# Detachable Soft Actuators with Tunable Stiffness Based on Wire Jamming
## 3 Results and Discussions  
### Characterization of Bending and Torsional Stiffness  
In order to investigate stiffness characteristics of wire jamming structures in terms of response to deflection, vacuum pressure, thickness and rotation angle, three-point bending experiments and torsion experiments are performed. Figure 4a presents the experimental setup for three-point bending experiments, where a wire jamming structure is placed on the support platform and an air tube (orange color) is connected to a vacuum system. The vacuum is provided by a peristaltic vacuum pump (KVP8 PLUS-KB-S, Kamoer Fluid Tech Co. Ltd., Shanghai, China) and the vacuum pressure is controlled through a pressure regulator (ITV2090-312 BL5, SMC Corp., Tokyo, Japan). In this study, the force sensor moves at a slow speed during measurement processes so that the applied force can be considered equal to the elastic force generated by the wire jamming mechanism. Therefore, the stiffness property can be reflected by comparing values of the force sensor under the same deflection. Moreover, it should be mentioned that each test in this section is repeated five times. As shown in Figure 4b, three different jamming materials (i.e., kraft rope, hemp rope and nylon wire) presented in Figure 2d are tested, and all applied force-deflection curves show an increasing trend in that the applied force increases as the deflection increases. The detailed demonstration of hemp rope and nylon wire is presented in Figure S12 in the Supplementary Materials. For each jamming material, two sets of experiments under different vacuum pressures (0 kPa and \(-\)60 kPa) are performed. It can be seen that the stiffness of all three materials has obviously increased after the vacuum is switched to \(-\)60 kPa, proving that all these materials can be applied to wire jamming. Comparing the results of these materials, kraft rope and hemp rope have similar stiffness characteristics, while the stiffness of nylon wire is significantly higher than the other two materials. The relatively low stiffness of hemp rope is probably due to increased frictional sliding and spacing between ropes caused by thin fiber branches around the surface of ropes. Additionally, nylon wire also has some issues, such as high initial stiffness (i.e., unjammed stiffness) and localized rearrangement. Therefore, kraft rope is selected as the jamming material for subsequent studies. To compare the performance of different jamming structures, we also conduct the three-point bending test on layer jamming structures with the same dimensions (Figures S13 and S14, Supplementary Materials). Moreover, Figure 4b shows that the curves exhibit good linearity at a vacuum pressure of 0 kPa, while they show pronounced nonlinear characteristics after the vacuum pressure decreases from 0 to \(-\)60 kPa. This phenomenon indicates that the jamming structures are mainly governed by elastic behaviors before the vacuum is off, and friction takes an important role in changing the stiffness characteristics after the vacuum is on. To further demonstrate the above phenomenon and the change in stiffness, the experiment is conducted by varying the vacuum pressure after the deflection reaches 11 mm. In Figure 4c, it can be clearly observed that the jamming structure shows low stiffness and the curve is very linear at a vacuum pressure of 0 kPa, while the stiffness is higher and shows pronounced nonlinearity at a vacuum pressure of \(-\)60 kPa. Since there is a gap between wires when the vacuum is off, the applied force has a period of decline after the vacuum is on. In Figure 4d, the applied forces of the wire jamming structure are measured under three different vacuum pressures, where the tests use the same jamming structure with a width \(d\) of 6 mm. As the vacuum pressure increases from \(-30\) kPa to \(-85\) kPa, the friction between the wires increases, thus changing the threshold point at which the relative sliding of the wires occurs.