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A new type of spherical gear is proposed, which is formed by combining the tooth profile of the plane involute annular tooth surface and spherical involute spherical cone tooth surface. 3-DOF of pitch, deflection and rotation can be realized without principle error transmission. Based on the forming principle of plane involute and spherical involute, the equations of annular tooth surface and spherical cone tooth surface are derived by coordinate transformation theory; Combined with MATLAB and Pro/E, the 3D accurate model of 3-DOF spherical gear was obtained, and the contact stress of tooth surface was analyzed based on the finite element method. The simulation results show that the stress concentration always occurs at the tooth root and the tooth top of the spherical and conical tooth surface under the condition of constant spherical distance and the same torque but different coaxial intersection angle, which can provide reference for the tooth surface modification and optimization of spherical gear.

Tooth Surface Modeling and Stress Analysis of 3-DOF Spherical Gear