Noncircular bevel gear can achieve variable transmission between intersecting axes. Based on polar coordinates, a design method for noncircular bevel gears is presented. The geometric characteristic of tooth profiles of the gears can be obtained by means of geometry principles for spherical engagement and a pair of conjugated crown racks, which can engage with the driver noncircular bevel gear and driven one, respectively. A series of new conception such as tangent azimuth angle, concavity of conical surfaces, and module angle are proposed to describe spherical geometry relationship in meshing. Meanwhile, geometrical characters of the crown rack cutter are derived. Based on this cutter, the accurate mathematical model of noncircular bevel gear tooth profile is deduced, and the determinant criterion for undercutting is presented. As an example, the three-dimensional models of noncircular bevel gear pair are established to demonstrate the feasibility of the proposed method. A noncircular bevel gear set can be designed by this method if the special included angle for intersecting axes and transmission function ratio are given.
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