# Design and Experimental Development of
## 4 Experiments  
### Experiment on the PVSU  
The purpose of this experiment is to verify the variable stiffness mechanism of the PVSU by testing its static stiffness. As mentioned previously, stiffness can be defined as the ratio of steady force acting on a deformable elastic medium to the resulting displacement. Thus, the relation between the forces and resulting displacements when constant pressure is applied to the PVSU is examined in the stiffness identification experiment. Figure 9 presents the schematic diagram of the experimental apparatus. The PVSU is placed on a frame, and its upper end is connected with a slider which can only move along the linear guide in the vertical direction. Below the whole PVSU hangs a weight which causes the PVSU to be compressed. A proportional valve (SMC Corp., Tokyo, Japan) is adopted to regulate the air pressure supplied into the pneumatic bladder. The compression of the PVSU is measured by a linear displacement potentiometer (Novotechnik Messwertaufnehmer OHG, Ostfildern, Germany) installed in parallel with the linear guide, and collected and recorded by data acquisition devices (Advantech Co., Ltd., Taipei, Taiwan) on the computer for further analysis.  
At the start of the experiment, the gauge pressure of the proportional valve was set to zero. Then different weights ranging from 0 to 1.8 kg were applied to the PVSU at a constant increment of 0.1 kg. The weight was changed after the compression of the PVSU stabilized. Corresponding compressions during the process were measured. After that, the above process was repeated in different cases where the gauge pressure was 10 KPa, 20 KPa, 30 KPa, 40 KPa, and 50 KPa, respectively.  
After experiments, the relationship between the external loads and the compressions is plotted in Figure 10. From this figure, several findings can be obtained. Firstly, in the point of the response of the PVSU under a certain gauge pressure, it is evident that each curve can be approximately regarded as three segments of straight lines, which signifies that three phases were indeed presented within the entire compression. Secondly, since the slope of the line indicates the system stiffness, the  
Figure 8: The prototype of the stiffness-adjustable foot system.  
Figure 9: Schematic diagram of the experimental apparatus.  
three-segmented curve means that the PVSU exerted different stiffness values during the three phases. Moreover, the stiffness of the second segment is lower than the first one, and the stiffness of the third segment is higher than the second one. This trend coincides exactly with the theoretical analysis in Section 2. Thirdly, the horizontal ordinate of the turning point of each curve is exactly the trigger displacement of the piston. Under different gauge pressures, the trigger displacement of the piston ranges from 2 mm to 3 mm, which is very close to the design value. Synthesizing the above three points, the proposed variable stiffness mechanism, as well as its mechanical structure, can be proved to be feasible.  
In addition, comparing all the measured curves under different gauge pressures, it shows that as the gauge pressure goes up, the piece-wise linearity of the stiffness becomes more obvious, and both the stiffness value in the high stiffness phase and the amount of compression in the low stiffness phase increase. Higher stiffness in the high stiffness phase means more stable support can be provided to the robot body when the foot is in contact with the ground, while a larger compression range in the low stiffness phase means larger unevenness that the pneumatic bladder is able to adapt to, which are exactly what we want. On this basis, taking the stiffness, adaptability, and pressure endurance into consideration together, 50 KPa is adopted as the ideal working pressure of the PVSU.