# Dimensional Synthesis for Multi-Linkage Robots Based on a Niched Pareto Genetic Algorithm
## 5 Engineering Example of the Method Application and Analysis
### Method Application in Salt Industry  
Solar salt is the process of making salt from seawater, including moisture absorption, halogen generation, crystallization, and other processes. The salt-making process of seawater is generally stored in the evaporation pond for 7-15 days. According to the influence from weather, brine concentration, and other external factors, occlusion of the solar salt evaporation pool is necessary, it has great significance for improving the solar salt efficiency. Without manual retracting and retracting, the shielding cloth (as shown in Figure 8) will get off the track and become entangled, affecting the evaporation of the salt field. At present, the occlusion cloth is put in with the help of human, as shown in Figure 8 Due to the large number of evaporation pools, so it is very labor-intensive, time-consuming, and also less efficient.  
As shown in Figure 9, a 2R linkage robot is designed instead of manually retracting or releasing of the shielding cloth. The two-lever robot actuator can clamp the blocking cloth to ensure the smooth rolling and releasing of the blocking cloth in the salt field, so as to save labor and improve the rolling and releasing efficiency of the blocking cloth in multiple evaporation pools in the salt field.  
Figure 8: Human assistance.  
In Table 1, dimensional parameters, we take \(l_{1}=12.0000\), \(l_{2}=16.0000\), \(\theta_{1}\in[0,36^{\circ}]\), \(\theta_{2}\in[0,120^{\circ}]\) after radian convert to angles.  
The design solution is based on NPGA method. For the calculation model constructed in this paper, the population size is set as 100 and the chromosome length is set as 32 bits in binary order to obtain the global optimal solution quickly based on experience. The choice of crossover operator affects whether it can converge to the optimal solution region, so the crossover operator is 0.08. If the mutation operator is selected larger, on the one hand, increasing the diversity of samples can also cause instability. On the other hand, if the selection is small, it can be difficult to find the global optimal solution. Thus, mutation operator is set to select 0.65, termination of algebra for 100 generations, and the result is shown in Figure 10. According to the data, the convergence is good, the global Pareto solution is set, some data are shown in Table 2.  
In Table 2, for dimensional parameters, we take \(l_{1}=11.0000\), \(l_{2}=17.0000\), \(\theta_{1}\in[0,33^{\circ}]\), \(\theta_{2}\in[0,117^{\circ}]\) after radian convert to angles.  
It can be seen from the data comparison in Table 3 that the multi-linkage robot is used to assist the rolling and releasing of the shielding cloth. From the rolling and releasing process of 3-6 times per day, it takes time 6'12\" for each evaporation pool under the KPCA method. While for the NPGA method, it takes time 5'26\". Only one evaporation pool saves 12.37% the rolling and releasing time, which improves the rolling and releasing efficiency of the evaporation pool shielding cloth in the salt making process. The energy consumption of multi-linkage robot was estimated from the change of joint angle, and the NPGA method reduced the energy consumption by about 3.85% compared with the KPCA method.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Links** & \(l_{1}(\text{cm})\) & \(l_{2}(\text{cm})\) & \(\theta_{1}(\text{rad})\) & \(\theta_{2}(\text{rad})\) \\ \hline Team1 & 12.1661 & 15.8215 & 0.5923 & 2.0844 \\ Team2 & 11.9238 & 16.0003 & 0.6235 & 2.0936 \\ Team3 & 11.9806 & 16.1216 & 0.6345 & 1.9962 \\ Team4 & 12.0201 & 15.9944 & 0.5812 & 1.8796 \\ Team5 & 11.0569 & 16.1725 & 0.5771 & 1.9236 \\ Team6 & 11.9754 & 16.0258 & 0.6121 & 2.0612 \\ Team7 & 11.8962 & 16.3501 & 0.5956 & 2.1003 \\ Team8 & 12.0821 & 15.9812 & 0.6135 & 2.0732 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Partial data table of two-link dimensional synthesis (NPGA).  
Figure 9: Robot assistance.