A beveloid gear can be viewed as an involute gear of which the profile-shifted coefficient linearly decreases from the heel to the toe. Therefore, tooth undercutting occurs and singular points appear on the tooth surfaces near the toe. When undercutting occurs, the gear tooth is comparatively weak. In this study, the conditions of tooth undercutting of beveloid gears were derived and specific phenomena were also investigated by numerical illustrated examples. In addition, according to the characteristics of tooth undercutting on the beveloid gear tooth surface, a novel type hob cutter with varying cutting depths was designed to avoid tooth undercutting of the beveloid gear.

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