# The Center of Resistance of an Impacted Maximly Canine: A Finite Element Analysis
## 4 Discussion  
In classical mechanics, a force refers to an action that can change the motion, direction, or shape of an object. The force consists of three factors: magnitude, line of action, and point of action, and all three factors are involved in interaction with an object. In other \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Pericoronal Tissue**} & \multicolumn{2}{c}{**Location from the Cementoneamel Junction (mm)**} & \multicolumn{2}{c}{**Percentage of Root/Crown Length (\%)**} \\ \cline{2-5}  & **MD** & **BL** & **MD** & **BL** \\ \hline Air & \(-5.18\) * & \(-5.26\) * & 38.1\% \(\dagger\) & 38.7\% \(\dagger\) \\ Granulation tissue & \(-5.18\) * & \(-5.26\) * & 38.1\% \(\dagger\) & 38.7\% \(\dagger\) \\ Fibrous tissue & \(-2.82\) * & \(-3.46\) * & 20.8\% \(\dagger\) & 25.5\% \(\dagger\) \\ Immature woven bone & 4.25 & 4.30 & 40.8\% \(\ddagger\) & 41.3\% \(\ddagger\) \\ Mature woven bone & 4.64 & 5.18 & 44.6\% \(\ddagger\) & 49.8\% \(\ddagger\) \\ \hline \hline \end{tabular}
* Negative means root apex direction; \(\dagger\) percentage of root length; \(\ddagger\) percentage of the crown length; BL, buccalingual direction; MD, mesiodistal direction.  
\end{table} 
Table 2: Center of resistance according to the stages of pericoronal tissue healing: locations from the cementoneamel junction and root/crown length percentages. Figure 8: Center of resistance of the impacted maxillary canine according to the stages of pericoronal tissue healing. (**A**) Buccolingual direction and (**B**) mesiodistal direction. words, the action is not determined solely by the magnitude of the force, but depends on the line of action and the point of action. [PERSON] [32] recognized the importance of the point of action and first introduced the concept of the COR from rigid body mechanics into dentistry in 1917. He concluded that when a horizontal force is applied to a tooth with a single root, there will be an action point that causes the bodily movement somewhere between the root apex and the alveolar crest, and he stated that it might probably exist at the midpoint between the alveolar crest and the apex. Since then, the COR has been defined in various ways, such as the point of action that shows the greatest resistance to tooth movement, or the point of action that shows only pure translation regardless of the direction of force [33; 34]. For effective orthodontic treatment, it is important to apply appropriate force to the teeth to control tooth movement. Orthodontic tooth movement consists of rotation, translation, and a combination of the two. This is achieved due to the relationship between the orthodontic force and the COR. If the COR is accurately known, the orthodontic force that generates a specific tooth movement can be predicted, enabling efficient tooth movement. A common definition of the COR is the point at which the object will be translated when a single force is applied. The COR of the tooth is determined using the material properties of the tooth and surrounding supporting structures [35]. In particular, it is crucial to accurately know the COR of the impacted tooth because an impacted tooth is an isolated tooth, so inappropriate tooth movement easily occurs due to an erroneous force. If the COR of the impacted tooth can be accurately identified, the probability of success in the orthodontic traction of the impacted tooth will increase, and the treatment period will be shortened, improving the quality of life of the patient. Various analytical or experimental methods [21; 22; 23] have been used to find the COR of the tooth. [PERSON] et al. [21] used three-dimensional laser holography to determine the COR of the maxillary central incisors. [PERSON] et al. [22] used an electrical resistance strain gauge method to determine the COR of the upper anterior segment. [PERSON] et al. [23] used a laser reflection technique to find the COR of the maxillary anterior teeth. However, most studies [14; 15; 16; 17; 18; 19; 20] have used the FEM.