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Magnetic-gearing effect has become increasingly attractive when designing direct-drive low-speed permanent-magnet machines. The machines derived from the magnetic-gearing effect can be termed as harmonic machines. Unlike the conventional types, harmonic machines rely on the field harmonics to achieve energy conversion and transmission. The detailed knowledge of the field distributions in the air gap is vitally important for predicting and optimizing its performance. In this paper, we present an analytical approach to calculate the magnetic field distribution in a low-speed permanent-magnet harmonic machine. A series-slot model which is composed of a group of partial differential equations concerning the scalar magnetic potential is built up. Then, the field solutions are obtained by using the method of separating variables and analyzing the field boundary conditions. Finally, the flux densities are derived from the scalar magnetic potentials. All the results agree well with those obtained from the finite element method.