This paper presents kinematic equations which can be used to mathematically generate and evaluate novel gear tooth systems. The equations apply to spur, bevel, and hypoid gearing but are used specifically to generate surfaces which engage flat-toothed hypoid gears. Curvatures of these surfaces are then used to determine and compare the maximum Hertz contact pressure corresponding to various parameters. The analysis shows that Hertz contact pressure is the smallest for surfaces having line contact perpendicular to the plane contain the common unit normal vector and unit, tangent (to the path of contact) vector.

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