## 5 Experimentation  
Using the final design results obtained from Section 4, an experimental model of the displacement reducer was fabricated using additive manufacturing technology. The final reducer is shown in Figure 18a. The experimental setup is shown in Figure 18b. In the experimental tests, the FSL40 ball-screw sliding table (Chengdu Fuyu Technology Co., Ltd., Chengdu, China) is used as the actuator for the mechanism to generate input force and displacement. The sliding table provides a continuous thrust of 200 N, with an effective stroke range of 0-500 mm and a repeatability accuracy of 0.05 mm. A laser interferometer (IDS3005, Attocube, Munich, Germany), with a resolution of 1 pm, is employed to measure the displacement of the output mechanism. The force sensor used is the SF-50 digital push-pull force gauge (Airuipu Technology Co., Ltd., Quzhou, China), with a maximum measurement capacity of 50 N and an accuracy of 0.25 N. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Nodes** & **1** & **2** & **3** & **4** \\ \hline FEA results (Hz) & 256.89 & 504.66 & 605.4 & 695.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: First 4 natural frequencies of the displacement reducer. Figure 17: The shapes of the first 4 modes of the displacement reducer: (**a**) 1 st Mode; (**b**) 2 nd Mode; (**c**) 3 rd Mode; (**d**) 4 th Mode. Figure 19a,b shows the variation in input-output displacement and reduction ratio when the input displacement is increased to 4000 \(\upmu\)m. From Figure 19a, it can be seen that the experimental results of the displacement reducer at 2000 \(\upmu\)m matches the linear relationship calculated by the analytical model. After this point, the slope gradually decreases, reaching the maximum output value around 3000 \(\upmu\)m. This indicates that, in the later stages of the stroke, due to the influence of the geometric relationship, the continuous increase in input displacement causes significant nonlinear changes in the structure, resulting in discrepancies between the modeling results and experimental data. In Figure 19c, in the range of 0 to 2000 \(\upmu\)m, the experimental results are superimposed on the analytical model curve, and a consistency is observed. Figure 19d compares the experimental results of the displacement reducer's reduction ratio with the analytical model results. The constant reduction ratio of the displacement reducer is approximately 11.03, slightly higher than the predicted values from the dynamic-static model and the finite element model. After 2000 \(\upmu\)m, nonlinear deformation occurs as the input displacement continues to increase. Therefore, the range of constant reduction ratio is from 0 to 2000 \(\upmu\)m.  
Figure 19: The experimental results of the displacement reducer: (**a**) The input–output displacement relationship in the range of 0 to 4000 \(\upmu\)m; (**b**) The input–output reduction ratio in the range of 0 to 4000 \(\upmu\)m; (**c**) Zoom in on the image from (**a**), 0 to 2000 \(\upmu\)m; (**d**) Zoom in on the image from (**b**), 0 to 2000 \(\upmu\)m.  
Figure 18: Experimental testing setup: (**a**) The prototype displacement reducer; (**b**) The experimental devices. The experimental results were conducted within the load range of \(-10\) N to \(10\) N at the output end, as shown in Figure 20. The results generally show a constant value with small fluctuations. It can be observed that, within the range of \(-10\) N to \(10\) N, the variation in load has little effect on the displacement reducer. Increasing the load does not affect the reduction ratio of the displacement reducer. Even at the maximum load of \(10\) N, the change in reduction ratio does not exceed \(16\%\). This indicates that the displacement reducer maintains a constant reduction ratio over a long stroke and under external load conditions. Additionally, the output stiffness calculated from Figure 21a is \(0.7\) N/\(\upmu\)m.  
Figure 21b shows the relationship between input displacement and input force obtained from the experiment.