Abstract
Abstract
This work presents the design and test of a novel fabric-based versatile and stiffness-tunable soft gripper integrating soft pneumatic fingers and wrist. The morphology is designed into a compact tuning fork shape (130 × 110 × 260 mm, 389 g) with two bidirectional sheet-shaped soft fingers and a biaxial bidirectional (universal) cylinder-shaped soft wrist. The multi-degree of freedom of soft fingers and wrist makes the gripper versatile and adaptable to gripping objects of various shapes, sizes, and orientations in a wide range. The bidirectional fingers with double-side inflatable chambers can tune their gripping stiffness and force by varying the common and differential pressure of the two sides. The wrist can tune its deflecting stiffness and force in the same way. Therefore, the gripper can grip objects of various stiffness and weights. The soft gripper is tested to characterize its workspace, stiffness, gripping force, and dynamic response time. Gripping function tests are also performed to evaluate the achieved degree of functions of the gripper. Tests show that the proposed gripper can grip objects in the size of 0–245 mm and in the orientation of −88.2°–90.8° (pitch/roll) with a maximum gripping force of 40 N and a response time of 1.22–1.60 s to force and 0.56–2.61 s to motion, respectively. The gripping stiffness can be tuned in the range of 0.029–0.137 N/mm (i.e., the tunable scope is 79%) by varying common pressure in the range of 0–0.2 MPa. Functional tests verify that the proposed soft gripper is versatile and adaptable to gripping objects of various shapes, sizes, weights, and orientations. Therefore, the proposed soft gripper has great potential applications in production and daily life.
Introduction
In recent years, soft robotics are increasingly attracting the interest of engineers and researchers, who apply soft materials to robots and actuate them to perform motion of continuous infinite degree of freedom (DOF). Compared with conventional rigid robots, soft robots are more flexible, adaptable, and safe, which allows them to interact with an unstructured environment better and perform tasks in a more dynamic manner. 1 A high-impact area of soft robotics is soft grippers and manipulators, which can grip and manipulate fragile objects such as food more safely and interact with humans in a more friendly manner than rigid ones. Generally, active or passive adaptability to objects of various shapes, sizes, weights, stiffness, and orientations is required of soft grippers, which mainly depends on the applied materials and morphologies. Therefore, it is essential to choose proper materials and design effective morphologies in the development of soft grippers.
Materials applied to soft grippers should have features of high compliance and flexibility, good self-actuated performance, and easy fabrication. Since different materials have different actuation methods and thus are made into different types of actuators, we introduce actuators and grippers with their materials together. According to previous studies, soft actuators and grippers mainly include PneuNets or fiber-reinforced elastomeric pneumatic actuators,2–16 fabric-based pneumatic actuators,17–19 cable-driven/shape memory alloy (SMA)-driven flexure-hinge fingers based on thermoplastic and elastomer,20–22 SMA-driven bimorph actuators,23,24 pneumatic elastomeric flexure-hinge fingers with stiffness tuned by shape memory polymer,25,26 Fin Ray® grippers based on rubber-like materials,27,28 VERSABALL® gripper based on particle jamming,29–31 trunk-like manipulators based on pneumatic elastomer4,32 or fabrics 33 or cable-driven polyethylene, 34 hydraulic skeleton gripper using rubber bag as joints, 35 helical inflatable gripper using plastic film, 36 untethered grippers based on magnetic-coated flexible polymer,37,38 grippers using micro-fibrillar adhesives, 39 membrane gripper based on dielectric elastomer,40,41 ionic polymer-metal composites or electroadhesive polymer,42,43 and multiresponsive paper grippers based on conductive polypropylene. 44
Among these soft actuators and grippers, the fabric-based pneumatic ones have some advantages over others due to their high flexibility,45,46 relative high range of motion (ROM) and force output,46,47 stiffness customizability,48–50 little power consumption of elastic deformation, and high force-to-weight ratio. In addition, the fabric-based pneumatic actuators are also easier to fabricate and actuate and have lower cost. The most classical fabric actuators are pneumatic artificial muscles (PAMs), such as McKibben muscles, 51 which have been applied to robots and exoskeleton very commonly. 52 However, a PAM only has one DOF (elongation, contraction, bending, or twist) and for constructing multi-DOF grippers, several PAMs have to be combined generally by rigid connectors,18,53 which will make them bulky and impractical. Therefore, it is necessary to develop integrated multi-DOF fabric-based pneumatic soft actuators for constructing compact versatile grippers.
In previous studies, most of the multi-DOF or multi-gait soft actuators are elastomer ones 54 and there are very few such reports about fabric-based soft actuators. Actually, fabric materials have an essential advantage over elastomers in constructing multi-DOF soft actuators, that is, almost no resistance of unactuated parts to the actuated ones. For example, elastomer bidirectional bending soft actuators 55 generally have limited ROM because the unactuated side produces large bending resistance to the actuated side. By contrast, fabric-based bidirectional bending soft actuators do not have this problem because fabric materials perform high flexibility in the unactuated state. Therefore, we design multi-DOF pneumatic soft actuators with fabric materials to construct a versatile soft gripper.
Regarding morphologies of soft grippers, they generally fall into four categories: (1) multi-fingered, (2) trunk-like, (3) particle jamming ball, and (4) membrane-shaped. The multi-fingered soft grippers use double,13,26–28 triple,2,5,6,10,11,16,18,20,23,24 quadruple,8,9,14,17 or hexatruple37,38 actuators as fingers on a holder to grasp objects, which are bio-inspired by human fingers. The trunk-like soft grippers4,32–34,36,56 combine several soft actuators of different motions in parallel to imitate gripping motion of the elephant trunk. The particle-jamming ball-shaped grippers29–31,39 exploit the jamming effect of particles to switch the ball's state between softening and stiffening and, thus, achieve wrapping and gripping objects. The membrane-shaped grippers40,41 use a membrane that is usually made of electro-activated or thermo-activated polymer to wrap and grip objects by opening and closing the membrane.
Performance of each morphology can be evaluated by their gripping force, ROM, adaptability, and stability. The gripping force depends on tip force of the actuators and contact area between the actuators and objects, in which the particle-jamming gripper performs best, followed by the trunk-like and multi-fingered grippers. The ROM of grippers indicates the range of size of objects that can be grasped, in which the multi-finger grippers perform best because they can grasp large objects by the whole part of fingers as well as pinch small objects by fingertips. The adaptability of grippers indicates the ability to grip objects of various shapes in various orientations. There is no doubt that the multi-fingered grippers have the best adaptability or are versatile since they imitate human fingers. However, gripping stability of the multi-fingered grippers is not so good as the membrane-shaped and particle-jamming ones because the multi-fingered grippers interact with objects by point contact rather than edge or surface and the beam-shaped fingers tend to perform instable transverse bending. Designing the fingers of multi-fingered grippers into sheet shape can change the point contact to edge or surface contact and reduce transverse bending, and thus improve gripping stability. In previous studies, several grippers with double sheet-shaped fingers based on electro-activated polymer42–44 were developed. However, their gripping force is limited by the material. Therefore, we consider using fabric material to construct a double-fingered pneumatic soft gripper with two sheet-shaped fingers.
In addition to fingers of the soft gripper, we also consider integrating a soft wrist actuator in the gripper to orientate the fingers to grip objects in various orientations. In previous studies, very little reports about combining the finger and wrist joints in soft grippers were published. Although the soft gripper can be orientated by installing it on a robotic manipulator, a soft wrist is still needed for passive or active adaption of orientation, which can avoid complex compliance control of the manipulator. Festo, Inc. developed a soft gripper integrated on a soft manipulator, 56 in which the soft manipulator functions like a wrist or even the whole upper limb. However, due to its large length, the manipulator bears a very large bending moment applied by weight of objects and the response speed is slow because a large volume of air needs to be filled in it. Therefore, we design a short universal soft wrist of small volume for the soft gripper to orientate the fingers to grip objects in various orientations with a fast response.
This article presents the design and test of a novel fabric-based versatile and stiffness-tunable soft gripper integrating soft pneumatic fingers and wrist. The gripper is constructed by fabric-based pneumatic multi-DOF bidirectional soft fingers and wrist and is versatile and adaptable to gripping objects of various shapes, sizes, weights, stiffness, and orientations. Design of the soft gripper includes the functions, structure, and parameters of the soft fingers and soft wrist. Testing is conducted to obtain: (1) tip force and bending curvature of the soft actuators; (2) workspace, stiffness, gripping force, dynamic response, and gripping functions of the soft gripper.
It is versatile for the following reasons: (1) tunable gripping stiffness allows it to grip objects of various stiffness safely, (2) morphology of two sheet-shaped fingers allows it to grip objects of various shapes more stably, (3) bidirectional bending of the finger actuators extends the size range of objects that can be gripped, (4) large controllable gripping force extends the weight range of objects that can be gripped, (5) the universal soft wrist allows it to grip objects in various orientations, (6) bidirectional bending of the finger actuators allows it to grip objects at their outer surface as well as to grip open-hollow objects at their inner surface, and (7) out-plane bending of the sheet-shaped fingers allows it to pinch very small objects, grip convex objects with more uniformly distributed contact force, and rotate gripped objects axially.
The gripping stiffness is tunable because the sheet-shaped finger actuators are bidirectionally bendable and have inflatable air chambers on both sides. Varying the common pressure in chambers of the two sides can vary the stiffness of the fingers. Deflecting the stiffness of the biaxial and bidirectional wrist can also be tuned in the same way as the fingers.
Design
This section presents the design of the proposed soft gripper, including the design of function, structure, and parameters.
Function
The proposed soft gripper is designed to grip objects of various shapes, sizes, weights, stiffness, and orientations safely by combining soft pneumatic fingers and wrist that are stiffness tunable. It constitutes two sheet-shaped fingers (Fig. 1a, 1; c, 1) and one cylinder-shaped wrist (Fig. 1b, 1; c, 1).

Function design of the proposed versatile soft gripper.
Each finger is made of four Bidirectional Soft Pneumatic Bending Actuators (BSPBAs) in parallel (Fig. 1a, 1) and can perform in-plane motions, including flexion/extension bending (Fig. 1a, 5, 9), as well as out-plane motions, including partial bending (Fig. 1a, 6), twist (Fig. 1a, 2), and bending with transverse arching (Fig. 1a, 10) by pressurizing different chambers of the actuator, which largely extends the grasping modes and enhances the adaptability to various shapes and sizes of objects. For example, flexion of the two fingers achieves inward gripping on the object's outer surfaces (Fig. 1a, 8) whereas extension achieves outward gripping on the object's inner surfaces (Fig. 1a, 4). Partial flexion of the two fingers achieves pinching tiny objects with the fingertip corner (Fig. 1a, 7). Twist achieves picking and placing obliquely orientated objects (Fig. 1a, 3). Flexion with transverse arching achieves gripping convex objects with more uniformly distributed contact force (Fig. 1a, 11).
The wrist is made of a Biaxial BBSPBA (Fig. 1b, 11) and can perform flexion/extension (Fig. 1b, 2, 4), ulnar/radii deviation (Fig. 1b, 3, 5), and bending in other directions by pressurizing different chambers with different pressures, which makes the soft gripper much easier to grip objects in various poses.
For small objects, the gripper can pinch them by the two fingertips (Fig. 1c, 2) or grasp (fully grip) them by closing the two fingers (Fig. 1c, 3). For large objects, the gripper opens the fingers with enough span first and then pinches or grasps them (Fig. 1c, 5, 8). For objects with an open cavity such as cups and tanks, the gripper can grip them on their inner surface by extension motion of the fingers (Fig. 1c, 4). For some objects with two lifting handles such as bags and pans, the gripper can extend fingers to hook the handles and, thus, lift the objects (Fig. 1c, 9).
For objects in deflected orientation such as on an inclined plane, it is preferred to pick and place them obliquely, which can be achieved by flexion or extension of the wrist and flexion of the fingers (Fig. 1c, 7). In the case that objects are located in a small space, we have to oblique the fingers and use corners of the fingertips to grip them, which can be achieved by ulnar or radii deviation of the wrist and partial flexion of the fingers (Fig. 1c, 6). In addition, the soft wrist also enhances the compliance of the gripper.
Stiffness of the wrist and fingers can be tuned by differentially pressurizing the air chambers on opposite sides of the BSPBAs or BBSPBAs with various common pressure. This characteristic helps the gripper to grip objects of various stiffness more safely. Gripping force can be controlled by the differential pressure of two side chambers of the fingers, which help the gripper grip objects of various weights.
Structure
Figure 2 a shows assembly of the soft gripper, which is mainly composed of two soft fingers (made of four BSPBAs in parallel) and one soft wrist (made of BBSPBA), which are fixed at their proximal ends, respectively, by holders (three-dimensional [3D] printed by HORI H1+/H1D/H2, HORI® with PLA material, China) with screws and nuts. The distal end of the wrist is also connected with the holder of fingers. A customized interface is added on top of the wrist holder for installing the gripper on a manipulator.

Structure and dimensions of the soft gripper.
Figure 2b and c, respectively, shows the structure of the wrist and finger soft actuators in detail. As shown in Figure 2b, the main body of the wrist is a quarter-divided hollow cylinder, which is made of longitudinally elastic fabric (polyester and latex), reinforced at the center by an inextensible fiber (Dyneema®), and sealed at two ends by two 3D-printed caps (Fig. 2b). To ensure air tightness, four latex inner bladders (S350; Sempertex®, Columbia) are inserted into the four cavities, respectively, to form four closed air chambers. Each bladder is connected to a tube connector via a rubber collar. The tube connectors can be placed in taper holes of the upper wrist cap and pressed tightly by the wrist holder. Finally, the actuator is covered by a Spandex pocket and tied at the two ends by two hose clamps.
As shown in Figure 2c, the main body of the finger is a 4 × 1 array of hollow cylinders in parallel, which are made of longitudinally elastic fabric (polyester and latex) and bisected at the middle plane by an inextensible fabric layer (cotton and linen). To ensure air tightness, eight latex bladders (S26001, Sempertex) are inserted into the eight cavities, respectively, to form eight closed air chambers. Each bladder is connected to a tube connector via a rubber collar. The tube connectors are tied with the fabric via hose clamps. Finally, the actuator is covered by a Spandex pocket with frictional rubber pads dispensed on it to improve the frictional coefficient.
Compared with the previous multi-fingered gripper integrated with a long arm, 53 the proposed soft gripper in fork-shaped morphology is more compact and has more stable gripping performance due to using sheet-shaped fingers, as explained in the Introduction section.
Parameters
Geometric parameters of the proposed soft gripper are shown in Figure 2b–d and listed in Table 1. These parameters are mainly designed according to the required ROM and gripping force. For example, to ensure proper variable range of open span, the initial open span and length of the two fingers should be designed carefully. To ensure enough gripping force, the two fingers should be designed with a sectional diameter that is large enough but not too long. The sectional central angle of the fingers influences both the gripping force and the range of open span, and, thus, it should be designed not too small. For the wrist to generate enough bending moment to deflect the gripper, its diameter should be large enough and the length should be appropriate.
Geometric Parameters of the Soft Gripper
The diameter of the inner bladders should be approximate to and less than that of the actuators. On the one hand, bladders with too small a diameter will be initially inflated before the actuator bends on pressurization, which consumes extra pressure on deformation of the bladders and enlarges their strain. On the other hand, bladders with too large a diameter will wrinkle in the actuator and, hence, make uneven bending performance.
In addition to the ROM and gripping force, response speed of the gripper is also considered, which means that the initial air volume in the gripper should be small. Therefore, the diameter, length, and number of actuators are all constrained by the response speed. All parameters are designed under the working condition: 0.2 MPa of maximum pneumatic pressure and less than 1 L/min of air flow.
Figure 3 shows images of the completed soft gripper. It shows that the gripper can achieve considerable ROM with an inflating pressure of 0.12 MPa. In addition, it has lighter weight than most of the commercial soft grippers (337–1386 g) developed by Soft Robotics, Inc.

Images of the soft gripper.
Characterization of the Soft Actuators
Soft actuators are mainly characterized by tip force and free bending curvature, which can be obtained by blocked bending and free bending experiments, respectively.45,57 For the proposed finger and wrist soft actuators, some out-plane bending motions are also tested such as partial flexion, twist and flexion with transverse arching of the finger actuators, and diagonal bending of the wrist actuator. Figure 4 shows the experiment setup for testing them. The soft actuator is fixed at the proximal end on an aluminum frame by a 3D-printed fixture.
For testing the tip force, a load cell (DYLY-102, China, scale 10 kg, accuracy 0.03%) is used, which is also fixed on the aluminum frame. To interface with the tip of the soft actuators more reliably, the load cell has a pallet installed on it. Since bending of the soft actuator is blocked upward by the aluminum frame and downward by the pallet, on pressurization it will exert tip contact force on the pallet, which is then sensed by the load cell and amplified by an amplifier (BSQ-001, China, input, 0–20 mV, output DC 0–5 V, supplied by DC 24 V, accuracy 0.2% full scale).

Experiment setup for testing the soft actuators.
For testing the free bending curvature, a flex sensor (FS-L-0095-103-ST; Spectrasymbol, Inc.) is used, which is installed by helix stitches on the lateral side and in the neutral plane of the soft actuator (Fig. 5b). Since an inextensible fabric layer or fiber is on the neutral plane (Fig. 2b, c), the soft actuator performs almost no stretch relative to the flex sensor during bending deformation. If any, no stretch force will be transferred to the flex sensor because it can slip in the stitches slightly. Therefore, the flex sensor is free of stretch during its bending with the soft actuator and, thus, can measure the bending curvature reliably. Its resistance changing with the bending curvature is converted into a voltage signal by an analog circuit.
The electric system is supplied by a linear power source (APS3005S-3D, Gratten Technology Co. Ltd. China, DC 0–30 V/5A), whereas the pneumatic system is supplied by an air compressor (800W-40L, OUTSTANDING®, China, 0.4–0.7 MPa, 60 L/min) whose output pressure is regulated by a manual regulator (IR2000-02BG, SMC®, Japan, Pout = 0.005–0.2 MPa). Air pressure in the soft actuator is monitored by a pressure sensor (XGZP6847200KPG, China, 0–0.2 MPa), which synchronizes with the tip force signal from the load cell and the bending curvature signal from the flex sensor. The three signals are digitalized by the Arduino Uno board and finally transmitted to the computer via a USB wire. Each testing is repeated by three cycles of pressurizing and venting to expose the repeatability and hysteresis.
The finger actuators
In-plane bending
Figure 5a and b, respectively, show the experiment setup for testing in-plane tip force and free bending curvature of the finger actuator, whose results are shown in Figure 5c and d, respectively. The single-side pressurization (blue curves) means pressurizing and the venting process of the upper chambers, whereas the double-side differential pressurization (red curves) means the process of the lower chambers with the upper prepressurized by 0.14 MPa.
During the single-side pressurization (blue curves), both the tip force and bending curvature increase with pressure of the upper side. The dead zone at zero pressure in these curves can be explained by initial inflation of the inner bladder as mentioned in the Parameters section. During the double-side differential pressurization (red curves), the tip force and bending curvature decrease as pressure of the lower side increases because differential pressure between the upper and the lower sides decrease. It indicates that the tip force and bending curvature are positively correlated with the differential pressure, but this correlation is hysteretic. It is further speculated that the gripping force is also positively correlated with the differential pressure, which is proved in the Stiffness section. Specified values of the tip force and bending curvature are listed in Supplementary Table S1.
From Figure 5c and d, we also find that the relationship between the inflating pressure and tip force or bending curvature is nonlinear and hysteretic. The repeatability is also not so excellent. In fact, it reveals some general challenges that soft robots are faced with, that is, high nonlinearity, serious hysteresis, and poor repeatability, which mainly influence the accuracy. The nonlinearity is mainly determined by nonlinear mechanics of the soft materials, such as hyperelasticity of the latex bladder. The hysteresis is mainly caused by two factors. The first one is that the soft materials deform not fully elastically and, thus, transform part of the actuation power into heat energy, which is called the rate-independent hysteresis. 58 For instance, during the soft actuator bending downward (Fig. 5b), the fabric on the lower side would crease and, thus, consume some energy, which cannot be avoided by slowing the actuation speed. The second one is the rate-dependent hysteresis, 59 which is induced by the lag between input and output. For example, bending of the soft actuator may lag behind varying of the inflating pressure or sensing of the flex sensor may lag behind bending of the soft actuator, which can be reduced by slowing the actuation speed. After several trials, we find that the rate-dependent hysteresis can be almost eliminated if the rate of the inflating pressure is below 0.001 MPa/s, that is, a cycle of pressurization and venting takes at least 6.7 min. Therefore, for reducing the hysteresis, these experiments are all conducted with this rate. Without the expectation that soft robots would replace the rigid ones in every situation, this research mainly focuses on the ROM, force output, stiffness, response speed, and adaptability rather than accuracy.

In-plane bending of the finger soft actuator. Experiment setup for testing
Out-plane bending
Figure 6a–c shows three out-plane bending motions of the finger soft actuator, that is, partial flexion (pressurizing the upper right chamber), twist (pressurizing the upper right and lower left chambers), and flexion with transverse arching (pressurizing the upper and lower right chambers), respectively. In the former two motions, rotation angle of the tip edge is measured by an Inertial Measurement Unit (MPU6050; InvenSense®); whereas in the third motion, arching curvature of the tip edge is measured by the flex sensor. In each motion, bending curvature of the actuator is measured at the upper edge by the flex sensor. The results are shown in Figure 6d–f.
In the three out-plane motions, bending curvatures of the actuator (red curves) increase with the inflating pressure and they are all less than those of the in-plane bending motions (Supplementary Table S1) because only some same-side chambers or even opposite-side chambers are pressurized in out-plane bending. In partial flexion (Fig. 6d), rotation angle of the tip edge increases and then decreases with the pressure. In twist motion (Fig. 6e), rotation angle of the tip edge increases with the pressure. In flexion with transverse arching (Fig. 6f), curvature of the tip edge increases with the pressure. Specified values of the bending curvature and tip rotation angle are listed in Supplementary Table S1.
Due to using four BSPBAs in parallel, the proposed soft finger can produce larger tip force (55.09 N at 0.209 MPa) and more motions (in-plane and out-plane) than previous soft fingers.45,46,60

Out-plane bending of the finger soft actuator. Experiment setup for testing
The wrist actuator
Figure 7a–c shows the experiment setup for testing tip force and curvature in orthogonal bending (Fig. 7a, b) and curvature in diagonal bending (Fig. 7c) of the wrist soft actuator, whose results are shown in Figure 7d–f. Orthogonal bending test of the wrist actuator is conducted with single-side pressurization (blue curves) and double-side differential pressurization (red curves), which is the same as the in-plane bending test of the finger actuator except that the prepressure is 0.12 MPa (for tip force test) and 0.10 MPa (for bending curvature test) instead of 0.14 MPa.
Data analysis of the orthogonal bending is the same as that of in-plane bending of the finger actuator test, and main characters of the wrist actuator are listed in Supplementary Table S1. In the diagonal bending (Fig. 7c), only one upper chamber of the wrist actuator is pressurized. Figure 7f shows that the bending curvature increases and then decreases with the inflating pressure, and it is smaller than that in the orthogonal bending because only one chamber is inflated.

Bending of the wrist soft actuator. Experiment setup for testing
From Figure 7d with Figure 5c, we find that the wrist soft actuator shows more serious nonlinearity, hysteresis, and poor repeatability in tip force than the finger actuator, which is mainly caused by two reasons. On the one hand, the wrist soft actuator has a cylinder shape instead of the sheet shape like the soft finger, which makes it tend to perform lateral bending slightly and, thus, adds to irregularity of the tip force if any nonsymmetricity of geometry is induced in fabrication. On the other hand, even though the wrist actuator has been fully blocked in its initial state, on pressurization, its end still rotates a little and, thus, slides slightly on the pallet, which can cause variation of the contact point and, thus, induce some measurement error on the tip force. For such a soft actuator with a large diameter-length ratio, more reliable testing for its tip force is still a challenge for us to overcome in future work.
Test of the Soft Gripper
The soft gripper is tested to characterize its workspace, stiffness, gripping force, and dynamic response. Finally, the gripping function test is also performed by achieving the functions shown in Figure 1.
Workspace
Workspace of the gripper includes open span of the fingers and achievable orientation of the wrist.
Open span of the fingers
Open span is an important feature of the fingers' workspace, which determines the maximum size of objects that can be gripped. To obtain workspace of the fingers, we first mark the finger outlines with white lines on the front side, as shown in Figure 8a. Then, the fingers are pressurized from the natural state (Fig. 8a left) to full flexion (Fig. 8a middle) and full extension (Fig. 8a right) with pressure increment of 0.02 MPa from 0 to 0.1 MPa and 0 to 0.2 MPa, respectively, during which images in every pressure step are captured, as shown in Figure 8a. Next, the images are binarized (Fig. 8b), the marked lines are extracted (Fig. 8c), and, finally, they are skeletonized to abstract lines (red lines in Fig. 9). The area swept by the two fingers indicates the workspace (blue area in Fig. 9), without which objects are not reachable and cannot be gripped. The maximum open span is the distance between the two finger tips in full extension state, which is indicated in Figure 9 as 245 mm and about 280% of the natural open span 88 mm. It is concluded that bidirectional bending function (flexion/extension) of the fingers can significantly improve the gripper's adaptability to objects of different sizes. The proposed soft gripper can grip objects of sizes ranging in 0–245 mm, which is much larger than the commercial two-fingered soft gripper (M2FR-W; Soft Robotics, Inc.) that varies its open span in 15–65 mm with an initial value of 40 mm by pressurizing or evacuating finger actuators.

Extraction of the finger outlines by image manipulation.

Workspace and outlines of the finger actuators. The “*” indicates any point in the workspace. The workspace contains so many such points (depending on pixels of the camera) that single “*” cannot be identified from the plot and thus the workspace looks like a solid blue area.
Achievable orientation of the wrist
To measure achievable orientation of the wrist, we install an IMU sensor (MPU6050; InvenSense) on the finger holder with x-axis and y-axis aligned with two horizontal edges of the holder and z-axis vertically downward. Then, the wrist is pressurized (0–0.16 MPa) from natural state (Fig. 10e) to full flexion/extension (Fig. 10d, f), full ulnar/radii deviation (Fig. 10b, h), and full diagonal bending (Fig. 10a, c, g, i) to make the finger holder perform different orientations (pitch, roll, and diagonal deflection), during which the orientations are tracked continuously by the MPU6050. Finally, the unit vector of z-axis (also axial direction of the finger holder) can be obtained, whose end points are plotted in Figure 11.

Achievable orientation of the wrist.

Unit vector distribution of the axial direction of the wrist end.
Curves with different colors in Figure 11 mean orientations of the wrist in different bending modes, that is, flexion/extension, ulnar/radii deviation, diagonal bending, and anti-diagonal bending shown in Figure 10. From Figure 11b, we find that orientation curves of the four bending modes almost cover the horizontal unit circle, which means that the wrist can achieve most of the possible orientations of a cardan joint. In addition, more bending modes of the wrist can be actuated by pressurizing the four chambers with different pressures individually, which can achieve more orientations and whose curves can further fill the unit circle in Figure 11b.
Table 2 lists orientation ranges achieved by the four bending modes of the wrist, in which a negative sign means the opposite direction. It shows that these ranges are nonsymmetric, which is mainly caused by the geometric error in fabrication and uneven properties of fabric materials. This nonsymmetric phenomenon can also be observed in Figure 11b.
Orientation Ranges Achieved by Different Bending Modes of the Wrist
In addition to bending along x-axis and y-axis, the wrist also performs twisting along z-axis, that is, along its axial, which can be observed from Figure 10b. It means that the wrist is more like a spherical joint than a cardan joint. However, this twisting is generally produced by unstable dislocation of the chambers and coupled with the bending, which is not preferred for repeatability and controllability reasons. From Figure 11b, we also observed that the curves have rotation drift along the z-axis, which is mainly caused by zero drift of the MPU6050 due to lack of a compass. In further studies, we consider stabilizing chambers of the wrist to avoid its twisting and using a more accurate IMU sensor without zero drift to measure its orientation.
Compared with the previous pneumatic modular arm 32 (with diameter 100 mm) that achieves bending angle 85° on length 180 mm and the previous 4-PAM arm 61 that achieves bending angle 84° on length 300 mm, our proposed soft wrist has advantages of a larger bending range (up to 90.8°) and a smaller size (diameter of 40 mm and length of 70 mm).
Stiffness
When it comes to gripping soft objects, the gripper's stiffness kgrp is an important factor that affects the normal contact force F and the object's deformation Δx. Equation (1) shows that the normal contact force is produced by deformation of the object as well as by open span variation of the gripper. Solving Eq. (1), we obtain the deformation and normal force as expressed by Eqs. (2) and (3), respectively. Equation (2) indicates that to grip soft objects (with lower kobj), a softer gripper (with lower kgrp) is needed to decrease deformation of the object (i.e., Δx) and, thus, ensure safety, especially when gripping fragile objects such as eggs. In addition, a softer gripper also produces smaller gripping force according to Eq. (3), which further prevents the object from damages. To grip hard objects, a stiffer gripper is preferred for increasing the gripping force according to Eq. (3). Therefore, a stiffness tunable gripper is required for gripping both soft and hard objects, based on which the proposed soft gripper is developed.
where S is open span of the gripper at zero gripping force and usually decreases with the actuating degree such as inflating pressure of the pneumatic gripper; x is size of the object in undeformed state.
Stiffness of the proposed soft gripper can be tuned by varying inflating pressure and pressurizing modes, which makes it possible to grip objects of different stiffness. The stiffness is divided into three aspects: (1) inward-gripping stiffness and (2) outward-gripping stiffness of the fingers and (3) deflecting stiffness of the wrist. The former two describe the relationship between open span of the two fingers and normal force exerted on the objects, whereas the last describes that between horizontal deflection and deflecting force of the wrist. Since the finger and wrist actuators are bidirectional and have air chambers on both sides, we can pressurize one side only or both sides with equal or different pressures. Therefore, the pressurizing modes fall into three: (1) single-side pressurization, (2) double-side equal pressurization, and (3) double-side differential pressurization, which are the same as those described in The Finger Actuators section except that the two sides are called palmar and dorsal (for the fingers) or left and right (for the wrist) instead of upper and lower.
Stiffness of the gripper is tested by lateral tension experiments on the fingers (Fig. 12 and Supplementary Fig. S1) and wrist (Supplementary Fig. S2). We take the inward-gripping stiffness test as an example to illustrate the experiment setup. First, the gripper is fixed on a holder as an end-effector of a three-axis translational platform driven by leading screws and step motors. Then, we use a fiber string (diameter 0.32 mm, Dyneema) with two ends tied at middle points of the two fingertips, respectively, to pull the fingers outward. The string is guided by two pulleys, that is, Pulley 1 fixed with the load cell and Pulley 2 fixed with the vertical leading screw. The load cell is fixed with the left horizontal leading screw and keeps stationary.

Experiment setup for testing inward-gripping stiffness of the fingers. The L-shaped red solid line indicates the moving frame on which the soft gripper is installed, whose moving direction is indicated by the red arrow. The dotted line indicates the fiber string that pulls the gripper open.
When the gripper and Pulley 2 move right horizontally with the vertical leading screw, the string will be tensed due to increased distance between the two pulleys, and then the open span between the two fingers will increase. Tensing force of the string is equivalent to normal contact force between the fingers and object in inward gripping if frictional moment of the pulleys is ignored. Therefore, the normal force is half of that sensed by the load cell. Open span of the fingers can be determined by measuring distance between the two pulleys with a linear position sensor (AOGESON®, KTC-400 mm, accuracy ±0.05%, China) if length of the string is known and the stretch is ignored. For testing outward-gripping stiffness of the fingers, we just need to exchange the two ends of the string that are tied on the two fingertips, as shown in Supplementary Figure S1. For testing deflecting stiffness of the wrist, one end of the string is tied on the right fingertip whereas the other is tied on Pulley 2. Then, the fingers are pressurized to full close and its state is maintained during testing stiffness of the wrist, as shown in Supplementary Figure S2.
Each of the three stiffness tests is conducted on three pressurizing modes mentioned earlier, and each pressurizing mode is conducted with two or three different pressures. In each experiment, tension and release is performed by three cycles. The experimental results of force-displacement (F-S) curves are shown in Figure 13a–c and Supplementary Figures S3a–c and S4a–c. By fitting them with cubic curves and then differentiating the fitted curves, we can further obtain the parabolic stiffness-displacement (k-S) curves as shown in Figure 13d–f and Supplementary Figures S3d–f and S4d–f, where k = dF/dS.

Experimental results of the inward-gripping stiffness of the fingers with
From them, we find that the normal force varies with the displacement monotonically and nonlinearly whereas the stiffness varies with the displacement parabolically, that is, initially decreasing and then increasing. In addition, hysteresis exists in the F-S curves. In each pressurizing mode, the normal force and stiffness basically increases with the inflating pressure. The fingers can produce maximum normal force of 40 and 38 N at an open span of 200 and 10 mm with single-side pressure of 0.20 MPa in inward and outward gripping, respectively, whereas the wrist can produce maximum normal force of 16 N at deflection of −30 mm with single-side pressure of 0.12 MPa.
From the k-S curves, the initial stiffness kinitial (at zero normal force), minimum stiffness kmin, stiffness variation (1-kmin/kinitial), and nominal normal force (F at kmin) are extracted and then listed in Table 3 and Supplementary Tables S2 and S3. From them, we find that there is an obvious positive correlation between the minimum stiffness and the common inflating pressure (Ppalmar + Pdorsal)/2 or (Pleft + Pright)/2, and between the nominal normal force and the differential inflating pressure |Pdorsal−Ppalmar| or |Pleft–Pright|. The correlation coefficients are listed in Table 4, which shows that the correlation is strong. Therefore, it is concluded that gripping stiffness and force of the fingers can be tuned, respectively, by the common and differential pressure of two-side air chambers of the fingers. So do deflecting stiffness and force of the wrist. Tunable scope of the fingers' gripping stiffness is 0.029–0.137 N/mm (ratio of 79%, inward) and 0.061–0.106 N/mm (ratio of 42%, outward) by varying the common pressure in 0–0.2 MPa. Tunable scope of the wrist's deflecting stiffness is 0.029–0.089 N/mm (ratio of 67%) by varying the common pressure in 0–0.12 MPa.
Inward-Gripping Stiffness of the Fingers
single-side pressurization.
double-side equal pressurization.
double-side differential pressurization.
\, infeasible pressurization for the function.
Correlation Coefficients of Pressure, Stiffness, and Force
Compared with the previous stiffness-tunable soft gripper 18 that uses extensor and contractor PAMs and can tune stiffness in 0.036–0.096 N/mm with pressure 0.1–0.4 MPa, our proposed soft gripper has a larger tunable range 0.029–0.137 N/mm with pressure 0–0.2 MPa. In addition, our gripper is also more compact and can produce larger gripping force (up to 40 N at 0.2 MPa according to Fig. 13a) than the previous one (10 N at 0.4 MPa). 18
Dynamic response
Dynamic response time is an important character that influences the speed of gripping operation. Therefore, we tested the soft gripper's response time to motion and force with different inflating pressures. The tested motion includes open span of the fingers and deflection angle of the wrist, whereas the tested force includes gripping force of the fingers and deflecting force of the wrist. The experiment setup is the same as that of workspace and stiffness tests. Since the response time depends on flow and pressure of the air source and regulator, length and diameter of the pipes, and initial air volume in the soft actuators of the gripper, we list these parameters in Table 5.
Parameters That Influence Response Time of the Gripper
Force and motion response of the fingers and wrist is shown in Figure 14 and Supplementary Figures S5 and S6, in which ts is taken as the setting time when the error falls into 5% of final value. It can be seen that too low a pressure (0.05 MPa) leads to too long a response time. The wrist responds faster (average ts = 0.428 s to force and 0.792 s to motion) than the fingers (average ts = 1.332 s, 1.449 s to force and 1.233 s, 2.025 s to motion), which is explained by smaller initial air volume in the wrist actuator (Table 5). According to the rising rate, the actuator with higher pressure can vary its force and displacement faster.

Although the proposed soft gripper responds to motion a little slower than the previous one 18 that has a response time of 0.46 and 0.6 s, it can be improved by using an air source with higher flow and pneumatic pipes with a larger diameter, which will be taken in our future work, especially in studies of controlling the gripper.
Gripping functions
This part tests the grip functions presented in the Function section (Fig. 1). The proposed soft gripper can grip objects of different shapes, weights, and sizes by different gripping methods, as shown in Figures 15 and 16. With the wrist, the gripper can grip objects in different poses (Fig. 16c, d) and pour a bottle of water (Fig. 17). Figures 18 and 19 show the sequence of gripping objects of a large size on their outer and inner surface, respectively. Further, some additional functions such as tip pinch, more uniform-force pinch, and rotation of objects can be achieved by the out-plane bending of the fingers, as shown in Figure 20.

Grip poises of different weight and size in different poses by different methods.

Grip objects of different shapes.

Sequence of gripping a bottle of water (400 g, Φ65 mm) and pouring it in a container.

Sequence of gripping an object with large width (380 g, width 150 mm).

Sequence of gripping an object with a hole (2400 g, Φ110 mm).

Gripping functions achieved by out-plane bending of the fingers.
Therefore, the proposed soft gripper is verified to be versatile and adaptable to gripping objects of various shapes, sizes, weights, and orientations. Compared with the versatile RBO hand, 16 our proposed soft gripper has more degrees of freedom (due to integrating fingers and wrist) and more gripping modes and can produce larger gripping force.
Conclusion and Future Work
This work presents the design and test of a novel fabric-based versatile and stiffness-tunable soft gripper integrating soft pneumatic fingers and wrist. Morphology of the soft gripper is designed into a compact tuning fork shape (130 × 110 × 260 mm, 389 g) with two bidirectional sheet-shaped soft fingers and a biaxial and bidirectional (universal) cylinder-shaped soft wrist. The gripper is versatile and adaptable to gripping objects of various shapes, sizes, weights, stiffness, and orientations in a wide range. Stiffness of the fingers and wrist can be tuned by changing common pressure in the air chambers on opposite sides of the actuator. Tests are conducted on the soft gripper to obtain its workspace, stiffness, gripping force, and dynamic response time. Functional tests are also performed to evaluate the achieved degree of functions of the gripper.
Tests show that the fingers can perform open span ranging from 0 to 245 mm with an initial value of 88 mm, produce maximum gripping force of 40 N (inward) and 38 N (outward), response to force with time of 1.22–1.60 s (inward) and 1.15–1.97 s (outward), and response to motion with time of 0.56–2.61 s (inward) and 1.52–2.89 s (outward), respectively, with maximum pressure of 0.2 MPa. The wrist can perform orientation from −88.2° to 90.8° in flexion/extension, −48.6°–72.3° in ulnar/radii deviation, −73.2°–89.3° in diagonal bending, and −75.2°–82.6° in anti-diagonal bending; produce maximum deflecting force of 16 N and response to force and motion with time of 0.39–0.46 and 0.52–0.56 s, respectively, with maximum pressure of 0.16 MPa.
Correlation analysis shows that the gripping stiffness of the fingers is positively related with the common pressure whereas the gripping force is positively related with the differential pressure of chambers on their two sides. So is deflecting stiffness of the wrist actuator. Therefore, stiffness of the gripper can be tuned by varying the common inflating pressure of two sides of the actuators. Gripping stiffness of the fingers can be tuned in the range of 0.029–0.137 N/mm (inward) and 0.061–0.106 N/mm (outward) by varying pressure in 0–0.2 MPa, that is, the tunable scopes are 79% and 42%, respectively. Deflecting stiffness of the wrist can be tuned in the range of 0.029–0.089 N/mm by varying pressure in 0–0.12 MPa, that is, the tunable scope is 67%.
In gripping functional tests, the proposed soft gripper is verified to be versatile and adaptable to gripping objects of various shapes, sizes, weights, and orientations. and it has great potential applications in production and daily life.
Main contributions of the work include: (1) We developed the integrated fabric-based multi-DOF soft finger and wrist actuators that can produce high force, large ROM, and variable stiffness; (2) with the developed soft wrist and fingers, we constructed the versatile and stiffness-tunable soft gripper of compact fork-shaped morphology, which is adaptable to objects of various shapes, sizes, weights, stiffness, and orientations; (3) we tested characters of the soft actuators and gripper, in which the multi-DOF and stiffness-tunable features are fully exposed; and (4) we presented some gripping function tests that can fully demonstrate adaptability of the proposed soft gripper.
Future work will focus on modeling of the soft gripper and its force and motion control methods. Tensile tests of the fabric materials will be conducted, and then, the stress-strain relationship can be applied to construct a quasi-static or dynamic analytical model to predict gripping force and motion of the gripper in different working conditions. Based on the model, an open-loop control method can be used to control gripping force and motion of the gripper. If the open-loop method performs not well, a closed-loop control method will be considered. Then, sensors for capturing the gripping force and motion are needed. In this research, we have used flex sensor, load cell, IMU, and camera to measure the gripping force and motion. However, these sensors are difficult to integrate with the soft gripper and unsuitable to apply in actual working condition. Therefore, we will seek or develop some soft sensors that are compatible with the fabric materials and then integrate them with the soft gripper. In addition, we will also find effective control methods to reduce hysteresis of the soft gripper.
Footnotes
Acknowledgment
This work was supported by the National Natural Science Foundation of China under Grant No. 51475300.
Author Disclosure Statement
No competing financial interests exist.
References
Supplementary Material
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