## 3 Design Process of Single Suspension Unit
### Parameters of Compressed Spring  
The compressed spring is designed for the middle suspension unit; however, the given parameters are still valid for the other suspensions. The spring stiffness, \(k\), is determined based on the spring deflection when the freewheel of the middle suspension is in the contact point (situation 2) relative to the compressed spring at its natural length (situation 4). This deflection is calculated by the change in the length of the \(AB\) link, as follows:  
\[\Delta l=l_{A_{0}B_{0}}^{s_{4}}-l_{A_{0}B_{0}}^{s_{2}} \tag{22}\]  
where \(l_{A_{0}B_{0}}^{s_{4}}\) and \(l_{A_{0}B_{0}}^{s_{2}}\) are the lengths \(l_{A_{0}B_{0}}\), with the superscript \(s_{4}\) and \(s_{2}\) respectively stand for situation 4 and situation 2 (shown in Figure 3), of connected point \(A_{0}\). Specifically, \(l_{A_{0}B_{0}}^{s_{4}}\) is calculated by substituting \(j=0\) and \(z_{D_{0}}\) of Equation (3) into Equations (13) and (14). Similarly, \(l_{A_{0}B_{0}}^{s_{2}}\) also is calculated by substituting \(j=0\) and \(z_{D_{0}}\) of Equation (2) into Equations (13) and (14).  
According to [PERSON]'s law, the spring stiffness \(k\) is calculated as:  
\[k=\frac{F_{0}}{\Delta l} \tag{23}\]  
where \(F_{0}\) is the elastic force \(F_{j}\) with \(j=0\).  
The mean coil diameter \(D_{c}\) is determined as follows:  
\[D_{c}=Zd \tag{24}\]  
where \(d\) is the wire diameter, \(Z\) is the preferred value for the spring index. The values of \(d\) and \(Z\) are chosen according to [16]. The number of active coils \(N_{a}\) is determined as follows:  
\[N_{a}=\frac{Gd^{4}}{k8D_{c}^{3}} \tag{25}\]  
where \(G=79.3\) GPa is the shear modulus of steel. The natural length of the spring (\(l_{o}\)) is determined by the sum of the spring length at maximum compression \(L_{\text{min}}\) and its deflection,  
\[l_{o}=\Delta l_{\text{max}}+l_{\text{min}} \tag{26}\]  
where \(l_{\text{min}}=N_{i}d+\epsilon\) with \(N_{i}=N_{a}+2\). Preliminary selection \(\epsilon>0\) is the additional value to compensate for the spring gaps when it is maximally compressed; the value \(\Delta l_{\text{max}}\) is equal to the difference between the length \(l_{A_{0}B_{0}}\) of the middle suspension unit corresponding to situations 3 and 4.  
The adjustment range (\(L\)), as shown in Figure 1, is calculated as follows:  
\[L=l_{AB_{j}}-(l_{o}-\Delta l)-n_{o} \tag{27}\]  
where \(n_{o}>0\) is the natural length of the shock absorber. Specifically, the point \(D_{j}\) coordinates of the suspension units are determined by Equations (19) and (20) combined with Equation (15) to determine the angles \(\gamma_{1,j}\). The value of angles \(\gamma_{1,j}\) are substituted into Equation (11) to calculate the coordinates of all connection points \(B_{j}\) in situation (2). Using Equation (14) with the position of \(B_{j}\) to determine the length of \(l_{AB_{j}}\) links. If this occurs (\(n_{o}\leq 0\) or \(L<0\)), the length of the \(AB\) link is necessary to recompute. Finally, the process of designing the multi-suspension unit is summarized into a flow chart and described in Figure 12. It should be noted that the parameters with blue text format are values that need to be determined or preliminarily selected.