## 1 Introduction  
With the increasing demand of industrial automation and robots around the world for a multi-degree-of-freedom (DOF) motion mechanism, a motion mode for motors has been developed from simple 1-DOF motion to a multi-DOF motion, and the application of humanoid is actively proceeding [1, 2]. Conventionally, for joints and eyeballs of the humanoid, the multi-DOF systems are implemented with multiple motors to mimic the movement of human body [3, 4]. Multi-DOF systems are devices that can set orientation and positioning of the object in any direction [5, 6]. However, these systems have increasing weight and size. In recent years, various multi-DOF motors have been developed and designed to achieve the multi-axis or multi-DOF motion. These multi-DOF motors include 2-DOF motors [7, 8, 9, 10, 11, 12, 13], 3-DOF motors [14, 15, 16], 4-DOF motors [17], and 5-DOF motors [18] depending on their applications. For example, [PERSON] et al. presented a 2-DOF motor with an unlimited angular range [7]. [PERSON] et al. proposed a feedback control method for a 2-DOF motor [10]. [PERSON] et al. and [PERSON] et al. proposed some novel 2-DOF motorsfor camera modules [8; 9; 11; 12]. [PERSON] and [PERSON] proposed accurate and rapid analysis and optimal design methods for 2-DOF motor [13]. [PERSON] et al. proposed a novel 3-DOF linear oscillatory motor [16]. [PERSON] et al. proposed a novel 4-DOF motor for laser beam stabilization [17]. In camera modules, several methods were proposed in order to improve the efficiency, such as compliant mechanism [9; 15], chamfered edge magnet [11], L-shape coil [12; 18], optimization [8; 13], and so on. In addition, motors can be classified by shape, such as square and sphere [7; 10; 14]. According to the collecting information, the performance comparison list of the several kinds of 3-DOF motors is shown in Table 1. In this study, the voice coil type is selected due to its simple structure, high response, and high positioning accuracy. Spherical motors are electric devices capable of achieving multiple DOF rotary motions in a single joint [19; 20; 21]. Spherical motors have several advantages, such as a compact structure, a flexible motion mode, no accumulation of motion bias, and a simple control method compared with conventional multi-DOF actuating systems that consist of several single-DOF motors [1; 22; 23]. Therefore, they have been actively developed and have a wide application prospect in joints and eyeballs of the humanoid, unmanned aerial vehicles, autonomous cars, walking robots, and other fields. For these autonomous systems, environment and space recognition is a crucial function. The image information of the environment and space is captured by using a camera module, while these autonomous systems are moving [24]. As a result, developing a camera module with multi-DOF spherical motors to mimic the movement of human eyeball is an important issue in a wide application of the humanoid and autonomous systems. This study focuses on the design of a 3-DOF spherical motor for the camera module of the humanoid and autonomous systems. [PERSON]'s group proposed a novel 3-DOF spherical motor for image stabilization, and the dynamic characteristics were clarified through the electromagnetic field analysis using the 3D finite-element method (3D FEM) [25]. In keeping with consumers' preferences for electromagnetic actuators of ever smaller power consumption, it is necessary to improve the power efficiency of the electromagnetic motors used in unmanned aerial vehicles and robots without sacrificing their performance. Accordingly, this study modifies the 3-DOF spherical motor proposed by [PERSON]'s group in a previous study [25] to accomplish a 3-DOF spherical motor for camera module with higher torque output in the large rotation angle. The main contribution of this study is to improve the static torque in the \(X\)- and \(Y\)-axes with an improved electromagnetic structure and a particular controlling strategy.