# Detachable Soft Actuators with Tunable Stiffness Based on Wire Jamming
## Materials and Methods  
### Design of Wire Jamming Structures  
In order to achieve wire jamming structures with high load capacity, good reversibility and universal adaptability, many critical factors such as installation layouts, materials and dimensions, and wire arrangements need to be explored. As shown in Figure 2a, there are three candidate layouts for the wire jamming structures, where the main body and  
Figure 1: Application scenarios and characteristics analysis of the soft pneumatic actuators. (**a,b**) Soft actuators are applied to a robotic gripper and a wearable exoskeleton. (**c**) Bending display of a fiber-reinforced soft actuator with rectangular cross-section, where \(P_{\text{in}}\) is the air pressure. (**d**) FE simulation of the fiber-reinforced soft actuator (\(P_{\text{in}}=64\) kPa), where the air channel modeling is ignored, and the fibers are hidden from the results. the limiting layer represent the fiber-reinforced actuator. Comparing these three layouts, we can find that layout 2 does not cause severe compression or stretching after bending (Figure 2b,c), and therefore the internal structure design is the simplest (see Section S3 and Figure S4 in the Supplementary Materials for details). To realize the function of jamming or shape-locking, we should choose inextensible materials. Here, we propose three different materials (kraft rope, hemp rope and nylon wire) as optional jamming media, which have different bending stiffness, surface friction characteristics and twisting methods (Figure 2d, and see details in Figure S5 in the Supplementary Materials). It should be mentioned that the diameter of wires affects many properties. Smaller wire diameters may result in severe localized geometric jamming and rearrangement, while larger diameters result in poor flexibility and a small range of stiffness. Therefore, considering the jamming properties of the fiber-reinforced soft actuator, we empirically choose 1 mm diameter wires as the jamming material. Figure 2e,f shows two popular wire arrangement schemes. Compared to the rectangular arrangement, the circular arrangement is more prone to wire circumferential sliding after the bending, which we have observed by making samples. This circumferential sliding of wires may lead to misalignment and pre-jamming (Figure S6, Supplementary Materials). Therefore, we choose the rectangular arrangement as the final solution. Figure 2: Design and analysis of Wire jamming structures. (**a**) Installation methods for wire jamming structures. (**b,c**) Illustration of wire jamming structures under bending state, where \(d\), \(H\), \(l\), \(\theta\), \(R\) are  
jamming structure thickness, actuator thickness, actuator length, bending angle and bending radius, respectively. \(l_{1}\), \(l_{2}\), \(l_{3}\) are the maximum stretch or compression length after bending for layout 1, layout 2, layout 3, respectively. (**d**) Demonstration of kraft rope (one-strand twisted kraft paper), hemp rope (two-strand twisted rope) and nylon wire (PA6, Alead Rubber & Plastic Products Co. Ltd., Hangzhou, China). Scale bar is 1 mm. (**e**,**f**) Presentation of jamming arrangements of circular cross-section and rectangular cross-section. (**g**) Two localized postures (twisting and arching) should be avoided. (**h**) The trimmed free end weakens the gradient effect after bending. (**i**) Schematic operation principle of the wire jamming structure. (**j**) Three main types of external forces. (**k**) Illustration of the bending state of the wire jamming structure under applied force \(F_{\text{e}}\). During the bending motion, another problem is also presented, seen in Figure 2f. Due to the difference in bending radius, a gradient effect appears at the free end of the wires. As expected, the membrane wrapped around the outside of the wires also shrinks with the bending, in which the wires show an elongation-like phenomenon. When the wires reach the top of the membrane, localized twisting or arching is inevitable (Figure 2g), leading to irreversible deformation.