# Design and Analysis of Internal-External Composite Meshing Hy-Vo Chain
## 1 Introduction  
A Hy-Vo chain is a type of silent chain with rocker pin joints. Benefiting from the construction of the rocker pin joint, the Hy-Vo chain can not only carry a higher torque, but also has a lower system polygon action [1; 2]. Therefore, the Hy-Vo chain is extensively applied to areas of heavy loads and high speeds, such as the transfer case in hybrid vehicles. The previous studies have already proved that the internal-external composite meshing mechanism is the best way to improve the transmission performance of a round pin jointed silent chain system [3]. When an external meshing Hy-Vo chain meshes with a sprocket with the involute profile, because the essence of the external meshing is a kind of positioning, the meshing impact between the chain plate external profiles and the sprocket involute profiles is not avoidable [4]. Supposing that the internal-external composite meshing mechanism exists in the Hy-Vo chain system, as Figure 1 shows, the left internal profile of chain plate 3 will first mesh with the sprocket before the external profiles of chain plate 2 come into contact with the sprocket; thus, the meshing impact can be mitigated. Moreover, the classical meshing theory also holds that the internal meshing profile for the internal-external composite meshing Hy-Vo chain should be a kind of arc with a certain convexity [5]. However, the above analysis is only a kind of hypothesis, and it is just suitable for the round pin jointed silent chain system. Furthermore, whether in engineering or in a laboratory,there is no feasible internal-external composite meshing Hy-Vo chain system [6]. Although an internal-external composite meshing Hy-Vo chain does not exist, as Figure 2 displays, some researchers have found that the transmission performance of the Hy-Vo chain system can be improved if the internal-external composite meshing chain plates can be added to the external meshing Hy-Vo chain, and they named the mixed assembly silent chain as a new type Hy-Vo chain [7]. However, the mixed assembly Hy-Vo chain is not applied on a large scale because of its unstable performance. As a result, studying and analyzing the internal meshing profile and internal-external composite meshing mechanism of the Hy-Vo chain are necessary to perfect the meshing theory of the silent chain. The Hy-Vo chain has been studied for a long time, but its internal-external composite meshing mechanism is rarely studied. By building the rocker pin joint mathematical model, [PERSON] et al. [8] analyzed the jointed force between the rocker pin and the chain hole and proposed a corresponding optimization scheme. [PERSON] et al. [9; 10] developed the classical Hy-Vo chain design system, that is, the chain-sprocket-hob meshing system, proposed the appropriate meshing condition between the circular hole Hy-Vo chain and involute sprocket, and pointed out that the internal-external composite meshing Hy-Vo chain should be existed. [PERSON] et al. [11] studied the internal-external composite meshing mechanism of the mixed assembly Hy-Vo chain drive and then analyzed the nonlinear contact between the internal meshing profile of the mixed assembly Hy-Vo chain and the sprocket involute profile. [PERSON] et al. [12; 13] pointed out that the multiphase drive can improve the performance of the Hy-Vo chain system transmission and proposed the function for the internal meshing profile of the mixed assembly Hy-Vo chain in a dual-phase system. Obviously, the above studies may involve part of the contents of the internal-external composite meshing mechanism of the Hy-Vo chain system, but the achievements are mainly on the basis of the mixed assembly Hy-Vo chain system. Up to now, there has been no general and effective design approach for the internal-external  
Figure 1: Internal–external composite meshing of Hy-Vo chain system in classical theory. Figure 2: Mixed assembly Hy-Vo chain. composite meshing Hy-Vo chain, and its meshing characteristics have not been deeply analyzed.