# Optimization of a Truss Structure Used to Design of the Manipulator Arm from a Set of Components
## 3 Application
### The Arm as a Truss Structure-Model 1  
The arm body, represented by the block in Figure 3, is replaced by a truss structure. The truss structure was designed to contain only two lengths of components. The proposed structure lies between two flanges, and it can be divided into three equal parts with dimensions of 100 \(\times\) 100 \(\times\) 100 mm, as shown in Figure 4. This determines the first length  
Figure 3: The basic arm structure.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \(E\) & \(\mu\) & \(\sigma^{Y}\) & \(\rho\) \\  & **(MPa)** & **(-)** & **(MPa)** & **(kg/m3)** \\ \hline Steel S355J2 & 210,000 & 0.3 & 355 & 7850 \\ Steel S235J2 & 210,000 & 0.3 & 235 & 7850 \\ Aluminium alloy EN & 70,000 & 0.3 & 120 & 2700 \\ AW 5005 H14 & & & & \\ Aluminium alloy EN & 70,000 & 0.3 & 70 & 2700 \\ AW 1050A H14 & & & & \\ Plastic ABS M30 ([12]) & 1950 & 0.3 & 10 & 1000 \\ \hline \hline \end{tabular} The arm was solved three times:  
* Model 1 is a truss structure with a rod element type. It was used for an optimization;
* Model 2 is a component structure, where the components are simulated by a quadratic shell element. It represents the behavior of the real structure;
* Model 3 is a solid structure designed for additive manufacturing, which used a quadratic solid element [12];  
The rest of this chapter is arranged as follows: Section 3.1 shows the truss structure that replaces the body of the arm. The shape of the components for the construction kit is discussed in Section 3.2. In Section 3.3, a basic set of components is created, and in Section 3.4, the vector of components for optimization is selected. Section 3.5 describes the settings and shows some selected results of the truss structure optimization process. A model based on an optimized truss structure is described in Section 3.6.  
### The Arm as a Truss Structure-Model 1  
The arm body, represented by the block in Figure 3, is replaced by a truss structure. The truss structure was designed to contain only two lengths of components. The proposed structure lies between two flanges, and it can be divided into three equal parts with dimensions of 100 \(\times\) 100 \(\times\) 100 mm, as shown in Figure 4. This determines the first length of the components (100 mm), while the second length is given by the diagonal. The truss structure has 44 rods with 16 connection points. The rod numbers are also shown in Figure 4.  
The intersecting rods on the structure sides are not connected. There are two types of rod: a side rod and a corner rod. The flanges are designed from sheet metal of 2 mm thickness (material S355)2, see Table 3), and their boundaries are bent perpendicular with a length of 10 mm. The total weight of both flanges is 0.439 kg. The flange mesh is created from the shell element type with size 10 \(\times\) 10 mm, and the truss structure is from the a rod element type [16]. The boundary conditions are shown in Figure 3.  
The type of component connection (it can be screw, riveted joints or welded joints) is not analyzed here. Therefore, it is assumed that all connections behave perfectly and are suitable in terms of strength. The joints also increase the overall weight of the structure, but this effect is neglected.