Vernier permanent magnet (VPM) machines can be utilized for direct drive applications by virtue of their high torque density and high efficiency. The purpose of this paper is to develop a general design guideline for split-slot low-speed VPM machines, generalize the operation principle, and illustrate the relationship among the numbers of the stator slots, coil poles, permanent magnet (PM) pole pairs, thereby laying a solid foundation for the design of various kinds of VPM machines. Depending on the PM locations, three newly designed VPM machines are reported in this paper and they are referred to as 1) rotor-PM Vernier machine, 2) stator-tooth-PM Vernier machine, and 3) stator-yoke-PM Vernier machine. The back-electromotive force (back-EMF) waveforms, static torque, and air-gap field distribution are predicted using time-stepping finite element method (TS-FEM). The performances of the proposed VPM machines are compared and reported. ; Department of Electrical Engineering