## 1 Introduction  
The clinical use of clear aligners (CAs) is increasing as an alternative to traditional fixed orthodontic appliances due to their esthetics, convenience, and ease of oral hygiene [1, 2, 3]. In particular, advances in materials science and the incorporation of digital technologies, such as CAD-CAM technology, intraoral scanning, and 3D printing, have simplified the fabrication of CAs and expanded their clinical applications [4, 5]. However, while CAs have demonstrated effective results in the treatment of intrusion, distal bodily shift in molars, and retraction of incisors, they still have limited predictability in the treatment of incisbodily shift and torque control, and the mechanics of the forces and moments that cause tooth movement remain insufficiently understood [6]. Diastema is the presence of space between two adjacent teeth and has both esthetic and functional significance clinically. In esthetic terms, diastema can negatively affect a patient's facial appearance and self-esteem, and in functional terms, it can increase the risk of periodontal disease by promoting the deposition of food residue and calculus formation [7]. Recently, the use of CAs has been increasing as a treatment modality for diastema, but previous studies have shown that space closure involving incisor and canine movement with CAs can result in unwanted extrusive and rotational forces in addition to mesiodistal forces upon initial force application, which can further complicate treatment by causing tooth tipping and occlusal interference [8; 9]. Despite these findings, there is still a lack of quantitative understanding regarding force distribution and movement control during diastema closure with CAs. While previous research has identified issues such as uncontrolled tipping and rotational moments, the precise biomechanical mechanisms governing these movements remain unclear. Additionally, it is not well understood how structural modifications, such as localized reinforcements or the incorporation of intrusive forces, can improve bodily movement control and reduce unwanted forces [10]. While additional appliances such as attachments, power arms, and mini-implants can be used for effective tooth movement, they have limitations that increase the complexity of the treatment process and prolong the treatment time. In particular, attachments have limited application to the prosthetic surface, power arms can cause a foreign body sensation and poor esthetics, and mini-implants are at risk of inflammation and dislodgment. Structural design variations in CAs have been proposed as an alternative to overcome these limitations. Structural design modifications include the utilization of existing attachments, subgingival extension of the margins of CAs, adjustment of the device thickness, and creation of an enhanced structure by adding flowable resin directly to the interdental embrasure. A recent study by [PERSON] et al. reported that adding flowable resin locally to the molar region increased the stiffness of the appliance, altered the distribution of forces applied to the molar region, and enabled force transfer closer to the center of resistance [11]. However, although adjusting the overall thickness of the CAs affects the characteristics of the forces transmitted to the entire dentition, increasing the localized thickness of the aligners can improve the stiffness of the desired area, allowing for the precise control of the targeted tooth movement [12; 13]. Despite these advancements, there is still limited experimental data on how such modifications specifically affect the force and moment system during diastema closure. Furthermore, the potential benefits of combining structural reinforcements with intrusive forces for optimizing space closure efficiency have not been fully explored. In orthodontic treatment, force/moment measurement is essential for accurate prediction of tooth movement patterns and effective application of biomechanical principles.