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The engaged feature of a pair of gears was determined by the geometrical characteristics of their tooth surfaces. Through an analysis of gearing theory on epicycloidal bevel gears, the method to examine if there exists undercut during manufacturing of epicycloidal bevel gears, the approximate formulae to calculate the gap between the convex and concave tooth surfaces in meshing so as to guarantee against the occurrence of point-contact for tooth surfaces even in maximum angle of inclination are derived in this paper. Those formula derived are simple, compact and have practical value to the design and production of epicycloidal bevel gears.