## 2 Materials and Methods  
### Forces/Moments Measurement Apparatus Design and Fabrication  
The maxillary dentition model was designed using a Nissin dental model (NISSIN B3-305, Nissin Dental Products, Kyoto, Japan) with a 3D scanner (TRIOS 4, 3 Shape TRIOS A/S, Copenhagen, Denmark). The model was established with the maxillary right first premolar extracted to simulate the posterior bodily movement of the maxillary right canine.  
To measure the forces and moments applied to the maxillary canine by the CA, a force/moment measurement apparatus was designed and 3D printed using an STL file editing program (Meshmixer ver 3.5, Autodesk Inc., San Rafael, CA, USA) to connect a six-axis miniature force/torque sensor (Aidin Robotics, Seoul, Republic of Korea) to the maxillary right canine (Figure 1).  
The forces and moments were measured by mounting the thermoforming CA on the apparatus and maintaining it at 37 \({}^{\circ}\)C for 10 min using a Forced Convection Incubator (C-INDF, Changshin Science, Busan, Republic of Korea) to reproduce the intraoral environment. Following this, the average values of the measured forces and moments over the next 10 min were used for analysis. The directions of the force and moment on the multi-axis obtained were separated by \"+\" and \"\(-\)\" signs (Table 1).  
Design Modification and Fabrication of the Experimental CA for Distal Bodily Movement of the Maximly Canine  
In this study, CAs with four types of edentulous area designs were fabricated to measure the forces and moments on the right maxillary canine during a 0.25 mm posterior bodily movement of the tooth. The 0.25 mm bodily movement simulation of the maxillary canine was modeled using 3D dental software (DentOne ver 1.0, Diorco, Yongin, Republic of Korea). The designs of the four CAs were as follows (Figure 2):  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Definition** & **Sign Convention** \\ \hline Force (X) & Buccolingual & (+) Buccal, (\(-\)) Lingual \\ \hline Force (Y) & Mesiodistal & (+) Distal, (\(-\)) Mesial \\ \hline Force (Z) & Oclusogingival & (+) Oclusal, (\(-\)) Gingival \\ \hline Moment (X) & Angulation & (+) Mesial, (\(-\)) Distal \\ \hline Moment (Y) & Inclination & (+) Buccal, (\(-\)) Lingual \\ \hline Moment (Z) & Rotation & (+) Distal, (\(-\)) mesial \\ \hline \hline \end{tabular} The ”+” sign indicates the direction described first in each pair (e.g., (+) Buccal for Force (X)), and the ”\(-\)” sign indicates the opposite direction (e.g., (\(-\)) Lingual for Force (X)).  
\end{table}
Table 1: Sign conventions of the force/moment measurement system.  
Figure 1: Experimental apparatus design. The maxillary right first premolar is extracted, and the canine is connected to a six-axis miniature force/torque sensor.  
Group 1: 0.25 mm distal bodily movement of the canine;  
Group 2: 0.25 mm distal bodily movement of the canine + replacement of the edentulous space with a first premolar pontic;  
Group 3: 0.25 mm distal bodily movement of the canine + replacement of the edentulous space with a pontic that is half the buccolingual width of the first premolar (height: original premolar's height);  
Group 4: 0.25 mm distal bodily movement of the canine + replacement of the edentulous space with a beam shape column (height: inferior to the proximal contact point; thickness: half the buccolingual width of the adjacent premolar).  
The CAs were fabricated by a thermoforming method using 0.75 mm thick polyethylene terephthalate glycol (Easy-Vac, 3A MEDES, Goyang-si, Republic of Korea). Each experimental group included 33 CAs to account for any losses, resulting in a total of 120 CAs used in the experiment.