# Optimization of a Truss Structure Used to Design of the Manipulator Arm from a Set of Components
## 3 Application
### Application of Components to the Truss Structure-Model 2  
In Model 2, the truss structure is replaced by a set of components, and the components are designed according to the solution given in Table 5. During the preparation of this model, the following were performed:  
* The flange dimensions were corrected to 110 \(\times\) 110 mm with the holes for component connection were 100 mm apart. Roundings were added at the edges (2 mm). Holes (4 mm) for connecting the components and flanges were added. * The profile for the side rods was selected based on the results of a linear buckling analysis (LBA). The F-profile of the component was used for the tensile-loaded side rods. The L-profile of the component was used for pressure-loaded side rods, where the value of the critical force was less than the value of the loading force of the rod. In others, the F-profile was also used (see Appendix D, F/L profiles). The boundary conditions for the solution of the critical forces are shown in Figure 10, where \(F=1\) N. The values of critical force \(F^{Buck}\) for all profiles and two lengths are given in Table 6.  
Figure 10: Boundary conditions for estimating critical forces for I and L profiles. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & **Member No.** & \(\sigma^{Max}\) & \(\sigma^{Min}\) \\  & & **(MPa)** & **(MPa)** \\ \hline \(C_{1}\) & & & \\ \(C_{2}\) & 5,6,7,8,11,12 & 135 & 98 \\ \(C_{3}\) & 9,10,13,14,32 & 162 & 72 \\ \(C_{4}\) & 4,15,16,28,29,31,33,39 & 49 & 10 \\ \(C_{5}\) & 1,2,3,17,18,19,20,21,22,23,24,25,26, & 51 & 1 \\  & 27,30,34,35,36,37,38,40,41,A2,43,44 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The optimized design for Model 2. Two types of simulations were performed with Model 2:  
* Nonlinear static structural analysis where geometrical non-linearities were activated and full Newton-Raphson solution procedure and default convergence criteria (Force, Moment, Displacement) was used. The simulation took place in twenty loadsteps. After the analysis, it was found that some components of the F-profile loaded with pressure undergo a significant change in shape. These were replaced by L profiles (see Appendix D, where they are marked *). * Modal analysis (Block Lanczos mode extraction method was used). A description of the above methods can be found in [16]. Flanges and areas where components are interconnected were excluded from the evaluation. The equivalent stress Equation (A4) of the components is shown in Table 7. The maximum value of the stress \(\sigma^{EQV,Max}\) was searched for at a sufficient distance from the joints. The maximum displacement of the flange 2 is 1.5 mm, and the first natural frequency is 239 Hz (see Figure 13). The values of equivalent stresses often exceeded the permissible values. We believe that this is due to the additional bending that occurs in the resulting structure due to respecting the thickness of the sheet metals. The correction used, see Section 3.3.5, only takes into account the effect of the holes. This effect could be simulated using beam type elements. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & \(\sigma^{EQV,Max}\) & \(\sigma^{Y,j}\) \\  & **(MPa)** & **(MPa)** \\ \hline \(C_{1}\) & & \\ \(C_{2}\) & 481 & 355 \\ \(C_{3}\) & 508 & 355 \\ \(C_{4}\) & 200 & 120 \\ \(C_{5}\) & 142 & 120 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The results for components from the Set 1. Figure 12: Results for Model 2, with components \(C_{4}\) and \(C_{5}\). Figure 13 shows the first natural shape, which is mainly located in the longer F profiles of the component \(C_{5}\) (see Figure 12). Figure 13 also shows the effect of the fixed flange (the left flange is fixed, see Figure 3), and with increasing distance from the flange, the'size of natural shapes' also increases. The position of components on the arm is not uniform, see Figure 11\(C_{3}\) and Figure 12\(C_{4}\).