Directly driven in-wheel machines are required to generate high output power at low speed. The authors previously proposed the use of a permanent magnet vernier machine, which is suitable for applications that require large torque. The remarkable feature of the previously proposed machine is the use of only ferrite magnets in a 'V' configuration. This machine satisfied the required output characteristics of the in-wheel machine for EV and demonstrated high efficiency in computer simulations based on FEA. However, the design of this machine was somewhat problematic. Therefore, the present paper discusses downsizing of the machine, providing a wider air gap, and the use of concentrated windings. We have achieved an effective design for downsizing while maintaining the output and the torque density. The volume of the newly designed machine is 53% smaller than that of the previous machine, and target performances of 40 kW and 400 Nm were obtained.