## 7 Results  
The obtained values of the geometric parameters for the final optimization solution are given in Table 6. This is the obtained optimal solution for the values which are adopted and shown in Table 3 and for the chosen implementation of the fitness function (Equation (47)). It should be noted that optimization settings and fitness function implementation can be easily adapted for other applications. This paper's primary result is an algorithm capable of designing mechanisms with sufficient characteristics for flight simulation, taking into account all imposed constraints. Starting from values of geometric parameters that are generated based on a random uniform distribution with integer values within lower and upper bounds (later mapped to real values of geometric parameters), the algorithm has obtained a solution that can be manufactured and used for flight simulation. Termination of optimization occurred because the max stall generation stopping criterion was reached. As shown in Figure 14, optimization stopped before reaching 600 generations, with the best penalty value of 52.842. Optimization found a solution that satisfies all constraints after five generations and reached a penalty value of 55 after the first 100 generations. The kinematic model of optimized mechanism geometry is shown in Figure 15, and it is verified that this geometry of the mechanism has values of performance indicators the same as they are calculated within the optimization process. Figures 11 and 13 show the workspace for this particular set of geometric parameters. Optimization began without any assumption or known solution. In the first generation, values of geometric parameters for each individual of the population are generated using a random uniform distribution. In the first five generations, none of the 5000 individuals in the population satisfied implemented nonlinear constraints. In the sixth generation, the first individuals satisfied all constraints and obtained the penalty value as a result of the evaluation of the fitness function. This search for individuals capable of satisfying all constraints is possible thanks to the implementation of crossover and mutation functions. Later these functions, together with elitism and selection, enabled convergence towards the final result, as shown in Figure 14. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(a\) & 250 mm \\ \(s\) & 1000 mm \\ \(R_{p}\) & 490 mm \\ \(R_{b}\) & 700 mm \\ \(\gamma_{P}\) & 44\({}^{\circ}\) \\ \(\gamma_{b}\) & 25\({}^{\circ}\) \\ \(\varepsilon\) & 39\({}^{\circ}\) \\ \(\tau_{ll}\) & 19\({}^{\circ}\) \\ \(\tau_{jp}\) & \(-\)81\({}^{\circ}\) \\ \(\mu_{ll}\) & \(-\)31\({}^{\circ}\) \\ \(\mu_{l|p}\) & 14\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values of geometric parameters for the final solution. \begin{table}
\begin{tabular}{c c} \hline \hline
**Criterion** & **Value** \\ \hline Max generations & 1000 \\ Max stall generations & 200 \\ Max time & 12 h \\ Max stall time & 1 h \\ Desired fitness function value & 0 \\ Fitness function value tolerance & 10\({}^{-9}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Settings for stopping criteria of optimization. Figure 16a shows the maximum required actuator torque in the \(O_{xy}\) plane when all other external coordinates have zero value. Figure 16b shows the value of the dexterity indicator in the same plane. Figure 17a,b shows maximal reachable values of pitch and roll angles in the \(O_{xy}\) plane when all other external coordinates have zero value. As expected, the mechanism has the best performance near the home position, and its capabilities are reduced by changing the value of any external coordinate. The following two tables (Tables 7 and 8) show maximal and minimal values of each external coordinate. These values are maximal and minimal values of the particular external coordinate that the platform can reach (a solution of inverse kinematics exists).