The Vernier permanent magnet machine is a high-torque, low-speed system suitable for direct-drive applications such as in-wheel electrical machines and wind generation turbines. In this paper, specific critical parameters of the electrical machine for auxiliary tooth and slot are investigated in different conditions. It should be noted that all the models are fully optimized and compared under the same condition by FEA analysis. The results illustrate that the stator with α β θ is the best choice for stator split pole. Also, the concentrated winding is wound around the main stator tooth and the magnets mounted on the rotor surface. Besides, all essential characteristics for an electric machine such as torque, cogging torque, power factor, and efficiency are investigated. Furthermore, many basic formulas for designing a Vernier machine are proposed. This comparison helps designers choose the best combination among α, β, and θ in the split-pole structures. There is a nomenclature to organize this manuscript for the reader. It should be noted that all the figures are baked by ANSYS Electronics Maxwell version 19.0. Moreover, all of them are modified by Origin software to show with high quality.