## 2 Architecture and Kinematic Characteristics of MLTD  
The schematic configuration of MLTD is shown in Figure 1. It consists of a planetary gearset on the left side (PL), another one on the right side (PR), a traction motor (M), and a distributing motor (DM). The output shaft of traction motor (M) is mounted with pinions at left and right ends that are gear-meshed to the exterior rims of the ring gears (\(r\)) of PL and PR, respectively, forming reduction gears on the output shaft of M abbreviated as GM. The planetary carriers (\(c\)) of PI and PR are connected to the driving wheels on the left side (WL) and right side (WR), respectively. The sun gears of PL and PR are interconnected through a balance shaft which is coaxially coupled with the rotor of DM, which serves to distribute the left and right driving torques by the torque vectoring control. It should be noted that PL and PR are not the same type of planetary gearset. PL is a double-pinion planetary gearset, while PR is single-pinion one. The kinematic characteristics of MLTD are analyzed, and the corresponding functionality of lateral torque vectoring is explained as follows. The torque relationship of the driving shaft including M shown in Figure 2a is  
\[T_{m}=T_{ml}+T_{mr} \tag{1}\]  
where \(T_{m}\) is the torque generated by M itself, while \(T_{ml}\) and \(T_{mr}\) are the torque outputs from M to PL and PR, respectively. Figure 1: Schematic configuration of MLTD. The torque relationship of the balance shaft with DM shown in Figure 2b is  
\[T_{dm}=T_{sl}+T_{sr} \tag{2}\]  
where \(T_{dm}\) is the torque generated by M itself, while \(T_{ml}\) and \(T_{mr}\) are the torque inputs from DM to the sun gear of PL and PR, respectively. The torque relationship of PL shown in Figure 3a is  
\[\frac{T_{sl}}{1}=\frac{T_{wl}}{k_{l}^{\prime}+1}=\frac{r_{m}T_{ml}}{k_{l}^{ \prime}} \tag{3}\]  
where \(T_{sl}\) is the torque input from DM to the sun gear of PL, and \(T_{wl}\) is the torque input from WL to the planetary carrier of PL; \(r_{m}\) is the reduction ratio of GM; \(k_{l}^{\prime}\) is the basic ratio of PL, and since PL is a type of double-pinion planetary gearset, it is defined as \(k_{l}^{\prime}=-Z_{rl}/Z_{sl}\), where \(Z_{rl}\) and \(Z_{sl}\) are the number of teeth for the ring gear and planetary carrier of PL, respectively. The torque relationship of the system shown in Figure 3b is  
\[\frac{T_{sr}}{1}=\frac{T_{wr}}{k_{r}+1}=\frac{r_{m}T_{mr}}{k_{r}} \tag{4}\]  
where \(T_{sr}\) is the torque input from DM to the sun gear of PR, and \(T_{wr}\) is the torque input from WR to the planetary carrier of PR; \(k_{r}\) is the basic ratio of PR, and, since PR is a type of single-pinion planetary gearset, it is defined as \(k_{r}=Z_{rr}/Z_{sr}\), where \(Z_{rr}\) and \(Z_{sr}\) are the number of teeth for the ring gear and planetary carrier of PR, respectively. M transmits driving power to PL and PR through a reduction gear (GM) meshed with the ring gears of PL or PR, and thereby  
\[\omega_{m}=\omega_{rl}/r_{m}{=}\omega_{rr}/r_{m} \tag{5}\]  
where \(\omega_{m}\) are the rotational speed of M, while \(\omega_{rl}\) and \(\omega_{rr}\) are the rotation speed of the ring gears of PL and PR, respectively. Figure 3: Torque relationships of PL (**a**) and PR (**b**). Figure 2: Torque relationships of the driving shaft of M (**a**) and the balance shaft of DM (**b**). The rotational speed relation on PL is written as  
\[\omega_{sl}+k_{l}^{\prime}\omega_{rl}-\left(k_{l}^{\prime}+1\right)\omega_{wl}=0 \tag{6}\]  
where \(\omega_{sl}\)\(\omega_{rl}\) are the rotational speed of the sun gear and ring gear of PL, respectively, while \(\omega_{wl}\) is the rotational speed of WL. The rotational speed relation on PR is written as  
\[T_{m}=T_{ml}+T_{mr} \tag{1}\]0  
where \(\omega_{sr}\) and \(\omega_{rr}\) are the rotational speed of the sun gear and ring gear of PR, respectively, while \(r\) is the rotational speed of WR.