The dual-stage magnetically geared machine (DSMGM) has a high gear ratio. The first stage is a Vernier machine (VM), and the second stage is a coaxial magnetic gear (CMG). These two components share a common rotor (CR), and they are partially flux coupled. Two DSMGMs with different PM arrangements are fabricated and tested. The DSMGM-I with gear ratio 34 can work smoothly, while the DSMGM-II with gear ratio 14.875 is hard to be started up. The purpose of this paper is to reveal the failure of the DSMGM-II. Due to the magnetic flux coupling, there is a recessive CMG in DSMGM structure. The recessive CMG in DSMGM-II prototype is activated and results in high cogging torque and high torque ripple. The thickness of CR yoke controls the portion of flux penetrating through stator. When the thickness of CR yoke is large enough, the cogging torque of the DSMGM-II can be improved. Moreover, another effective method to improve the cogging torque is designing a flux barrier to magnetically decouple the VM and CMG components. For direct-drive robotic application, a DSMGM with Halbach-PM-array is presented. It has a high gear ratio, high torque capability and low cogging torque.