## 3 Kinetostatic Modeling and FEA
### Sensitivity Analysis: Geometric Positions and Beam Width  
In the design variables mentioned above, the geometric positions of the displacement reducer are given in the form of coordinates. The performance indicators of the displacement reducer are calculated using the analytical model presented in Section 3. Subsequently, the impact of different length and thickness parameters, as well as their relative coordinates, on the reduction ratio and output stiffness is discussed.  
Figure 5: Mesh generation of the structure.  
Figure 6: Comparison of the predicted results between the kinetostatic model and FEA: (**a**) Input and output displacements; (**b**) The input displacement and the input force.  
Figure 7: Analysis results in ANSYS: (**a**) Stress distribution results in ANSYS; (**b**) Deformation results in ANSYS.  
The effects of the variation in parameters of the displacement reducer within the specified range are shown in Figures 8 and 9. In the figures, \(x_{i}\) represents the horizontal coordinate variation of point \(i\), \(y_{i}\) represents the vertical coordinate variation, and \(x_{ij}\) and \(y_{ij}\) represent the relative position variations between points \(i\) and \(D\), where \(i,j=A,B,C,D,E,F,G,H\). Figure 8 shows that, as the horizontal distance between points \(A\), \(B\), and \(F\) increases, the reduction ratio of the displacement reducer gradually decreases, with similar variations. However, increasing the horizontal distance between points \(C,G,F\) and \(H\) leads to an increase in the reduction ratio. Among these, the change at point \(G\) has the most significant impact on the structure, causing the reduction ratio to first increase and then decrease. The reduction ratio reaches its maximum when \(x_{D}=-32\). Furthermore, increasing the relative distance between points \(C\) and \(D\) also results in an increase in the reduction ratio.  
As shown in Figure 9, the vertical direction changes for each point do not significantly impact the displacement reducer. Only point \(b\) leads to a substantial increase in the reduction ratio. Similarly, changes in the relative position between points \(A\) and \(B\) also have a significant effect on the mechanism.  
Figure 10 shows the sensitivity of the displacement reducer to different structural parameters. Figure 10a illustrates the impact of the coordinates of each point on the output characteristics of the displacement reducer. It can be seen that the displacement reducer is significantly affected by the geometric position changes of the structure, with the variation in the x\(-\)direction having a greater impact than the variation in the y\(-\)direction. Similarly, as shown in Figure 10b, the length of the beam also has a substantial effect on the reduction ratio of the structure, especially the changes in \(Beam-BE\) and \(Beam-HE\), which result in nearly 80%.  
Figure 8: Analysis of the influence of different points in the x\(-\)coordinates on the reduction ratio: (**a**) point \(A\), (**b**) point \(B\), (**c**) point \(C\), (**d**) point \(D\), (**e**) point \(F\), (**f**) point \(G\), (**g**) point \(H\), (**h**) the relative position of points \(C\) and \(D\).