Research On Involute Sperical Gear With Three Degree Of Freedom

With the development of robot and biomechanics technology,traditional gear can not meet the need of multi-degree-of-freedom transmission,and a spherical gears welltimely adapt to the need.A transmission device comprising spherical gear as a key component has the advantages of large range of motion,compact structure and flexible transmission.A spherical gear with three degrees of freedom is designed and its tooth surface generation,meshing principle and transmission characteristics are investigated.The main research efforts are presented as followed:1.Based on the analysis of conjugate motion for the available spherical gears,the spherical gear completed with two tooth surfaces of ring involute spherical gear and a semi-spherical bevel gear is designed.The mathematical model of the two tooth surfaces is developed,and its projection boundaries are simulated to select the design parameters for making the lost meshing area of the two tooth surfaces within allowable limits.The parametric design of the spherical gear is achieved at last.2.The meshing principle of semi-spherical gear is studied.According to the analysis of the relative movement and conjugate motion of semi-spherical gear,two derivation methods for meshing equation and conjugate surface equation are proposed.The simulation of meshing principle of semi-spherical gear shows that its curved teeth surface in engagement are conjugate surfaces.3.To analyze the transmission performance of the spherical gear,the correct meshing condition and no-interference condition of the spherical gear are studied,and then the contact stress,sliding coefficient and meshing efficiency of the curved tooth surface are calculated respectively.The results indicate that the curved tooth surface meshing at the tip position and transverse profile is prone to contact fatigue damage and wear respectively,and the meshing efficiency decreases as the pitch angle increases.4.The meshing motion and interference check of the spherical gear and the semispherical bevel gear are performed to verify the correctness of the tooth profile design and virtual solid model.The finite element method was used to simulate the contact stress and tooth root bending stress of the two gears for verifying theoretical calculation.