## 2 Design of the System
### Mechanical and Control Design  
As a first step, the geometries of the optical elements were designed. These components were fixed to the sides (only). Furthermore, the design was affected by the weight of the fluid and the solid casing. Considering these parameters, the maximum possible length was determined. In this case, the safety factor (relation between the load that a system can withstand before failure to the actual applied load) was not the most critical parameter, since small deformations may have led to optical aberrations, and defocusing that would reduce optical efficiency. For this reason, the maximum allowable deformation (bending) was limited to 3 mm for achieving a satisfactory concentrated spot based on the optical-simulation results. For deformations above 3 mm, the optical performance begins to be negatively affected. Figure 4 illustrates the maximum deformation as a function of concentrator length (the length ranges from 1 to 4 m). It can be seen that the maximum length of the concentrator should not exceed 2.5 m (in this case, the deformation was 3 mm).  
The present study was conducted considering an assembly comprising concentrating elements whose numbers ranged from 8 to 32. Figure 5 shows the 8-element configuration (Figure 5a), the displacement with respect to the initial position (Figure 5b) and details of the connecting rods, the lateral covering of the optical element and the supporting axle with a block piece to avoid displacement of the connecting rods along the length of the axle (Figure 5c). The diameter of the axle was found to be critical in terms of concentrator bending, being necessary to maintain a diameter of 2 cm in order to obtain a maximum displacement of 3 mm. The thicknesses of the connecting rods ranged from 2 to 4 mm, depending on the number of concentrating elements. In both cases (connecting rods; axle), standard stainless steel was used.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(V_{\text{oc}}\) (V) & \(J_{\text{sc}}\) (mA/cm\({}^{2}\)) & \(FF\) (\%) & \(\eta\) (\%) & \(\gamma\) (\%/\({}^{\circ}\)C) \\ \hline
0.662 & 40.11 & 79.85 & 21.1 & \(-\)0.375 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of the PV cells [38].  
Figure 4: Maximum displacement (bending) and safety factor as a function of the module/ concentrator length.  
As a first step, the dimensions were determined based upon the mechanical study. As a second step, the drivers to achieve solar altitude tracking were designed and incorporated into the model. Two types of mechanisms were necessary. The first one was a mechanical spindle system that controlled the distance between the subunits of the collector (subunits = the individual concentrating elements) using a \"scissor\" configuration. The second one was a system that drove the rotation of the modules so that their aperture plane tracked apparent solar altitude movement, using a linear actuator and a pivot. Both mechanisms were automatically guided by a comparator based on two photoresistors and a shading element that continuously acquired values required by an Arduino Mega(r) device. The system adequately focused sunlight when the two photoresistor signals were equal; otherwise, the shading element resulted in two signals that were different. The control programme had one loop (the first one) based on astronomical ephemeris (clock on the Arduino board) and another loop (the second one = precision loop) associated with the comparison of the analogue readings of the photoresistors. The control programme also included some loops that allowed manual control of the motors that drove the mechanisms.  
For this study, and due to practicality in construction and suitability for testing, the prototype included 8 concentrating elements, each 1 m long. Under these conditions, the mechanical features were less restrictive (taking into account the limitations related to the maximum bending of 3 mm) and the requirements could be fulfilled with a 2 mm thick connecting-rod and an axle with a diameter of 8 mm.