## 2 Architecture and Kinematic Characteristics of MLTD
Since DM is directly coupled with the sun gears of PL and PR, the rotational speed of DM is expressed as  
\[T_{m}=T_{ml}+T_{mr} \tag{1}\]1  
when MLTD is operated at normal drive in a straight ahead direction with torque vectoring function off, also termed as neutral, all the related torque value is denoted with a superscript '\(\circ\)'. In this situation, it is required that \(T_{wl}^{\circ}=T_{wr}^{\circ}\) and \(T_{dm}^{\circ}=0\). Substituting \(T_{dm}^{\circ}=0\) into Equation (2), it becomes  
\[T_{m}=T_{ml}+T_{mr} \tag{1}\]2  
Furthermore, substituting \(T_{wl}^{\circ}=T_{wr}^{\circ}\) into Equations (3) and (4), it is found that  
\[T_{m}=T_{ml}+T_{mr} \tag{1}\]3  
From Equations (9) and (10), the following kinematic relation can be attained:  
\[T_{m}=T_{ml}+T_{mr} \tag{1}\]4  
Now replacing \(k_{l}^{\prime}\) by \(-(k_{r}+2)\), it follows that  
\[T_{m}=T_{ml}+T_{mr} \tag{1}\]5  
Then, to check whether MTLD possesses the functionality of differential or not, the deduction of the rotational relationships from Equations (5) to (8) yields  
\[T_{m}=T_{ml}+T_{mr} \tag{1}\]6  
\[T_{m}=T_{ml}+T_{mr} \tag{1}\]7  
Equation (13) can be illustrated as a nomograph of rotational speeds shown in Figure 4, verifying that differences in the rotational speeds between WL and WR are allowed for a given rotational speed of M; that is, the functionality of differential can be fulfilled for MLTD. Furthermore, according to Equation (14), the balance shaft as well as DM cannot remain stationary when either driving straight or turning. If driving straight, all the related value of rotational speed is denoted with a superscript '\(\circ\)' as well. Substituting \(\omega_{wl}^{\circ}=\omega_{wr}^{\circ}\) into Equations (13) and (14), it follows that \(\omega_{wl}^{\circ}=\omega_{wr}^{\circ}=\omega_{sl}^{\circ}=\omega_{sr}^{ \circ}=\omega_{m}^{\circ}/r_{m}\)= \(\omega_{dm}^{\circ}\). Therefore, it can be seen that both PI and PR rotate like a rigid body in straight driving condition. If the torque vectoring function is activated, i.e., \(T_{dm}\
eq 0\), it follows that  
\[T_{m}=T_{ml}+T_{mr} \tag{1}\]8\[T_{m}=T_{ml}+T_{mr} \tag{1}\]9  
Adding up Equations (15) and (16) gives  
Figure 1:0  
Accordingly, applying the torque of DM will change the total driving torque. Hence, in order to maintain constant driving torque at torque vectoring mode, the tractive torque of M with torque vectoring, termed as \(T_{m}^{\prime}\), must be adjusted according to how much \(T_{dm}\) is applied, as indicated below:  
Figure 1:1  
For the purpose of quantifying the degree of lateral torque vectoring, a parameter called lateral torque vectoring ratio, \(\zeta_{lr}\), is defined as below:  
Figure 1:2  
According to this definition, \(\zeta_{lr}=1\) and \(-1\) indicate that the total driving torque is entirely transmitted to the right wheel and left wheel, respectively, while, \(\zeta_{lr}=0\) means that the total driving torque is evenly distributed to the right wheel and left wheel, i.e., in neutral mode. Substituting Equations (12), (15), and (16) into Equation (19), \(\zeta_{lr}\) can be expressed as a function of \(T_{dm}\) and \(T_{m}^{\circ}\), i.e.,  
Figure 1:3  
Figure 5 visualizes the relations of \(\zeta_{lr}\) vs. \(T_{dm}\) given by Equation (20). Accordingly, DM operating in motor mode, i.e., \(T_{dm}>0\), results in the driving torque of WR increasing and that of WL decreasing, i.e., \(\zeta_{lr}>0\). This provides a yawing moment suitable for turning left. On the contrary, DM exerting generative load in generator mode, i.e., \(T_{dm}<0\), leads to the condition that the driving torque of WL increases and that of WR decreases, i.e., \(\zeta_{lr}<0\). This gives a yawing moment beneficial to turning right. Figure 1:4 Rotational speed nomograph for WL, WR, and M.