## 4 Discussion
In orthodontic treatment, uncontrolled tipping is the most common type of tooth movement due to the forces applied to the crown [30]. However, excessive uncontrolled tipping leads to unwanted 3D tooth movement; bodily movement or controlled tipping is desirable. Body movements require greater forces in the cervical region; therefore, thermoderm CAs are the most susceptible to deformation and irregularities in the cervical region, and the lack of stiffness limits body movements with CAs alone [21; 27; 30; 31; 32]. Although attachments are essential, they are limited in achieving bodily movements, requiring additional methods to increase stiffness (e.g., CA design modifications) [33]. In this attachment analysis, group 3 exhibited higher moments in all directions compared to other movements, requiring additional methods to increase the stiffness (e.g., CA design modifications). This suggests a synergistic effect between the attachment and enhanced structure on moment formation. The mesiodistal angulation moment (Mx) results demonstrated significantly high values in group 3, with a larger difference between groups 3 and 4 than between groups 1 and 2, indicating that the enhanced structure plays a more significant role than attachment in generating x-axis moments. The z-axis rotational moments exhibited strong buccal rotational moments in group 3, suggesting effective posterior movement of the second molars, whereas forces were relatively low in group 2, where neither attachment nor enhanced structure was applied. These findings are consistent with those of previous studies that evaluated tooth movement through aligner design modifications or thickness variations [24]. An appropriate moment-to-force ratio is crucial for minimizing uncontrolled tipping during molar distalization. [PERSON] et al. reported that a moment-to-force ratio of 10.7:1 was necessary for bodily movement in maxillary premolars, indicating that a larger moment was required compared to uncontrolled tipping movement [34]. In this study, we compared the ratio of mesiodistal angulation moment (Mx) to distal force (Fy) between groups, as this ratio is integral to efficient molar distalization. The results revealed a significantly low moment-to-force ratio in group 2, without attachment and enhanced structures. This finding suggests a high likelihood of uncontrolled tipping in this group. These findingsunderscore the importance of CA with a firm grasp on the teeth, either through attachment or an enhanced structure, to achieve effective molar distalization. Although IQRs were relatively wide for certain measurements (e.g., Fz in groups 3 and 4), effect size values were additionally calculated and included in the results to enhance interpretability. These values support the statistical significance and help to contextualize the biomechanical differences among groups, even in the presence of data variability. This study identified that increased local CA thickness improved molar distalization when combined with attachments. Different CA fabrication methods have many limitations. Thermoforming leads to uneven thicknesses during fabrication. Direct 3D printing requires additional design, and the fabrication of new CAs for treatment is cumbersome. However, the enhanced structural method using a flowable resin proposed in this study offers several advantages. First, the technique is easily applicable in clinical settings, thereby reducing chair time. Second, the method facilitates easy adjustments during the treatment period, eliminating the need for new device fabrication. This approach, allowing adjustments without the need for new aligners, also enhances the patient's comfort and convenience. These findings may offer practical value in clinical situations where attachment bonding is difficult, such as in patients with short clinical crowns or partially erupted molars. Incorporating reinforced designs could supplement conventional protocols, aiding clinicians in achieving efficient molar distalization under challenging conditions.