# A New Tooth Profile Modification Method of Cycloidal Gears in Precision Reducers for Robots
###### Abstract  
The tooth profile modification of cycloidal gears is important in the design and manufacture of precision reducers or rotary vector (RV) reducers for robots. The traditional modification design of cycloidal gears is mainly realized by setting various machining parameters, such as the size and center position of the grinding wheel. The traditional modification design has some disadvantages such as complex modification calculation, uncontrollable tooth profile curve shape and unstable meshing performance. Therefore, a new tooth profile modification method is proposed based on the consideration of the comprehensive influences of pressure angle distribution, meshing backlash, tooth tip and root clearance. Taking the pressure angle and modifications of tooth profile as the parameters of the modification function and the meshing backlash of gear teeth as constraints, the mathematical model for tooth profile modifications is built. The modifications are superimposed on the normal direction of the theoretical profile--the force transmission direction. The mathematical relationship between the modifications and the pressure angle distribution, which determines the force transmission performance, is established. Taking the straight line method, cycloid method and catenary method as examples, by means of the tooth contact analysis technology, the transmission error and minimum meshing backlash, which reflects the lost motion, of the newly modified profile are analyzed and verified. This proposed method can flexibly control the shape change of the modification profile and accurately pre-control the transmission accuracy of the cycloid-pin gear. It avoids the disadvantages of traditional modification methods, such as uncontrollable tooth profile shape and unstable meshing accuracy. The method allows good meshing characteristics, high force transmission performance and more precise tooth profile curve. The study provides a new design method of the modified profile of cycloidal gears. robot precision reducer; cycloidal gear; tooth profile modification; pressure angle distribution; transmission error; minimum backlash angle +
Footnote †: journal: Applied Softcomprehensive performance of precision reducers for robots [1]. In cycloidal-pin gear planetary transmission, in order to compensate the assembly error and maintain reasonable backlash for the conveniences of lubrication and assembly, the theoretical tooth profile of the cycloidal gear is generally machined through the modification design and the tooth profile modification quality is the key to ensure the motion accuracy of precision reducers for robots [2]. Many experts and scholars have carried out in-depth studies on the profile curve, modification design and meshing characteristics of the cycloidal gear in the precision reducer and have achieved fruitful results. In the aspect of the profile curve characteristics of the cycloidal gear, [PERSON] and [PERSON] developed a general method for the generation and design of cycloid tooth profile, and avoided the profile and surface singularities of cycloid gear through improving the design [3]. [PERSON] and [PERSON] presented the computer-aided analysis and synthesis of cycloid drives and defined the kinematic relationships between tolerance drive parameters and performance indices in detail [4]. [PERSON] et al. proposed a new type of cycloid double-enveloping meshing pair with high transmission accuracy, low backlash and high torsional stiffness [5]. [PERSON] and [PERSON] provided a unified set of equations for optimizing the design of cycloid drives and introduced the sources and effects of various tolerances, such as profile reduction, backlash and torque ripple and maximum gear ratio [6]. [PERSON] et al. established a translation-torsion coupled nonlinear dynamic model with multiple degrees of freedom for a planetary gear train system, and indicated that the load sharing coefficient varied more significantly with the increase in the pressure angle range of gear pair [7].