# Detachable Soft Actuators with Tunable Stiffness Based on Wire Jamming
## 3 Results and Discussions
### Characterization of Bending and Torsional Stiffness
With the vacuum pressure from \(-30\) kPa to \(-85\) kPa, the sliding point occurs at deflections of \(0.5\) mm, \(1\) mm and \(3\) mm, respectively. This phenomenon is similar to the experiments with wires of square cross-section [33]. In addition, we compare the force versus deflection curves for three different thicknesses, and the results demonstrate that the applied force increases dramatically with the increasing thickness of the wire jamming structure (Figure 4e). To quantify the bending stiffness in the three-point bending test, we defined bending stiffness as the ratio of applied force to deflection. Figure 4f compares the bending stiffness of the jamming structures with different thicknesses, where the best stiffness performance (i.e., bending stiffness is \(0.89\) N mm\({}^{-1}\)) is obtained for a thickness of \(8\) mm. The maximum increase in stiffness is nearly seven times after the vacuum pressure is switched from \(0\) to \(-85\) kPa. It should be noted that the thickness of the jamming structure  
Figure 4: Characterization of bending and torsional stiffness of wire jamming structures. **(a)** Experimental setup for three-point bending stiffness tests and detail display of wire jamming structure using kraft rope, where \(l_{\text{w}}\) is the length of wires (range from 140 to150 mm), \(U\) is the width, \(P_{\text{w}}\) is the vacuum pressure, and \(d\) is the thickness of jamming structures. **(b)** Applied force versus deflection curves of wire jamming structures (\(d=6\) mm) using three different jamming media (i.e., kraft rope, nylon wire and hemp rope) at \(0\) kPa and \(-60\) kPa vacuum pressure. **(c)** Applied force versus deflection curve with a vacuum pressure change at a deflection of \(11\) mm. **(d)** Influence of different confined vacuum pressures on the bending stiffness. The thickness \(d\) is \(6\) mm. **(e)** Influence of different confined thicknesses on the bending stiffness. The vacuum pressure is \(-85\) kPa. **(f)** Comparison of bending stiffness with different thicknesses at a deflection of \(15\) mm. **(g)** A typical mechanical behavior curve of wire jamming structures. **(h)** Experimental setup for torsional stiffness. **(i)** Comparison of the torsional stiffness at a rotation angle of \(60^{\circ}\). The thickness of all jamming structures is \(6\) mm. **(j)** Torque versus rotation angle curves under different thicknesses, where kraft rope is used as jamming material. should not be too large, which would lead to an increase in the initial bending stiffness (Figure S15, Supplementary Materials) and volume, as well as a more severe gradient effect. To further understand the bending stiffness characteristics of jamming structures, we present a conceptualized curve of applied force versus deflection (Figure 4g). When the vacuum is off, the wire jamming structure is in an unjammed state, resulting in low stiffness. When the vacuum is on, the jamming structure enters a jammed state and shows similar mechanical behavior to the layer jamming structure [29]. The jammed state can be divided into three phases: (1) during phase 1 (pre-slip regime), the applied force shows a rapid linear increase as the deflection increases, during which the wires are cohesive without slipping; (2) during phase 2 (transition regime), the growth of the applied force slows down and the wires start to slip. In this phase, the curve shows a remarkably nonlinear characteristics; (3) during phase 3 (post-slip regime), the applied force shows a slow linear increase, similar to the characteristics seen when the vacuum pressure is off and the wires enter into a full slip. Figure 4h shows the experimental setup for the torsional stiffness of wire jamming structures. In order to approximate the real torsional condition, the side with an air hose coupler is fully locked to the right fixture, while the left fixture provides torque as the servo rotates, leaving the front side of the jamming structure free to slide.