# Modification and Optimization of Cycloidal Gear Tooth Profile Based on Machining Error Compensation
## 1 Introduction  
The rotary vector reducer (the RV reducer) is based on a precision reduction mechanism using the cycloid pinwheel planetary transmission, as shown in Figure 1. It possesses excellent characteristics, such as high transmission accuracy, extensive transmission ratio range, strong bearing capacity, and compact structure [1], and it is widely utilized for motion and torque transmission in industrial robots [2], medical equipment, aerospace applications, precision machine tools, and other fields. Ideally, although the standard cycloid pinwheel transmission is a backlash-free meshing transmission, it cannot compensate for errors caused by manufacturing, installation, and bearing deformation, which will lead to problems such as assembly difficulties, interference jamming, and extremely poor lubrication effects during actual use. Therefore, the cycloid pinwheel must be modified to improve meshing transmission. Since the pin teeth in the cycloid pinwheel transmission are cylindrical, the cycloidal gear segment is usually modified. Figure 1: The RV transmission diagram. The tooth profile shape of the cycloidal gear significantly influences the cycloid pinwheel transmission [3; 4] and also presents a technical difficulty in designing and producing RV reducers. It is of great significance to study the modification of the cycloidal gear to improve the transmission performance of the RV reducer. [PERSON] et al. [5] proposed a procedure to calculate the forces on various elements of the speed reducer and their theoretical efficiency. They also studied the effects of design parameters on forces and contact stresses. [PERSON] et al. [6] considered the application of the cycloidal gear in some actual products and performed in-depth research on the generation and geometry of the cycloidal gear. [PERSON] et al. [7] modeled the machining tolerances of the cycloid drive and studied the influence of machining tolerances on backlash and torque ripple. [PERSON] et al. [8] verified the effect of design parameters on the force of the cycloidal gear. [PERSON] et al. [9] described the sources of tolerances and their effects on backlash and torque ripple, without compensating for these effects. [PERSON] et al. [10] used the finite element method to study the stress distribution of the rotating parts of the cycloidal reducer simulated in a dynamic environment, analyzing the stress and deformation changes with time in one cycle. [PERSON] et al. [11] studied the kinematic error and tolerance design of cycloidal gear reducers, using the Monte Carlo method to analyze the distribution of kinematic errors and optimize the tolerance. [PERSON] et al. [12] proposed an improved load distribution model of the mismatched cycloid-pin gear pair with ring pin position deviations and demonstrated the influences of ring pin position deviations on the distributed load, contact stress, loaded transmission error, and instantaneous gear ratio of the mismatched cycloid-pin gear pair. [PERSON] and [PERSON] studied the diagnosis of problems in the cycloidal gears and cycloidal gearboxes, respectively [13; 14]. Additionally, many scholars have also conducted research on cycloidal gearboxes [15; 16; 17; 18; 19]. However, the technology related to cycloidal gear modification is kept strictly confidential and blocked, and there are few published reports. The RV reducer research started late in China, and since then, many scholars have performed various studies on cycloidal gear tooth profile modification. Several modification methods have been presented in the literature, such as equidistant modification, radial movement modification, angle modification, and their combined modification [20]. Accordingly, many scholars have developed additional modification methods [21; 22]. Although machining error is a critical factor affecting the actual cycloidal gear profile and theoretical profile, few related studies considered the machining error compensation. [PERSON] et al.