Taking the torus-involute gear as study object,according to the theory of gear meshing and the gear hobbing process,the tooth surface equations of torus-involute gears with convex and concave teeth are derived by using the tooth surface equation of counterpart rack.According to the mathematical conditions of neither undercutting nor tooth pointing,based on MATLAB,the Graphical User Interface which contains geometric parameter designs of torus-involute gear is developed.In the light of the tooth surface equations of torus-involute gear,the three-dimensional coordinates of torus-involute gear are calculated which can be used to develop the3-D solid models.The Hypermesh is used to mesh the 3-D models of torus-involute gear.Based on the nonlinear contact algorithm,the finite element models of convex and concave torus-involute gears meshing are established which can be used to implement the dynamic contact analysis in ABAQUS.The results reveal that the width of torus-involute gears is limited by gear undercutting or tooth pointing and the maximum contact stress will be steady after hobbing for a while.The contact stress is small when just a pair of gear teeth are meshing,while the contact stress is large when two pairs of gear teeth are meshing.