同族共轭齿廓啮合的几何理论

he complete conjugate conditions and connate conditions are firstly proposed in this paper. Based on the conditions, one universal analytical formula of connate conjugate gear tooth profile and fillet are deduced. The analytical theory of connate symmetric spur gear generated by rack-cutter is built completely. Finally, some new connate gear tooth profiles such as Fresnel Integral, Sine Integral and the Inverse Cosine Transform Class are discussed.