## 2 Materials and Methods  
### Forces/Moments Measurement Apparatus Design and Fabrication  
The maxillary dentition models were obtained by scanning a Nissin dental model (NISSIN B3-305, Nissin Dental Product, Kyoto, Japan) with a high-resolution TRIOS 4 intraoral scanner (3 Shape TRIOS A/S, Copenhagen, Denmark) for precise digital impressions. The resulting STL files were processed using Meshmixer (Autodesk Inc., San Francisco, CA, USA) for standardization, including artifact removal and alignment correction. The final models were 3D printed using G10-Br (Gruck, Seoul, Republic of Korea). To increase reproducibility, the same digital workflow and printing parameters were applied to each experimental setup to create identical models under all test conditions. A 6-axis miniature force/torque sensor (Aidin Robotics, Seoul, Republic of Korea) was connected to measure the forces and moments exerted by the CA on the maxillary left central incisor dentition model, and calibration followed the manufacturer's recommended protocol and repeated calibration tests were performed to minimize system error (Figure 1). To comprehensively evaluate the biomechanical effects of diastema closure, all six force and moment components (Fx, Fy, Fz, Mx, My, and Mz) were measured. Although Fy represents the primary intended movement, actual tooth displacement occurs in a three-dimensional pattern due to continuous contact changes between the aligner and tooth  
Figure 1: Experimental apparatus design. The maxillary dentition model was set with spaces between the central incisors, and the maxillary left central incisor was connected to a six-axis miniature force/torque sensor (yellow arrow). surfaces. Measuring Fx and Fz enabled the quantification of unintended forces that may influence treatment outcomes. Similarly, Mx, My, and Mz moments were analyzed to assess rotational effects, distinguishing between bodily movement and tipping. This selection was based on a previous finite element analysis study [9], which demonstrated that even with planned unidirectional movement, CAs induce complex force distributions across multiple planes (Table 1). To ensure measurement consistency, we standardized the sensor mounting, calibration, and data acquisition procedures. The sensor was calibrated before each session following the manufacturer's protocol, and the same mounting procedure was applied across all test specimens. All measurements were conducted at a controlled temperature (37 \({}^{\circ}\)C) to minimize variability and ensure reliable data across groups. Forces and moments were measured by mounting a CA made from thermoforming material (polyethylene terephthalate glycol, PETG) (Flexera, GwangMyeong Co., Seoul, Republic of Korea) on the experimental device and maintaining it at 37 \({}^{\circ}\)C, the temperature of the oral cavity, for 10 min using a Forced Convection Incubator (C-INDF, Changshin Science, Seoul, Republic of Korea), and then recording the average value of the measured forces and moments for the next 1 min for analysis. Design Modification and Fabrication of the Experimental CA for Mesial Bodily Shift in Maximally Left Central Incistor  
In this study, in order to close the diastema closure between the maxillary central incisors, the CA was designed into 4 groups to measure the force and moment exerted on the maxillary central incisor by the CA (experimental group) according to whether the maxillary central incisor was intruded or not and the enhanced structure added to the buccal interdental embrasure of the CA (Figure 2). Since the maxillary model is left/right symmetrical, the experiment was conducted on the left central incisor. Group 1: 0.3 mm mesial bodily movement of maxillary left central incisor. Group 2: 0.3 mm mesial bodily movement of maxillary left central incisor + 0.1 mm intrusive movement. Group 3: 0.3 mm mesial bodily movement of maxillary left central incisor with enhanced structure (direct flowable resin adding).