# Transmission Efficiency of Cycloid-Pinion System Considering the Assembly Dimensional Chain
## 1 Introduction  
Industrial robotic arms are widely used in industrial production for their excellent efficiency. In addition, RV reducers are required in joint positions where the robot arm is subjected to a heavier weight compared to harmonic reducers [1, 2]. Moreover, they have the functional benefits of high transmission precision and high torque [3]. The principal reason is that they adopt the simultaneous mesh structure of a two-part, 180-distributed cycloidal gear. Theoretically, half of the teeth are involved in the meshing, which allows the system to work smoothly with low noise and high resistance to impact. In terms of structural design, because of the compound reduction of planetary and cycloidal gears in two steps, it has the features of small size and light weight. These benefits allowed RV reducers in engineering fields [4, 5]. However, they can often only be studied from the perspective of the whole machine. A theoretical evaluation basis for local structural optimization is lacking, especially for the cycloid-pinion system's core drive component. Transmission efficiency [6], a critical evaluation criterion for RV reducers, is generally measured by the ratio of the measured power at the output and the input. Further, there are studies on efficiency testing through auxiliary parts [7]. There is a lack of research on the efficiency drive of core components. The cycloid-pinion system plays a vital role in the RV reducer's stability [8], efficiency [9], and accuracy [10, 11]. Therefore, the cycloid-pinionsystem is often studied as a primary drive mechanism for RV transmissions, such as in cycloid encapsulation, dynamics mesh characteristics [12], lubrication, etc. [13; 14; 15; 16; 10]. For the drive system, efficient transmission means high energy efficiency, low vibration, and less noise. It also determines, to some degree, the precision service life of the transmission system. The current study of the transmission efficiency of the cycloid-pinion system is solved directly by empirical equations [17]. The popular models are the Malhotra method [18], the [PERSON] method [19], and the Kudrijavcev method [20]. The above model integrates the frictional losses of the parts directly connected to the cycloid, such as the input port, the output path, and the mesh pin teeth. The energy dissipation of the system is calculated comprehensively. However, there is no separate analysis of the surface of the cycloid tooth--that is, the part that touches the pin teeth. Simultaneously, the cycloid tooth profile model serves as the basis for the study [21; 22; 23], and a more efficient tooth profile model can effectively improve the computational efficiency. A strong correlation between system power loss and lubrication characteristics is easily associated. Many researchers have investigated the lubrication characteristics of the main components of the gearbox by considering the cycloid-pinion contact characteristics and the geometric characteristics of the cycloid gear [24]. [PERSON] developed a lubrication model for the cycloid-pin-gear system by combining micro-geometry, contact forces, natural surface roughness, and contact area [25]. Meanwhile, [PERSON] [26] and [PERSON] [27] further investigated the lubrication characteristics of the cycloid-pinion system by focusing on tooth profile modification. [PERSON] [16] solved the problem of lubrication failure by considering the force, surface morphology, and geometric tooth profile of the RV reducer's turning arm roller bearing. In the above study, most calculations are based on the premise that the contact pressure is lower than 1 GPa, and the objective is to avoid a sharp increase in viscosity as the pressure increases. Furthermore, the machining process has an important influence on the performance of the gearbox [28]. In particular, the precision transmissions have high requirements for assembly because the clearance caused by assembly tolerances affects the contact force and elastic deformation of the contact tooth surface.