## 4 Discussion  
This study measured the forces and moments generated by CAs of different designs on the canine during its distal bodily movements using the six-axis force/moment sensor introduced by [PERSON] et al. [19]. By measuring the forces and moments, the biomechanics of CAs can be clearly revealed, and an optimized design of the edentulous area for the bodily movements of the canine can be proposed. The thermoplastic material, CA, exhibits viscoelastic behavior, i.e., it has elastic and plastic properties [16]. Therefore, in distal bodily movements of the canine using a CA, the elastic deformation of the CA can cause the distal tilting and rotation of the canine. If the elastic energy is well transferred to the canine, the canine can become upright and undergo distal bodily movement [20]. To achieve this, a large contact surface between the CA and the tooth is required, and attachments are often used [21]. When attachments are used, the attachment shape does not have a significant effect on efficiency [21; 22]; however, it has been reported that without attachments, teeth can easily tip and rotate [9]. Therefore, rectangular attachments were used for the canines in this study [23]. This study used four types of CAs to simulate the distal bodily movements of canines. The results showed that, in all groups, the canines tended to move by intrusion in the buccal and distal directions, although the magnitudes of the forces and moments differed with the different designs of the edentulous region. These results are consistent with those of a study by [PERSON] et al., which showed that when a canine is subjected to distal forces, it is subjected to extrusion and lingual forces initially when the canine is inclined proximally; however, after the canine is upright, buccal and intrusion forces predominate [24]. Although the main force is applied on the proximal side of the canine, the irregularity of the contact surface between the tooth and the CA may cause the vector to vary in three dimensions. However, when only the CA design is modified in the edentulous area, as carried out in this study, the directionality of the forces and moments does not seem to be affected. Furthermore, differences in the magnitudes of the forces and moments were observed. Group 1 exhibited the largest forces, mainly intrusive and buccal forces, and relatively weak distal forces, while Group 4 exhibited the largest distal forces with moderate intrusive and buccal forces. Groups 2 and 3 exhibited moderate forces in all three dimensions. The distal force values for all groups were within the range of optimal intrusive forces (10-20 cN) [25]. It is considered that Group 1 generated strong intrusive forces, and the possibility of the CA being off the track was much higher than in the other experimental groups as the tooth movement progressed. Although we simulated 0.25 mm of distal bodily movement in all groups, the distal force on the canine located at the corner of the dental arch was significantly smaller than the intrusive force. The contact between the CA and the tooth is important in determining the forces that the CA generates on the tooth. [PERSON] and [PERSON] reported that close contact between the CA and the tooth helps distribute stress more uniformly across the tooth surface [26]. [PERSON] et al. reported that the contact between the CA and the tooth surface is important in determining the distribution of forces [27]. These contacts are affected by the manufacturing method and material of the CA. Moreover, environmental factors, such as intraoral humidity and temperature, can cause changes in the material properties, changing the stiffness of the CA and affecting the contact [28]. The setting of the contact of the CA with the distal surface of the tooth can affect the distribution of distal forces even if the contact at the proximal surface of the tooth is the same, as was the case in this study.