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The 3-DOF spherical gear is proposed and its tooth surface is composed of involute ring tooth surface and semi-spherical bevel tooth surface， the error-free transmission can be realized. Based on the involute forming principle and the coordinate transformation theory， the curved surface equations of annular tooth and arc tooth are derived. According to the meshing principle and motion analysis， the conjugate tooth surface of the arc tooth surface is obtained. The simulation tooth surface and 3D model of 3-DOF spherical gear are obtained by computer， the correctness of tooth surface equation is verified. The basis for the kinematics and dynamics analysis of the 3-dof spherical gear mechanism is provided.

The three-dimension coordinate equation of tooth surface of spiral bevel gear is obtained based on the forming principle of spiral bevel gear. According to the spiral bevel gear computational adjustment cards provided by the Gleason company,the three-dimensional model of spiral bevel gear pair is established by writing the MATLAB program to solve out the 3 D coordinates of discrete points on the tooth surface and using three dimensional modeling software. The contact analysis of bevel gear pair is completed by importing the 3 D model into the finite element software Abaqus to create the finite element model of spiral bevel gear. According to the analysis results,the change of the contact positive pressure of a pair of gear teeth in a complete meshing cycle is obtained,and the accuracy of the simulation results is verified by experiments which provides reference and technical support for the design,manufacture and optimization of spiral bevel gear.

In view of the shortcomings of involute gear drive,the advantages of synthetic face gear drive are summarized. The circular arc profile is applied to the face gear,and the gear drive with circular tooth profile is put forward. By means of theoretical analysis,numerical calculation and physical experiment,the design of the tooth surface of the circular tooth profile is carried out. Based on gear meshing theory and differential geometry theory,the tooth surface equation of the conjugate tooth profile of the basic tooth profile of the circular rack is modeled firstly,and then use the envelope forming theory to derive the equation of gear face machining arc face gear,and the cutter and circular arc tooth profile gear for each envelope forming work on tooth surface and the derivation of the face gear transition surface equation. Finally,the MATLAB software program is used to solve the set of tooth points and imported into the CATIA software. The EXCEL table with macro program runs the macro program and generates the contour curve in the CATIA software. And then the 3D physical tooth surface of the arc gear profile is obtained by surface fitting method. Compared with the simulation model of gear cutting envelope,the accuracy is verified.

The quadruple arc spiral bevel gear is a new type of gear with quadruple arc tooth profile applied to the spiral bevel gear. The three-dimensional model is built in Solid Works based on the tooth surface equation of spiral bevel gear with circular arc tooth profile. The static finite element analysis is carried out by using a pair of teeth based on Abaqus. Compared with the double arc spiral bevel gear,it is concluded that the load capacity of quadruple arc spiral bevel gear is 30% higher than that of double arc spiral bevel gear.

Based on generating method machining pinion of hypoid gear,according to the cutting coordinate system of milling cutter and tooth surface equation,the mathematical model of machining pinion of hypoid gear is established,the theoretical tooth surface equation of pinion. The theoretical tooth surface is dispersed,the coordinates of the discrete points are solved,the tooth surface points are imported into UG and the modeling of tooth surface is carried out. According to the anti-conjugate principle,the tooth surface equation and tooth surface points of tool gear that fully conjugated with pinion are solved and three dimensional modeling is carried out. The motion simulation of three dimensional model is carried out,through the contact area to verify the correctness of modeling. According to the principle of equal volume,the rolling round billet is solved. Introduced the rolling models into DEFORM to carry out numerical simulation. The feasibility of the processing technology is verified by the simulation result,and theoretical guidance for the follow-up experiment is provided.

In order to explicitly solve the tooth surface model of forming face gear,and exactly solve the minimum inner radius of face gear with top-cut. The orthogonal face gear envelope coordinate system is established and the tooth surface equation of generating gear is given. The face gear working tooth surface equation,transition surface equation and top-cut surface equation are derived. According to the tooth surface equation,the simulation analysis of face gear tooth surface is carried out by using the MATLAB 7. 5 and CATIA V5. According to the simulation comparison of tooth surface and the analysis of top-cut boundary line,the top-cut minimum inner radius key point is got,the key point is the intersection of the face gear tip surface and top-cut boundary line. Through the explicit solving the key points,the minimum inner radius of the face gear without top-cut can be got. Comparing with the existing literature results of the implicitly solving inner radius,and the difference on numerical is small between the two. Finally,through the simulation cutting tooth way,it shows the accuracy of this method is superior to the method of literature.

The cylindrical gear with arc tooth trace is a novel cylindrical gear with the features of good meshing performance,large overlap coefficient,smooth transmission,low noise,high efficiency,long service life and so forth. It can make up the deficiency of the existing gear transmission pairs. In order to further study its characteristic,the tooth surface equation is deduced according to the processing principle of rotationary cutter for the cylindrical gear with arc tooth trace and meshing principle. Also,in order to improve the modeling efficiency,the parametric three- dimensional modeling of the rotating disk method is completed based on the secondary development technology. This provides the correct 3D model for the following simulation analysis.

Aiming at the cycloidal gear used in RV reducer of robots,based on the concept of the single tooth without side clearance,the tooth surface equation of the cycloidal gear after modification is deduced by directly adding the second- order parabolic modification amount to the theoretical conjugate tooth profile along the normal direction. The modification amount of different meshing position on tooth profile curve could be flexibly controlled by controlling the tooth profile modification coefficient. The differences between the parabolic modification and the traditional modification method of the combination of isometric and travel distance,the proposed parabolic modification method is much closer to the complete conjugate tooth profile on the main meshing areas.The TCA program of cycloidal- pinwheel transmission which is written in Matlab formed parabolic transmission errors and the correctness of this modification is proved,which provides a new thought for the modification design of cycloidal gear used in RV reducer.