# Detachable Soft Actuators with Tunable Stiffness Based on Wire Jamming
## 1 Introduction  
Soft machines fabricated with soft materials have been rapidly developed in recent years. They have proven to have great potential for applications in industrial robot manipulators, medical devices, biomimetic robots, wearable exoskeletons and aerospace structures [1; 2; 3; 4; 5]. The Young's modulus of soft materials is defined in the order of \(10^{4}\)-\(10^{9}\) Pa [1]. Compared with conventional rigid mechanisms, soft machines and actuators can handle fragile or irregular objects without massive computations or sensing systems, and interact with human bodies safely [6], but still carry with drawbacks due to their low stiffness and hyper-elastic properties. Soft actuators are unsuitable for working in areas with large load capacity, high-speed motion and precise control. Many soft robots can be stiffened by simply increasing air pressure, reducing size, adding rigid components or using higher hardness materials [7; 8; 9]. However, these solutions have limited effect and may lead to reduced flexibility. In order to address these drawbacks, researchers have focused on developing stiffness tunable materials and structures such as shape memory alloys (SMAs), shape memory polymers (SMPs), low melting point alloys and jamming structures [10; 11; 12; 13; 14]. Among these stiffness-tunable schemes, jamming structures are favored by scholars owing to their advantages of structure simplicity, ease of fabrication and wide range of stiffness variation. Two main types of jamming structures, granular and laminar jamming structures, have been extensively studied [15]. Granular jamming consists of particle elements such as grains, coffee grounds, hollow spheres or interlocked granular particles in an airtight envelope [16; 17; 18; 13]. The jamming principle is to change the particles from a flowing state to a solid-like state byapplying vacuum pressure or external force [19; 20]. These granular jamming mechanisms have been integrated into soft actuators and soft robotic grippers, which fit well on irregular surfaces and provide significant stiffness tunability [21; 22; 23]. However, passive jamming of particles due to bending behavior can reduce the bending range of the integrated soft actuator [22]. Depending on the applications, there are challenges in selecting the optimal particle size, shape and material. For example, smaller irregular particles lead to poor fluidity and thus affect the flexibility of the jamming structure, while larger particles reduce the compliance to object shape. In addition, it is difficult to resist significant tensile stresses with vacuum-driven granular jamming structures [24]. Laminar jamming structures, also known as layer jamming, are developed using papers or other flexible layers [25; 26; 27]. When vacuum pressure is applied, the raised friction between the layers will prevent them from sliding against each other. The tunable-impedance mechanisms based on laminar jamming were well studied by [PERSON] et al. [28; 29; 30]. The layer jamming structure exhibits beam-like deflection characteristics when the vacuum pressure is open, showing a higher performance-to-mass ratio compared to other variable stiffness structures. In addition, layer jamming has a compact structure often applied to slender soft robots. However, these stacked planar layers are only suitable for movement in a single plane. The deformability of layer jamming is lower than that of granular jamming. Therefore, a reconfigurable jamming skin has been designed [31]. This structure consists mainly of small overlapping sheets that allow for stretching and 3D deformation. However, this structure is more complex, and some mechanical problems still need to be optimized. Recent investigations have shown that fiber jamming is an alternate scheme for tunable stiffness mechanisms in which fibers or wires are used as the jamming medium [32; 33]. Fiber jamming, which can also be called wire jamming [34], exhibits features similar to granular jamming and layer jamming in cross-sectional and axial planes, respectively.