## 2 Theoretical Background
To describe the altitude of the freewheels, a coordinate system named \(Oxz\) is assigned at the center of the primary timing pulley. Let the curve \(\Delta\) represent the deformed profile of PV panels under the weight of SPCRs in the \(Oxz\) coordinate, defined as a polynomial function with the \(n^{th}\) degree as follows:  
\[z_{d}(\triangleq f(x))=a_{n}x^{n}+\ldots+a_{1}x+a_{0} \tag{1}\]  
Figure 4: Multi-contact points between track-wheeled and deformed PV panel. Figure 3: SPCR movement situations. Figure 2: Kinematic diagram and 3D CAD model of a single suspension unit: (**a**) kinematic diagram; (**b**) 3D CAD model. where \(z_{d}\) represents the deformation of PV panels, while \(x\) denotes the position along the center line of the PV panel in the \(Oxz\) coordinate. The coefficients of the polynomial, \(a_{0},a_{1},\ldots,a_{n}\), are determined through least squares interpolation using experimental or simulation data. The degree of the polynomial depends on the level of correlation between the actual data and the fitting curve. Furthermore, it can be seen from Figure 4 that the curve \(\Delta\) passes through all contact points \(G_{i}\), disregarding the PU timing belt thickness. Figure 5 illustrates the altitude of the freewheels corresponding to situations 3 and 4. When the SPCR crosses the gap, the freewheel attains the lowest altitude, corresponding to the natural length of the compressed spring, as shown in Figure 5a. Conversely, when the freewheel passes over a mounting clamp, it reaches the highest altitude, resulting in the shortest length of the compressed spring, as shown in Figure 5b. Let \(h_{1}\) represent the lower maximum displacement of the contact point \(G_{0}\) from its basis position, while \(h_{1}\) represents the upper maximum displacement of the contact point \(G_{0}\) from its basis position. These \(h_{1}\) and \(h_{2}\) values determine the working area of the suspensions, thus influencing the design process of the shock absorber. The value \(h_{1}\) is determined to ensure that when the SPCR passes over the gap between two adjacent PV panels the center of the freewheel remains higher than the surface of the next PV panel, allowing for a successful recovery of the freewheel, as shown in Figure 6a. On the contrary, if \(h_{1}\) is inadequate, the freewheel might fail or get damaged during the crossing, as illustrated in Figure 6b. Similarly, determining the value of \(h_{2}\) depends on the installation structure of the PV panel array, as it is directly related to the height of obstacles such as mid-clamps, end-clamps, and end-caps. However, a higher \(h_{2}\) value results in a longer travel distance for the shock absorber. Table 2 presents the parameters of the single suspension unit that have been determined and obtained during the design process. Several factors were considered in this process, including the weight of the SPCR (\(m\)), the radius of the freewheel (\(r\)), the radius of the timing pulley (\(R\)), the distance between the centers of the two timing pulleys (\(l_{w}\)), and the tilt angle of PV panels relative to the ground (\(\alpha\)). The symbols \(A_{j}\), \(B_{j}\), \(C_{j}\), and \(D_{j}\) represent the connected points of the \(j\)-index suspension unit, as described in Figure 2.  
Figure 5: Displacement of the freewheel in situations: (**a**) The lowest altitudes; (**b**) the highest altitudes. Figure 6: Displacement of the freewheel in situations: (**a**) The lowest altitudes; (**b**) the highest altitudes. For the sake of simplicity, the following assumptions are necessary for the design process. 1. As the SPCR passes over the center point of the PV panels, it induces the largest deflection at this point. Therefore, we assume that the contact point \(G_{0}\) coincides with this point, defined as the lowest altitude of \(G_{0}\) in situation 2, without loss of generality;
2. The structural parameters of the suspensions are assumed to be the same, so the design process of the middle suspension unit can be applied to the others.