An important research direction of gear geometry is noncircular gear transmission. Its complex tooth surface geometry and special transmission performance have attracted a large number of researchers. Theoretically, as long as there is a constant speed ratio transmission, there must be a corresponding speed ratio transmission. Limited by various aspects, the current research of noncircular gear transmission is still dominated by noncircular gear, In recent years, the research on non – conic gear has shown a growing trend, involving straight non – conic gear, helical non – conic gear, end – tooth non – circular gear and so on
At present, the research of noncircular gear transmission mainly includes three directions: the design and application of transmission mechanism, the principle and method of gear geometric design, and the principle and technology of gear manufacturing. The design and application of transmission mechanism mainly studies the use of noncircular gear transmission to achieve special transmission requirements or improve the dynamic characteristics of existing transmission mechanism; The principle and method of geometric design of non-circular gear is mainly to study the problem of geometric construction of tooth surface of non-circular gear, that is, how to obtain a pair of conjugate gear surface of variable speed ratio transmission, which is the geometric basis of non-circular gear to realize variable speed transmission; the principle and technology of non-circular gear manufacturing is mainly to study how to use the existing processing technology for circular gear to manufacture non-circular gear, This paper studies some problems of gear machining, such as machine form, machine movement and machining accuracy.
Because it can achieve accurate transmission with variable ratio, non-circular gear can be used in many occasions with special motion and force requirements, so the research on its transmission mechanism is the basis of practical application of non-circular gear theory. According to the different requirements of application occasions, the geometric shape of non-circular gear varies greatly, which also puts forward many problems and challenges to its design and manufacturing related theory and application technology
The research of non-circular gear transmission mechanism in foreign countries can be traced back to the 1930s and 1940s. Almost all the scholars engaged in the research of gear geometry have explored in the research of non-circular gear transmission mechanism and put forward many reliable transmission schemes, many of which have been applied in industrial automation production
Litvin et al. Studied the application of non-circular gear in variable speed transmission and function generation device, and realized various complex function outputs with non-circular gear. Compared with cam and linkage mechanism, this function generation device has more compact structure form and accurate motion relationship. Terada et al.  studied the application of non-circular gear cam mechanism in joint robot, Compared with the traditional cam mechanism, the mechanism has better dynamic characteristics, which can effectively improve the dynamic response and position accuracy of the joint robot. Barkah et al. Put forward the basic idea of using non-circular gear drive to balance the swing force and moment of the linkage mechanism at the same time, studied the basic principle of using non-circular gear to realize the dynamic balance of the mechanism, and deduced the dynamic balance equation of the mechanism; Han applied the principle to the spatial linkage mechanism, elaborated the parameter solution method of the non-circular gear to realize the complete dynamic balance of the mechanism; modler et al. Carried out a comprehensive analysis of the non-circular gear linkage mechanism, analyzed the type and mechanical characteristics of the non-circular gear linkage mechanism, laid a theoretical foundation for its application; emura et al. Put forward the concept of the non-circular gear ratio steering gear; then, Petre et al. Studied the characteristics and geometry design method of the variable ratio steering gear
Mundo has studied the tooth surface design method, motion characteristics and application occasions of the non-circular gear planetary drive; Kumar et al. Have studied the principle of using the non-circular gear to realize the mechanical stepless transmission and the configuration method of the corresponding transmission system; freudenstein et al. Have studied the basic principle and potential application fields of the gear chain drive mechanism with variable ratio; Dooner studied the principle and method of using non-circular gear to optimize the acceleration and torque fluctuation of mechanical system; Ottaviano et al. Studied the kinematic characteristics of the non-circular gear cam function generator through the combination of numerical calculation and experimental analysis; Mundo et al. Studied the five link mechanism of non-circular gear, Based on the non-circular gear, the optimal design of the connecting rod curve of the traditional five-bar linkage was carried out; Liu et al. Studied the application of the non-circular gear train in the generation of the specific track curve.
Domestic scholars have also conducted a lot of research on the application methods of non-circular gears, most of which is a kind of non-circular gear planetary hydraulic motor. As shown in Figure 1, the motor can be divided into different types according to the transmission cycle of the inner ring gear and the sun wheel. The core is the two-stage variable center distance internal and external meshing variable speed ratio transmission mechanism as shown in Figure 2, Its basic principle is that the volume of space composed of two adjacent rows of star wheel, sun wheel and gear ring will change during operation. Xiong Zhenqin et al. Studied the design principle and method of the port of the hydraulic motor; Zhang Shizhai et al. Studied the numerical design method of the pitch curve of the planetary wheel and sun wheel of the motor
Another important non-circular gear product is the gear ratio steering gear used in the automobile (see Fig. 3). Its forms include gear ratio rack direct drive and gear ratio fan circulating ball type, which correspond to two kinds of commonly used mechanical steering gear on the vehicle. Its basic idea is to change the constant ratio gear rack drive of the common steering gear into gear ratio drive, In this way, the steering balance and comfort of the vehicle can be improved. According to the basic principle of gear sector transmission with variable ratio, He Jingliang et al. Deduced the gear surface square of the steering gear; Jia Jumin et al. Studied the meshing principle of gear strip steering gear with variable ratio, The mathematical model of transmission is established and the tooth surface equation of gear ratio rack is deduced
In addition, foreign scholars have also studied a series of non-circular gear transmission devices, such as non cylindrical gear mechanical stepless transmission device, non cylindrical gear series dividers (see Figure 4) and vegetable bowl seedling picking mechanism
Although the non-circular gear has obtained some positive applications in many special occasions, compared with other mechanisms, these applications have not been popularized and popularized. The main reason is that the design theory of the non-circular gear is not mature, and the processing and measuring methods of the non-circular gear are still almost blank, which greatly limits its large-scale production and application