Abstract: To increase the capacity of the gears in a central transmission system in agricultural machinery and other mechanical systems, to decrease the overall size and the body ground clearance, a possibly ideal spherical arc bevel gear was studied. Based on arc bevel gear meshing theory and the geometric coordinate transformation, the method of spherical trigonometry was applied. The contact point arc trajectory equations of spherical arc bevel gears and the profile of gears tooth surface equations were determined. Therefore the spherical arc bevel gear design theory was further improved and the three dimensional shape of the gears was generated. The results provide a theory basis for correct designing and processing spherical arc of spiral bevel gear with an ideal spherical surface on the main transverse plane and with an arc spiral tooth profile of the end face. They also provide a theoretical foundation for the followed up parameterized designing and digitalized processing for spherical arc bevel gears.