## 2 Design of Original 3-DOF Spherical Motor  
This section reviews the basic structure of the original 3-DOF spherical motor proposed by [PERSON]'s group in a previous study [25]. Its basic structure is shown in Figure 1. As shown, the original 3-DOF spherical motor includes a rotor and a stator. It belongs to the moving magnet type VCM and its detailed components are shown in Figure 2a. As shown, the rotor includes an inner yoke and 8 permanent magnets. Figure 2b illustrates \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type** & \begin{tabular}{c} **Voice Coil** \\ **Motor Type** \\ \end{tabular} & \begin{tabular}{c} **Stepping** \\ **Motor Type** \\ \end{tabular} & \begin{tabular}{c} **Induction** \\ **Motor Type** \\ \end{tabular} & \
\begin{tabular}{c} **Synchronous** \\ **Motor Type** \\ \end{tabular} &
\begin{tabular}{c} **Relectance** \\ **Motor Type** \\ \end{tabular} \\ \hline Control & Simple & Complex & Complex & Complex & Medium \\ \hline Structure & Simple & Complex & Complex & Complex & Simple \\ \hline Response & High & Medium & Medium & Medium & Low \\ \hline Positioning accuracy & High & Low & Low & High & Low \\ \hline Force/Torque & Low & Medium & High & Medium & High \\ \hline Cogging effect & No & Yes & No & Yes & No \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance comparison list of several kinds of 3-DOF motors. the magnetization directions of the 8 permanent magnets. The stator includes an outer yoke A, an outer yoke B, 8 coils, and a support part. A spherical bearing is used to connect the rotor and the stator. The spherical bearing and the support part are made of non-magnetic materials. As shown in Figure 1, 4 symmetrical coils are wound around the outer yoke A. Among the 4 coils, 2 coils are used for rotating around the \(X\)-axis, and other coils are used for rotating around the \(Y\)-axis. In addition, 4 symmetrical coils wound around the outer yoke B are used for the rotating around the \(Z\)-axis. The design parameters of the original 3-DOF spherical motor are illustrated in Figure 3, and their corresponding dimensions are listed in Table 2. The movable angle of the original 3-DOF spherical motor around the \(X\)-axis and \(Y\)-axis is \(\pm 25^{\circ}\), and that around the \(Z\)-axis is \(\pm 5^{\circ}\). Note that for a more comprehensive description of the original system, the reader is referred to [25; 26]. Figure 1: Basic structure of original 3-DOF spherical motor. Figure 2: (**a**) Detailed components and (**b**) magnetization of permanent magnets in original 3-DOF spherical motor. The operating principles are based on the Lorentz force of a voice coil actuator (VCA) or a voice coil motor (VCM) and the magnetic attractive force between the outer yoke A and the permanent magnet. Figure 4a,b shows the Y-Z cross-section of the original 3-DOF spherical motor when the rotor is rotating around the \(X\)-axis at \(0^{\circ}\) and \(25^{\circ}\), respectively. It can be observed that when the rotor is rotating around the \(X\)-axis from \(0^{\circ}\) to \(25^{\circ}\) in a counter-clockwise direction, the Lorentz force from a part of the coils and the permanent magnets is very small due to the weak magnetic flux [27]. In other words, the power efficiency of the original 3-DOF spherical motor is low and could be improved. As a result, the original 3-DOF spherical motor [25] is modified in this study to accomplish a 3-DOF spherical motor for a camera module with higher torque output in the large rotation angle.