This paper presents designs of the surface-mounted permanent magnet (SPM) motor and Vernier motor for the Collaborative Robot (Cobot) applications. Design constraints and operating conditions are referred from a commercial 12-slot 10-pole SPM motor using in the Cobot UR10 model. The Vernier motor is proposed considering a double air gap, 12-slot 20-pole, and distributed winding configuration. The performance of the two motors is compared in terms of torque and power density. The preliminary design shows that a Vernier motor with a double air gap, the distributed winding can generate the higher torque but lower power density than the conventional SPM motor due to the end-winding loss. A different Vernier motor design using concentrated winding is also discussed.