# Optimization of a Truss Structure Used to Design of the Manipulator Arm from a Set of Components
## 5 Discussion  
The main optimization criterion used in the task was the weight minimization in Equation (1), but this complicates the optimization when using different materials with the same density, for example, steels with different yield strengths (see Table 3). This leads to a significant reduction in the number of components in **C** (Figure 9). A possible solution to the problem are weight coefficients adjusting the densities of individual materials, e.g., in terms of the material price and their application to the objective function. Component design is one of the most important and time-consuming parts of the present process. In Section 3.5, two sets of components were proposed for optimization. The components in \(\textbf{C}_{A}\) have a higher load capacity at the same weight, whereas for \(\textbf{C}_{B}\), a lower price would be achieved with a higher arm weight. At the point of connection of several L-profiles on the walls of the arm, the components overlap. This can be solved by modifying the geometry of the L components (e.g., the size of the holes) or by designing special (side rod) components. A comparison of the results of Model 1 and Model 2 (see Tables 5 and 7, respectively) shows a significant increase in the stress values compared to the yield stress. Critical forces in the buckling analysis were also unfavorable (see Appendix D and Table 6). This is probably due to the bending moment in the connection points in Model 2. The loading forces of the L/F-profiles on the sides of the arm do not lie in the neutral axis of the profile. The offset is determined by the shape of the profile and the thicknesses of the components, and it can be different for each connection point. Because the structure was dimensioned by yield stresses, the use of a safety factor would eliminate the problem. Another option is to design special (side rod) components. The main results of Model 1, Model 2 and Model 3 are shown in Table 9. In the following paragraphs, the results are discussed in more detail. The main goal of the optimization was to minimize the weight, which is significantly lower in Model 2 than in Model 3. From this, we conclude that the method is applicable for optimizing this component system. However, the weight does not include fasteners (screws, rivets), so the actual weight of the resulting structure will be higher. Flanges are also part of the arm. With the component system, the flanges can be easily replaced and the screws available for installation, see Figure 3. For Model 3 and Flange 2, there may be a problem with mounting the screws, see Figure 14. When using HELICOIL(r) inserts, for example, the flanges would have to be much more massive (with a higher weight). In addition, the arm is manufactured with flanges, which cannot be changed afterwards. The maximum displacement value is also 1 mm lower in Model 2 compared to Model 3. Displacements are one of the key criteria for manipulators, and the component approach came out much better when compared. On the other hand, this value may be affected by the fasteners used, such as the screws that we assume for a given component system. The \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Model 1** & **Model 2** & **Model 3** \\ \hline Weight of the optimized & & & \\ structure (kg) & 0.284 & 0.262 & 0.673 \\ Weight of the flanges (kg) & 0.439 & 0.5 & 0.2 \\ Max. displacement (mm) & 1.84 & 1.44 & 2.7 \\ \(\sigma^{EQV}\) (MPa) & 162 & 508 & 10.8 \\
1 st natural frequency (Hz) & - & 239 & 140 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Results for the three models of the arm. clearances between the screws and the holes can cause the real values to differ more from the simulated ones. The values of the equivalent stress in both cases exceeded the value of the yield strength. For Model 3, critical areas can be eliminated by further smoothing, rounding, etc., with a minimal effect on the final weight. For Model 2, it is necessary to strengthen the components, i.e., to use a the other component in \(\mathbf{C}\).