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This paper presents two pole shoe shapes used in interior permanent magnet (IPM) machines to produce a sinusoidal air-gap field. The first shape has an air-gap length which varies with the inverse cosine of the angle from the pole shoe middle. The second shape uses an arc with its centre offset from the origin. Although both designs are documented in the literature, no design rules exist regarding their optimum geometry for use in IPM machines. This paper corrects this by developing optimum ratios of the q-axis to d-axis air-gap lengths. The centre-offset arc design is improved by introducing flux barriers into its geometry through developing an optimum ratio of pole shoe width to permanent magnet (PM) width. Consequent pole rotors are also investigated and a third optimum ratio, the soft magnetic pole shoe angle to pole pitch, is developed. The three ratios will aid machine designers in their design work.