## 3 Results
### Biomechanics of Malar Uprighting Using a Conventional Urighting Spring  
With the clinical duration of each simulation iteration now established, the biomechanical results for the molar uprighting process when using a conventional uprighting spring are expressed in terms of both clinical time and iteration number. Figure 10 displays the changes in the mandibular second molar position. Throughout the uprighting process, the molar showed approximately 3.75 mm of distal movement, 2.15 mm of vertical extrusion, and a 22\({}^{\circ}\) counterclockwise rotation. Throughout the simulation, the molar exhibited a steady biomechanical response, with distal movement and vertical extrusion progressing at average rates of approximately 0.31 mm/week and 0.18 mm/week, respectively, while counterclockwise rotation advanced at an average rate of \(\sim\)1.83\({}^{\circ}\) per week. According to the current study's calculations, the center of rotation (C\({}_{\text{Rot}}\)) of the second molar was located approximately at the midpoint of the internal surface of the distal root, as shown in Figure 11. During molar uprighting, the C\({}_{\text{Rot}}\) exhibited a slight shift occulsally of approximately 0.34 mm, while remaining nearly stable in the meso-distal direction. This variation was minimal and nearly unnoticeable in Figure 11, which illustrates the C\({}_{\text{Rot}}\) position at the first and last iterations. The anchorage unit, consisting of the mandibular canine, first premolar, and second premolar, exhibited progressive vertical intrusion throughout the treatment simulation. As illustrated in Figure 12, the second premolar experienced the greatest intrusion, reaching approximately 0.37 mm by the end of the treatment. The first premolar followed with a total intrusion of around 0.30 mm, while the canine showed the least intrusion at approximately 0.21 mm. The rate of displacement appeared nearly constant across all anchorage teeth, falling within the range of 0.02-0.03 mm per week. Figure 9: Calculated iteration duration in days (black curve, left y-axis) and corresponding cumulative clinical time in weeks (red curve, right y-axis), throughout the molar uprighting simulation. When analyzing the forces acting on the mandibular second molar in Figure 13, the graph presents the evolution of the uprighting moment at the buccal tube slot, the extrusion force, and the length of the spring's short lever arm. Here, the short lever arm is defined as the distance between the resultant upward mesial and downward distal contact forces applied at the opposing corners of the buccal tube slot. At the beginning of the treatment simulation, the spring generated a counterclockwise uprighting moment of approximately 15 N\(\cdot\)mm (\(\sim\)1530 g\(\cdot\)mm) and an extrusive force of 0.6 N (\(\sim\)61 g) acting on the molar. This extrusion resulted from the mesial contact force, applied to the upper corner of the buccal tube, being larger than the opposing distal force. As the molar uprighted over time, both the moment and extrusion force decreased steadily, reaching approximately 2.5 N\(\cdot\)mm (\(\sim\)255 g\(\cdot\)mm) and 0.09 N (\(\sim\)9 g), respectively, by the end of the treatment simulation. Insets A and B of Figure 13 highlight changes in the dimensions of the spring's short lever arm throughout the simulation. Initially, the effective lever arm length was 3.25 mm, defined by the distance separating the two resultant contact forces between the spring and the buccal tube slot. As uprighting progressed, these contact points shifted laterally toward the slot's outer edges. By the final iteration, the center of the distal force had moved closer to the lower distal  
Figure 11: Estimated center of rotation (C\({}_{\text{Rot}}\)) of the second molar during the uprighting process. The red dot indicates the C\({}_{\text{Rot}}\) location, shown between the superimposed positions of the first and last iterations.