## 5 Conclusions  
This paper proposed the two force models in order to theoretically calculate the generated force in a thin wobble motor with the EPM device. First, the EPM can change the holding force on and off by applying a momentary electrical pulse, and the structure and driving principle are presented. It is difficult to establish an analysis model that accurately presents the magnetic leakage fluxes, but by assuming their paths to consists of straight lines and arcs, the mean length of the flux path could be obtained. Therefore, in order to increase the accuracy of the theoretical force model of the EPM device, a method considering the leakage fluxes was proposed. Comparing the FEM results and the force calculated using the proposed method, it was confirmed that there was a reduction in the error of the force generated when considering leakage fluxes were considered. However, there were differences between the theoretical and the experimental results, because the loss of friction and assembly error of the magnets and the iron influenced the experimental measurements. Despite the assembly error, it successfully generated holding force at the rotating shaft.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Current (A)**} & \multicolumn{2}{c}{**By Theoretical Method (mNm)**} & \multirow{2}{*}{**By FEM (mNm)**} & \multirow{2}{*}{**By Experiment (mNm)**} \\ \hline
0.1 & 0.166 & 0.134 & 0.118 \\
0.2 & 0.672 & 0.523 & 0.456 \\
0.3 & 1.488 & 1.173 & 1.034 \\
0.4 & 2.64 & 2.088 & 1.843 \\
0.5 & 4.128 & 3.264 & 2.857 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of stall torque according to current variation.  
Figure 14: Experiment results, and comparisons of the force vs. air, calculated using the mantle circuit with and without leakage flux.  
These results can not only be used in selecting the initial design parameters necessary for FEM analysis for the design of EPM devices, but also indicate that the proposed magnetic circuit analysis results can be used as the basis for its design. Secondly, we simply presented the optimal design of the electromagnets with respect to various parameters, as well as a partial differential equation on the basis of the distribution parameters as a function of the variation of the air gap between the stator and the rotating shaft. The theoretical force model for the generated force of the electromagnetic field using the distribution parameters was calculated by approximating the model using a linear coordinate system. We conducted experiments using a prototype motor with respect to the changing current. As shown in Table 2, it was confirmed that the theoretical method results and the FEM results were similar. Differences were observed in the experimental results owing to the loss of friction and error occurring when manufacturing the rotating shaft. However, our study shows advantages in that this method is less time consuming and systematic, because a large number of iterative analyses are not required during the initial design step. As a result, the proposed a thin motor with EPM device has great potential for commercialization as a driving part of small robots, in the medical industry, and especially in thin portable equipment in the future.  
FEM analysis, designed and manufactured of the motor, controller, and wrote the paper, S.Y.P.; edited and revision, analyzed the date, B.S.; investigation and validation S.Y.P. and B.S.; supervision, Y.S.B. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
This paper is no data.  
The authors declare no conflict of interest.