The fundamental geometrical characteristics of bevel gears have been discussed in this study. The mathematical modeling of the tooth surface geometry of bevel gears can be developed based on the basic gearing kinematics and involute geometry along with the tangent planes geometry. The parametric representations of the spherical involute and the involute spiraloid, which are the tooth surface geometry of straight bevels and spiral bevels, respectively, have been derived in this paper. This study may provide some fundamentals for computer numerical controlled manufacturing of bevel gears.

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