## 1 Introduction  
Since rotary vector (RV) speed reducers can achieve high transmission accuracy and large torque conversion, they are widely used in elbow joints of robots that are key components in the high-precision manufacturing industry. Due to manufacturing errors of parts, assembly errors, load deformation, and thermal deformation of a gear transmission, a transmission error (TE) of the gear transmission is unavoidable [1; 2]. The TE is one of the main factors that cause vibration of an RV speed reducer, and is the primary indicator for its transmission accuracy. The TE is a deviation between an actual output rotation angle of a gear transmission and its theoretical output rotation angle. Hence, the TE of a gear transmission can describe the fluctuation situation of its speed ratio [3]. TEs of the gear transmission are mainly caused by manufacturing errors of its components and contact deformation of loaded tooth surfaces [4; 5]. TEs of the gear transmission can increase vibration and noise in its driving condition, and reduce the life of the gear transmission [6]. Therefore, the reduction of the TE of the gear transmission can effectively improve its contact performance. A nonlinear dynamic model of the gear transmission with side and radial clearances was proposed in Refs. [7; 8]. [PERSON] and [PERSON] [9] analyzed influences of clearances, time-varying meshing stiffness, and other nonlinear factors on the dynamic performance of the gear transmission. [PERSON] [10] simulated free and forced vibrations of the gear transmission during acceleration and gear shifting processes. [PERSON] et al. [11] proposed an active modification method for cylindrical gears based on a fourth-order TE model and an error sensitivity analysis model, and used this method for the form-grinding process to improve the dynamic performance of the gear transmission. [PERSON] et al. [12; 13] developed a high-order TE model to reduce vibration and noise of cylindrical helical and herringbone gears. Many preliminary works of RV speed reducers focus on their transmission accuracy. [PERSON] and [PERSON] [14; 15] studied the transmission accuracy of a single-stage cycloidal gear transmission by using a geometric model and discussed the relationship between backlash and speed ratio fluctuations and the relationship between backlash and torsional vibrations. The geometric model that they analyzed considered transmission accuracy of the cycloidal gear transmission that has single-stage and single-cycloid reels, while transmission accuracy of a two-stage RV speed reducer with cycloids and cranks cannot be analyzed. Only the relationship between the influence of the radius error of a pinwheel and torsional vibrations was analyzed in previous studies, influences of manufacturing and assembly errors on transmission accuracy of the two-stage RV speed reducer with cycloidal gears, cranks, and other components were not studied. [PERSON] et al. [16; 17; 18] proposed a TE analysis method by using a mass-spring equivalent model to analyze the transmission accuracy of the two-stage RV speed reducer with two cycloidal gears and three cranks. Recently, static and dynamic transmission accuracy considering the influences of more error factors of the RV speed reducer was gradually studied in some works. For calculation of tooth profile modifications of pinwheels, [PERSON] and [PERSON] [19] developed a non-Hertz flexibility matrix to analyze contact failure of cycloidal gear transmissions with heavy loads. The load distribution of a tooth profile of the cycloidal gear can be quickly and accurately analyzed, and axial modifications of pinwheels can also be calculated to improve contact conditions. [PERSON] et al. [20] proposed a loaded tooth contact analysis model to predict contact conditions on various components of cycloidal gear transmissions with clearances and eccentricity errors.