# Simulation-Based Reliability Design Optimization Method for Industrial Robot Structural Design
## 3 Demonstrative Example  
### Simulation Model of a Mechanical Arm  
The ANSYS software was used to perform a static structural analysis. Taking an industrial robot with a load weight of 6 Kg as the object, the reliability design optimization of its big arm and small arm was carried out by using the proposed method. The structure of the mechanical arms is shown in Figure 4.  
When the finite element analysis model was established, the body mesh method was employed in order to measure more precise values during the mesh analysis. The three-node triangular element was chosen as the element type, and the element size was set to 2 mm. For the big arm, the number of nodes was 108,657 and the number of element was 58,479, while for the small arm, the number of node was 87,781 and the number of element was 50,160. The mesh analysis of the big arm and the small arm is shown in Figures 5 and 6.  
Figure 4: Structure of the mechanical arms.  
Figure 5: Finite element analysis model of the big arm.  
The limit state (that is, the horizontal position) was considered to finish the simulation analysis, and the force analysis of the mechanical arm is shown in Figure 7. In Figure 7, \(G_{arm1}\) and \(G_{arm2}\) represent the gravity of the big arm and the small arm, respectively. \(G_{drive}\) and \(G_{arrist}\) represent the motor gravity and wrist gravity of the big arm and the small arm, respectively. \(F_{max}\) is the maximum load that the robot arm can lift. According to the force analysis and to Ref. [9], the loads and constraints of the mechanical arms could be applied as shown in Figure 8. In Figures 7 and 8, A, B and C represent the joins of the robotic arms, and the details are as follows: A represents joint of first and second links, B represents joint of second and third links, C represents joint of third and fourth links.  
For the big arm, the full constraints were applied to the end A, while the force \(F_{1}\) and the moment \(M_{1}\) were applied to the end B. For the small arm, the full constraints were applied to the end B, while the force \(F_{2}\) and the moment \(M_{2}\) were applied to the end C. The force and the moment can be calculated by  
\[\begin{array}{l}F_{1}=G_{arm2}+G_{wrist}+F_{\max}\\ M_{1}=G_{arm2}L_{3}+G_{wrist}(L_{3}+L_{4})+F_{\max}(L_{3}+L_{4}+L_{5})\\ F_{2}=G_{wrist}+F_{\max}\\ M_{2}=G_{wrist}(L_{3}+L_{4})+F_{\max}(L_{3}+L_{4}+L_{5})\end{array} \tag{6}\]  
The material properties and loads are listed in Table 1, and the stress and deformation distribution on the big arm and the small arm are shown in Figures 9 and 10.  
Figure 8: Application of loads and constraints.  
Figure 6: Finite element analysis model of the small arm.  
Figure 7: Force analysis.  
It can be seen in Figures 8 and 9 that, in the current design, the maximum stress on the big arm was 8.1465 MPa, and the maximum deformation was 0.056077 mm, whereas the maximum stress on the small arm was 7.0092 MPa, and the maximum deformation was 0.12715 mm.  
The 3D parameter simulation models of the big arm and the small arm above-mentioned were established by the parameter design language of ANSYS (APDL). The APDL command of the full simulation process contains geometric modeling, mesh generation, material property settings, load and constraint imposition and simulation solution settings. The APDL command was used to complete the simulation of the different samples in order to obtain the performance function of the reliability design optimization model.