A general mathematical model for describing the geometries and geometric properties of conjugate tooth profiles is presented. Three kinematic parameters and a first order differential equation are introduced to characterize this model. The condition for determining the cusp of tooth profiles is also presented. Using this model, two types of tooth fillets with their minimum radii of curvatures generated by the rack cutter and pinion cutter are described. The peculiar application of this model is that the investigated tooth profiles can be parameterized by specifying one of the three kinematic parameters as a parametric function. It is believed that the parameterization may provide a logical method for gear design.

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