-loops showed the lowest load/deflection values when centered and highest when placed close to an end. For L-loops facing right, the lowest load/deflection was found when positioned close to the left-end and highest when positioned close to the right-end. It can therefore be concluded that position affected loop properties differently for different designs. Consequently, clinicians should take into account specific characteristics of each loop configuration to create desired tooth movements.