A complete tooth geometry of the circular-cut spiral bevel gears has been mathematically modeled. The mathematical model has been divided into several independent modules, each representing an individual kinematic relation or tool-setting, with examples included. A comparison with the spiraloid model has also been made in this paper. The mathematical model can be applied to simulate and calculate the tooth profiles for the Duplex Method, Helical Duplex Method, Formate Method, and Modified Roll Method for circular-cut spiral bevel gears. It can also be applied to the computer numerical controlled (CNC) machining, computer-aided finite element stress analysis, and tooth contact analysis (TCA) for the spiral bevel gear.

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