## 2 Materials and Methods  
### Design and Fabrication of a Force/Moment Measurement System  
A 3D scanner (TRIOS 4; 3 Shape, Copenhagen, Denmark) was employed to scan the Nissin dental model (NISSIN B3-305; Nissin Dental Product, Kyoto, Japan) to create a digital maxillary dentition model. This model was used to simulate the distal bodily movement of the maxillary second molar. To measure the forces and moments applied by the CA on the maxillary second molar, a six-axis miniature force/torque sensor (Aidin Robotics, Seoul, Republic of Korea) was designed to connect to the maxillary second molar, and the experimental device was 3D printed (Figure 1). Force/moment measurements were acquired by mounting the CA consisting of a thermoforming material (polyethylene terephthalate glycol; Easy-Vac; 3A MEDES, Goyang-si, Republic of Korea) onto the experimental device. The setup was maintained at 37 \({}^{\circ}\)C, simulating the oral cavity temperature, for 10 min in a Forced Convection Incubator (C-INDF; Changshin Science, Seoul, Republic of Korea). Average values of the measured forces and moments were recorded. Force/moment directions on different axes were differentiated using the +/ - signs (Table 1). Each CA was placed on the measurement setup and left for approximately one minute until the values stabilized. The average of the stabilized force and moment readings was then recorded. The interquartile range (IQR) was also presented to indicate measurement variability. A six-axis force/torque sensor was used to measure forces and moments, with a resolution of 0.1 N for forces and 0.3 Nmm for torques, and measurement limits of \(\pm\)25 N and \(\pm\)150 Nmm, respectively, as specified by the manufacturer. The sensor was pre-calibrated, and all values were recorded digitally. Figure 1: Experimental device design. **(A)** Maximillary right and left second molars are connected to a six-axis miniature force/torque sensor. **(B,C)** The maxillary right first molar exhibits a vertical rectangular attachment on the buccal surface, whereas the left first molar did not exhibit the attachment. Design Modification and Fabrication of the Experimental CA for the Distal Bodily Movement of Maximally Second Molars  
Four CA groups with different designs were fabricated to measure the forces and moments on the maxillary second molars. The designs varied based on the presence or absence of attachments on the first molars and the addition of enhancement structures on the outer surfaces of CAs. The maxillary second molars were posteriorly moved by 0.25 mm in all groups (Figure 2). The groups were classified as follows:  
Group 1: #6 attachment and non-enhanced structure  
Group 2: #6 no attachment and non-enhanced structure  
Group 3: #6 attachment and enhanced structure (addition of a direct flowable resin)  
Group 4: #6 no attachment and enhanced structure (addition of a direct flowable resin)  
All second molars and first molars in groups 1 and 3 had a vertical rectangular attachment (\(3.5\times 1.5\times 1\) mm) digitally applied to the buccal surface of the molar, and a dental model of the applied attachment was 3D printed. From the 3D printed dental cast \begin{table}
\begin{tabular}{c c c c} \hline
**Component** & **Definition** & \multicolumn{2}{c}{**Sign Convention**} \\ \hline Force (X) & Buccolingual & (+) Buccal & (\(-\)) Lingual \\ Force (Y) & Mesiodistal & (+) Distal & (\(-\)) Mesial \\ Force (Z) & Occlusoginyal & (+) Occlusal & (\(-\)) Gingival \\ Moment (X) & Angulation & (+) Mesial tipping & (\(-\)) Distal tipping \\ Moment (Y) & Inclination & (+) Buccal & (\(-\)) Lingual \\ Moment (Z) & Rotation & (+) Distal rotation & (\(-\)) Mesial rotation \\ \hline \end{tabular}
\end{table} 
Table 1: Sign convention of force/moments measurement system. Figure 2: Clear aligners design. (**A**,**B**) Occlusal view: (**B**) clear aligners with enhanced structures (addition of a direct flowable resin). (**C**,**D**) Sagittal view: clear aligners with non-enhanced structures.