## 5 Finite Element Analysis in ANSYS of the ASPIRE Robot Flexion/Extension Module  
In this section, the results of a finite element analysis in ANSYS for the ASPIRE robot flexion/extension module will be presented. The objectives of this study are as follows:  
* Determine the stress concentrators that occur in the structure;
* Optimize the design by eliminating these stress concentrators. Figure 19: Translational deformations of the centre of mass of the flexion/extension module in relation to the X, Y and Z axes: (**a**) marker attached to flexion extension module mass centre; (**b**) X axis translational deformation; (**c**) Y axis translational deformation; (**d**) Z axis translational deformation. Figure 20: ASPIRE robot total deformation distribution map in two different moments: (**a**) at the moment t = 0.001; (**b**) at the moment t = 0.008 s.  
The steps taken to achieve these goals are described below. The verification of interferences and discontinuities was made (lack of contact between elements for the virtual assembly of the flexion-extension module). The existence of interferences prevents the discretization in finite elements for structural analysis. Discontinuities lead to erroneous results because the connecting forces between the components of the subassembly are no longer transmitted. At the same time, the elimination of stress concentrators was made by making a fillet radius in the area of sharp edges or jumps in diameter between circular sections. The optimized model was transferred to the ANSYS software in order to obtain maps of equivalent stresses based on the finite element method analysis, which represents a modern and very powerful method which is useful for understanding the behavior of the robotic structures, rehabilitation devices and human biomechanics [22; 27; 55]. It is observed that the analyzed element is composed of six distinct parts which are assembled by threaded joints. The combination of all these pieces to obtain a single element (part) with the help of ANSYS Design Modeler is performed. This aspect is shown in Figure 21. The discretization of the whole set of bodies in finite elements (Figure 21) is achieved using a size of the finite element of 2 mm. Additionally, in the areas where filled radius appears, a refinement of discretization was performed by using the option \"mesh refinement\". The next step was to fix the cylindrical surface of the coupling B shaft. The load of the element comes from the contact pressure, which has a value of 0.47 MPa. This results from the dynamic model made in MSC.ADAMS, which appears between the guidance surface and the circular portion. By finite element analysis of the optimized structure (which was obtained by changing the geometry and introducing the fillet radius), equivalent stresses with lower values were obtained compared to those registered at the initial structure, not optimized, when equivalent stresses were 123 MPa. Due to the bending of the circular portions, the contact edge, visible in Figure 22c), produces stress with high values. Filleting these edges reduces the values of these maximum mechanical stresses. The maximum von Mises stress obtained in this case is 64.271 MPa and is recorded at the contact of the joint surfaces. Figure 21: _Cont._  
Figure 21: Discretization in finite elements of the flexion/extension module. Figure 22: Distribution of equivalent stresses in the optimized model of the structure: (**a**) flexion/extension module view; (**b**) upper corner assembly detail; (**c**) lower corner detail view. The maps with the distribution of the displacements recorded along the X and Y axes of the coordinate system are presented in Figure 23. The maximum values recorded are relatively small, at 0.40 mm along the X axis and 0.34 mm along the Y axis, and do not prevent the proper functioning of the module made of aluminum alloy Al 1060. The vertical movement of the module free end reaches 2.6 mm, keeping it within acceptable limits.