# A New Tooth Profile Modification Method of Cycloidal Gears in Precision Reducers for Robots
###### Abstract
In the aspect of tooth profile modification of cycloidal gears, [PERSON] et al. indicated the requirements of the modification of cycloidal gears used in robots and proposed the optimum mathematics model for the modification of cycloidal gears in order to achieve the high kinematic accuracy, little backlash, high-load capacity, high rigidity and high transmission efficiency of RV reducers [8]. [PERSON] et al. presented a new method of cycloid disc tooth modification and designed the modification clearance curves by adjusting the positions of five key points according to different modification targets, and they found that the method could improve the carrying capability of cycloidal drive, eliminate noise and vibration and increase the transmission accuracy [9]. [PERSON] et al. designed a new two-stage cycloidal speed reducer with tooth modifications, studied the profile generation and modifications of cycloidal gears, analyzed the kinematic errors with the tooth contact analysis method and presented the quantitative results of different modification combinations of the gear profile [10]. [PERSON] et al. found that the cycloidal gear profile modification was sensitive to the backlash of RV reducer and they proposed a modification method of the cycloidal gear tooth profile based on the compensation of deformation, realized the backlash optimization of RV reducers and significantly reduced the gear side clearance caused by the cycloid gear modification [11]. [PERSON] et al. proposed a new tooth surface topography modification method for spiral level gears and corrected the machine settings by establishing the modification mathematical model between the tooth surface deviations and machine settings [12]. Regarding the meshing characteristics of cycloidal-pin gear pairs, [PERSON] et al. studied the geometry modification of rotor profiles of a cycloidal pump and determined the virtual pair of contacting profiles, the backlash between the profiles that were not in mesh and the transmission errors in the rotation transformation at any time [13]. [PERSON] et al. proposed a new method for the gear tooth contact analysis to avoid two considerable disadvantages of the numerical instability and computation process complexity [14]. [PERSON] et al. proposed an analysis method, called non-Hertz flexibility matrix method (NHFMM), for the tooth contact of the modified profile of pin gear [15]. [PERSON] et al. proposed a new method for calculating the cutting force during processing hypoid gears [16]. [PERSON] and [PERSON] investigated the impact of tooth profile modification on spur planetary gear vibration, proposed an analytical model and discussed the static transmission error and dynamic response [17]. From the above studies, it can be seen that the traditional modification design is mainly realized by changing the size and center position of the grinding wheel in the generation process. At present, the gear grinding technology and precision measurement technology are increasingly mature [18; 19; 20], so the modification methods of cycloidal gears are more flexible [21] and various tooth profile optimization technologies are available. The profile shape of a cycloidal gear directly affects its transmission performance and the pressure angle distribution on the cycloid profile determines the force transmission performance of gear teeth in meshing. Therefore, in the profile modification design of a cycloid gear and its meshing performance analysis, the pressure angle, the backlash of gear teeth, the tooth tip and root clearance should be considered. In the study, based on the comprehensive consideration of the profile pressure angle, backlash, tooth tip and root clearance, a new modification method is proposed. Based on the mathematical model for the profile modification of a cycloid gear, the mathematical relationship between the modifications and the pressure angle distribution is established and the meshing performance of the modified tooth profile is discussed in depth.