I. Introduction
For some applications (e.g., elevator hoists, machine tools, and traction machines), direct-drive systems have several advantages, such as high-resolution positioning (non-backlash), low friction loss, and no maintenance due to a lack of gears. A motor that has high torque at low speed is required for such applications. Brushless DC motors or stepping motors are typically used in traditional direct-drive systems; however, these motors have pulsating torque. Therefore, various vernier motors, which theoretically have no pulsating torque, have been developed [1]–[4]. Surface permanent magnet (PM) vernier motors (PMVMs) have been developed [5] and their voltage equations and torque equation have been derived [6]. A high-torque surface PMVM that uses a Halbach array PM and a design method for improving the power factor of surface PMVMs have been reported [7], [8]. A spoke array PMVM, whose rotor has spoke array PMs, has been proposed [9] for achieving a high power factor. The geometric factor of spoke array PM rotors has been investigated [10]–[14].