## 2 Materials and Methods
### Boundary Conditions  
#### 2.1.1 Case 1  
Numerical analysis was performed using LS-Dyna(r) software, attaching each of the springs and dampers of the system, which were established based on commercial catalogs [17,18] mentioned in Table 1, a rail (T) that allows the displacement of the mass concentrators (M\({}_{1}\) and M\({}_{2}\)), and the bearing on which the CRS is mounted (C) on the \(x\)-axis. In addition, the rail would be fixed to the bearings (J\({}_{1}\) and J\({}_{2}\)), which allow movement along  
Figure 1: Mechanical coupling.  
Figure 2: Distribution of springs and dampers in mechanical coupling, (**a**) Top view (**b**) frontal view.  
the \(y\)-axis (Figure 2). Bearing C has a mass of 30 kg, equivalent to 6.6 kg of the CRS plus 23.4 kg of the Hybrid III 6-year-old infant numerical model.  
Subsequently, parts were entered into the HyperMesh(r) V.14.0 (Troy, MI, USA) software to perform the discretization of each, with hexahedral elements (8 nodes) of 4 mm, as shown in Figure 3.  
For the Cartesian mechanism box, suspension box, J\({}_{1}\), J\({}_{2}\), C, and T, the mechanical properties are set as: aluminum 1100-H14 density of 2.71 \(\times\) 10\({}^{-6}\) kg/mm\({}^{3}\), [PERSON]'s modulus of 70 GPa, an elastic limit of 0.095 GPa, and Poisson's ratio of 0.33 [19]. For M\({}_{1}\) and M\({}_{2}\), properties are those of A36 structural steel: density of 7.85 \(\times\) 10\({}^{-6}\) kg/mm\({}^{3}\), Young's modulus of 200 GPa, an elastic limit of 0.25 GPa, and Poisson's ratio of 0.32 [20]. The initial system speed is 13.34 m/s on the \(+x\) and \(+y\)-axes. The deceleration peak in the \(-\)x and \(-\)y directions are taken from the FMVSS 213 regulation for frontal impact (Figure 4) [21]. The same peak is used in both directions to obtain values on its performance under critical situations. The suspension box decelerates, as is shown in Figure 4. Its movement on the \(z\)-axis is restricted to simulate that its placement on the vehicle's rear seat with ISOFIX anchorage. Additionally, a translational joint from the suspension box to the Cartesian mechanism box was implemented. In this way, the Cartesian mechanism box will move along the \(z\)-axis concerning the suspension box. Gravity acts on the axis \(-z\) with a constant value of 0.00981 mm/ms\({}^{2}\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Device** & **ID** & **Value** & **Length (mm)** \\ \hline \multirow{4}{*}{Dampers (kN ms)/mm} & \(\text{A}_{\text{X1}}\), \(\text{A}_{\text{X2}}\), \(\text{A}_{\text{X3}}\), \(\text{A}_{\text{X4}}\) & 0.015 & 150 \\  & \(\text{A}_{\text{Y1}}\), \(\text{A}_{\text{Y2}}\) & 0.015 & 100 \\  & \(\text{A}_{\text{Y3}}\), \(\text{A}_{\text{Y4}}\) & 0.015 & 150 \\  & \(\text{A}_{\text{Z1}}\), \(\text{A}_{\text{Z2}}\) & 0.04 & 250 \\ \hline \multirow{4}{*}{Springs \(\text{kN/mm}\)} & \(\text{R}_{\text{X1}}\), \(\text{R}_{\text{X2}}\), \(\text{R}_{\text{X3}}\), \(\text{R}_{\text{X4}}\), \(\text{R}_{\text{X5}}\), \(\text{R}_{\text{X6}}\), \(\text{R}_{\text{X7}}\), \(\text{R}_{\text{X8}}\)} & \(1\times 10^{-5}\) & 50 \\  & \(\text{R}_{\text{Y1}}\), \(\text{R}_{\text{Y2}}\) & \(1.5\times 10^{-5}\) & 100 \\  & \(\text{R}_{\text{Y3}}\), \(\text{R}_{\text{Y4}}\) & \(1.5\times 10^{-5}\) & 150 \\  & \(\text{R}_{\text{Z1}}\), \(\text{R}_{\text{Z2}}\) & \(8\times 10^{-5}\) & 275 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Constants and dimensions of springs and dampers belonging to the mechanical coupling.  
Figure 3: Meshing with 4 mm hexahedra (8 nodes) elements.