## 3 Fea  
FEA is considered to be an accurate method for modelling robot stiffness [62; 63]. Due to multidimensional deformations, additional degrees of freedom (DOFs) are introduced into the robot system. Therefore, the FEA method is used to divide a continuous body with infinite DOFs into a specific number of flexible elements with mass and stiffness characteristics, reducing the problem to a structural problem suitable for numerical solutions. Moreover, based on the invariable mechanical properties, a certain distribution relation can be established for the displacement of the elements, the dynamics equations of the elements can be derived, and the dynamics equation of the robot system can finally be obtained through the element group [80]. A schematic diagram of a robot processed by the FEA method is shown in Figure 3.  
In FEA modelling, the accuracy of the analysis depends on the design of the CAD model, the boundary conditions of the parts, and the parameter settings of the simulation. A specific discussion of these three factors is as follows [31]:  
* A well-designed robot CAD model can improve the accuracy and calculation efficiency of the stiffness model. First, a 3D geometric model of each manipulator is established. Then, the transmission components, such as the bearings, motors, and gears, are removed. Mass units are used to replace the matching in each robot joint. This process simplifies the robot joint fit and reduces the calculation. Additionally, parts and features that have little influence on the stiffness of the robot, such as the pinhole and fillet of the non-bearing parts and rounded corners, are simplified. * The material properties, including the material of the mechanical arm and the type of heat-treatment process, are specific to the CAD model parts of the robot. * The parameter settings of the simulation model affect the complexity, calculation speed, and accuracy of the system modelling. Generally, reasonable mesh cell type, mesh density, and mesh quality settings not only save calculation costs but also maintain calculation accuracy. Starting with a simple beam model and ignoring complex shapes, [PERSON] et al. established a stiffness model of the H4 parallel robot using the FEA method. In good agreement with the experimental measurement, FEA was used as an effective and accurate tool for obtaining the mechanical parameters of the robot [81]. [PERSON] et al. used CAD models of each mechanical leg, added link parts and defined each rotary joint,  
Figure 3: Stiffness identification with FEA [59]: (**a**) CAD model of a link with a complex shape and (**b**) algorithm for the stiffness matrix identification procedure. and then established an FEA model of the parallel platform mechanism T3R1. Based on this model, the static stiffness of the robot was calculated and represented in the whole workspace [82]. [PERSON] et al. introduced a local 6-DOF virtual spring to replace the flexibility of a connecting link and used FEA modelling to determine the high-precision stiffness parameters of the spring. In their experiment, they added auxiliary objects to the CAD model of each link as a reference to evaluate the compliance of the link. In addition, unlike FEA modelling of the entire manipulator, this method only evaluated a single link at a time, which greatly reduced the FEA calculation cost [83]. Furthermore, [PERSON] et al. proposed a method for obtaining the stiffness parameters of the manipulator. Each robot connecting link was modelled using the FEA method. During the modelling process, the CAD model considered six parameters: the shape, cross-section, material distribution, physical properties of the connecting link, specificity of the connecting link joints, and coupling of translational/rotational deflection. In addition, the method reduced the error of FEA modelling. The reason for this is that additional random error was assumed in the \"stiffness transformation\", and the abnormal values of the experimental data were eliminated.