Study on Structure Design and Motion Characteristics of Pneumatic Flexible Wrist with Braking Function

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Introduction
As an essential connection component between the manipulator and the end gripper, the wrist is mainly used to adjust the position and pose of the gripper and determine the contact state between the target object and the gripper. Its performance directly determines the function and application level of the entire manipulator [1,2]. There are many types of developed wrists, which can be divided into motors [3,4], hydraulics [5,6], linear cylinders [7], shape memory alloy [8,9], and pneumatic artificial muscles (PAMs) [10,11]. The technology of motor-driven wrist is mature and widely applied. Despite large driving torque, fast execution speed, and high accuracy, there are still some problems, such as poor flexibility of the body structure, low safety of man-machine integration, and poor adaptability to unstructured environments. The hydraulically driven wrist can output a relatively high torque at low speed. At the same time, due to its small inertia and fast response, the wrist can easily achieve fast movement and frequent commutation. The disadvantage is that liquid leakage and compressibility cannot guarantee a strict transmission ratio. The linear cylinder can only realize point-to-point movement. Therefore, it needs to combine other rigid connecting rod components to achieve the bending deformation of the wrist. In addition, the static friction between the cylinder piston and the seal has a certain nonlinear effect on the motion. The wrist driven by shape memory alloy has problems, such as easy aging of materials, small output force, the difficulty of accurately controlling the driving temperature, and low driving frequency. Due to the features of simple structure, lightweight, and strong flexibility, the PAM can be applied as a driving component on the wrist to further enhance the security of human-machine interaction and dexterity of operation [12,13]. Hence, the research on the wrist driven by PAMs has important theoretical and practical significance.
In recent years, the structure, motion performance, and control methods of the pneumatic flexible wrist have been deeply studied by scholars at home and abroad. For example, Satio et al. [14] proposed a 2-degrees of freedom (DOF) spherical wrist robot with spherical bearings, which could realize the functions of abduction or adduction and flexion or extension with the same rotation centers in all directions. The shortcomings are that the wrist did not have the position maintenance function, and the pneumatic muscles used required a large driving pressure. In 2015, an exoskeleton wrist power assist device was designed at the University of Patras in Greece, which realized the wrist's 2-DOF movement through the coordination of four pneumatic muscles. At the same time, the rigid holder made of ABS was used to fix and guide the four muscles to ensure the consistency of muscle deformation coordination [15]. In the same year, Bartlett et al. [16] of Harvard University proposed a 2-DOF wrist rehabilitation device based on McKibben PAM that drives the wearer's wrist to perform flexion/extension and internal/external rotation. The disadvantage is that the actuator of the device is in direct contact with the skin. If the actuator is broken, it may cause inconvenience and danger. In 2017, Al-Fahaam et al. [17] designed a new portable and wearable wrist-powered glove. The glove uses two flexural artificial muscles to achieve wrist flexion/extension and three artificial contractile muscles to work together and achieve wrist abduction/adduction. The disadvantage is that there is nonlinear coupling between the two flexural artificial muscles, increasing the difficulty of modeling and control [17]. In 2018, Yanshan University designed a 2-DOF flexible wearable power glove. The device consists of four PAMs constrained by woven mesh and flexible wearing parts that can realize 2-DOF movement of the wrist. However, in the pressurization process, artificial muscles deform and separate from the glove surface, resulting in a partial torque loss [18]. In 2019, the National University of Singapore proposed a 2-DOF soft robot wrist that can control the air pressure in the four quadrant chambers of the wrist and achieve wrist flexion/extension or internal/external rotation motion. However, due to the printing materials and the thickness of the structural wall, the device can only meet the range of motion of 71.1% of the human wrist [19]. In 2020, the Okayama University of Science in Japan developed a tetrahedral wrist rehabilitation device that has 3-DOF and can achieve axial elongation and omnidirectional bending, where the bending angle can reach more than 90° [20]. In 2021, the Harbin Institute of Technology developed a flexible humanoid manipulator with a multidirectional bending wrist. The bending angle of the wrist in four directions can reach 30°, but it also has a strong load capacity [21]. In 2022, Shanghai Jiaotong University developed a flexible pneumatic wrist, where the air pressure can be adjusted in the four chambers of the wrist to control the bending direction and angle. The maximum bending angle can reach 90.8°under 0.2 MPa in no-load conditions [22]. Based on the antagonism principle, the Italian Institute of Technology developed an allpneumatic robot wrist composed of four parallel GRACE actuators. The wrist can achieve biaxial bidirectional bending function by controlling the internal chamber pressure of two adjacent GRACE actuators, with the bending angles being AE15°and AE30°, respectively [23]. Although the design of the above wrist makes full use of the properties of elastic materials to achieve bending, the stiffness of the wrist cannot be actively adjusted, and its shape is very susceptible to external loads. The main reason is that there is no rigid support structure, braking device, or variable stiffness device inside the wrist, which makes it unable to maintain the required position. In practical application, the wrist needs to be flexible, stable, and load-bearing in a particular circumstance. Hence, changing the stiffness of the wrist as needed is an effective solution.
This paper develops a new type of wrist with a spatial position maintenance function to solve the problems of difficulty in achieving position maintenance of the pneumatic flexible wrist. The wrist comprises four artificial muscles and a pneumatic spherical brake in parallel. It has a braking function, and the braking force can be flexibly adjusted while ensuring the flexible motion of 2-DOF, making the wrist more adaptable and more stable when contacting different loads. It can also be applied to various medical, service, and industrial areas requiring braking maintenance and flexible movement equipment and has higher theoretical value and practical significance.

Structure and Function of the Wrist
As exhibited in Figure 1(a), the flexible wrist is primarily made up of four axial elongation PAMs (silicone tube, spring, and plug constitute a seal cavity, namely artificial 2 Applied Bionics and Biomechanics muscle) and a pneumatic spherical brake in parallel. The wrist has 2-DOF, and each of the adjacent artificial muscles can simultaneously drive the wrist pitch and yaw motion, as shown in Figure 1(b). Four axial elongation pneumatic muscles of the same size are evenly distributed 45 mm from the center with a circumference of 90°. The spring outside the muscle not only limits the radial expansion of the silicone tube but also increases muscle elasticity to a certain extent. In the meantime, to further ensure that four PAMs are equidistant from the center, a linkage ring is added in the central position of the wrist to ensure the connection between the four muscles and the consistency of deformation coordination. The linkage ring can also improve the torsional stiffness of the wrist to a certain extent. During the axial elongation process, the spring will rotate around the axis in the opposite direction to its rotation direction. Therefore, left and right rotation springs are used to constrain the PAMs in the wrist, and alternate distribution is adopted to reduce the impact of rotation on wrist movement. The total mass of the wrist is 540 g, and the overall shape is a cylindrical structure. It has a diameter of 110 mm and a height of 100 mm. When compressed air enters PAMs, the silicone tube in the artificial muscle expands under air pressure. At the same time, the axial stiffness of artificial muscles is relatively small, and under the action of air pressure, the muscles elongate along the axis, and the higher the air pressure, the greater the elongation, as exhibited in Figure 1(c). Because the brake in the middle of the wrist is not axially retractable, the axial deformation of the wrist is limited, so it can only be bent and deformed. With the removal of the air pressure, the wrist returns to its initial position with the elastic action of the spring and silicone tube. When compressed air at various pressures enters four PAMs, the wrist can achieve multidirectional bending.
The brake is a thin-walled ball structure mainly composed of outer/inner ball seats, limit plates, friction plates, holder, and drum-shaped airbag, as shown in Figure 2. The ball seat is a rigid element that fits with the holder for clearance. The outer ball seat is cut into two symmetrical parts by wire cutting, making it easy to install. The holder is a hollow spherical body, and the upper position of the holder is a circular platform, which is convenient for positioning and assembling the upper limit plate. There are four identical trapezoidal windows uniformly and symmetrically distributed on the multihemisphere. Arc-shaped columns are formed between the adjacent windows, and the cross-section of the arc-shaped columns is a T-shaped section. A floating friction plate with the same shape as the trapezoidal window is installed between two adjacent arc-shaped T-shaped columns. The drum-shaped airbag is a thin-walled, hollow, and highly elastic bladder installed inside the holder. The drum-shaped airbag is made from Dragon Skin 30 liquid silicone by parting casting [1].
After compressed air enters the airbag, the airbag wall inside expands under pressure. Since the airbag is restrained by the limit plate in the vertical direction and the airbag's radial inward deformation is restrained by the retaining shaft, the airbag can only expand and deform radially outwards, thus pushing the floating friction plate to move radially towards the outer ball seat. As pressure increases, the floating friction plate contacts the outside of the left and right ball seat to generate friction force and achieve braking. When the air pressure decreases, the drum-shaped airbag resets under its elastic force, and the friction between the ball seat and the floating friction plate decreases to zero. Thus, the braking torque can be regulated by controlling the air pressure inside the airbag to adapt to the working state of different loads.

A Static Model of the Wrist
Upper limit plate Applied Bionics and Biomechanics the brake. The wrist is subjected to both axial force and bending moment simultaneously during the deformation.
To simplify the static model of wrist bending angle, the fundamental assumptions are made as follows: (1) Four artificial muscles forming the wrist have the same structure, and there is no manufacturing error. (2) The cross-section of the wrist is uniform, and the center of rotation remains unchanged when bending and deforming. The deflection curve is an arc under the action of pure bending moment. (3) The bending influence on the effective area of pneumatic action of the artificial muscle is ignored.
The bending deformation and stress model of the wrist are simplified to facilitate the analysis, as shown in Figure 3.
As indicated in Figure 3(b), artificial muscles 1 and 2 elongate under the action of air pressure, pushing the upper cover to rotate at a certain angle defined as θ. At this time, artificial muscles 3 and 4 are compressed. It can be seen from the geometric relationship in Figure 3(c) as follows: where R refers to the arc length radius of the wrist center line, H refers to the distance from the center of brake to the top face of the down cover, R q refers to the distance from the artificial muscle center line to the brake center line, θ refers to the wrist bending angle, ρ 1 refers to the arc length of the center line of the artificial muscle at the elongation side, and ρ 2 refers to the arc length of the artificial muscle on the compression side.
According to the equation of arc length calculation and Equations (2) and (3), the deformation amount of different artificial muscles after wrist deformation can be calculated as follows: where ΔL s refers to the change in the arc length of the center line of the artificial muscle at the elongation side, and ΔL y refers to the change of the artificial muscle on the compression side. As indicated in Figure 3(c), the torque balance analysis of the center of wrist rotation can be written as follows: where M p refers to the driving torque generated by artificial muscles under the action of air pressure, M k refers to the impedance torque generated by the spring, M n1 refers to the impedance torque produced by the silicone tube at the elongation side, M n2 refers to the impedance torque generated by the silicone tube on the compression side, and M f refers to the braking torque generated by the brake in the rotation process. The braking torque in the free rotation process is zero. The driving torque is calculated as follows: where p refers to the air pressure and S refers to the crosssectional area of the inner cavity of the artificial muscle. According to the various characteristics of the working section of the elongated artificial muscle, S can be expressed as follows [24]: Substituting S into Equation (7), the driving torque can be derived as follows: where D 1 and D 2 refer to the initial outer and inner diameters of the silicone tube.

Applied Bionics and Biomechanics
In accordance with the deformation coordination conditions of the wrist and the flexural stiffness characteristics of the spring [25], the impedance torque produced by the spring can be noted below: where E 1 refers to the elastic modulus of the spring, d refers to the spring wire diameter, D refers to the middle spring diameter, n refers to the effective number of coils of the spring, μ refers to Poisson's ratio, and k refers to the spring stiffness. The total impedance torque generated by the silicone tube is composed of the impedance torque produced by the silicone tube on the driving side and the impedance torque generated by the silicone tube on the compressed side as follows: Substituting Equations (9)-(12) into Equation (6), the wrist bending angle can be derived as follows: According to Equation (13), the wrist bending angle is approximately proportional to the value of the air pressure, and its bending direction depends on the ventilation combination of the artificial muscle. Figure 4, the airbag expands and deforms under the action of the air pressure, propelling the friction plate to contact the ball seat, thus generating friction and achieving braking. The braking torque is mainly related to the air pressure, the effective contact area between the friction plate and the ball seat, and the friction coefficient between them.

Brake Braking Torque Model. As exhibited in
The force balance of the airbag acting on the friction plate can be indicated by taking a single friction plate as an example as follows: where F pn refers to the driving force generated by air pressure on the airbag, F N refers to the positive pressure exerted by the airbag on the friction plate, and F nn refers to the resistance generated by airbag deformation, which is related to the size of the elastic modulus and deformation of the airbag. When the airbag is compressed and expanded to propel the friction plate to contact with the ball seat, the deformation of the airbag is completely limited, and there is no deformation. At this time, F nn is the constant value, and there is no change.
The driving force is related to the air pressure and acting area, which can be calculated as follows: where S c refers to the effective area of contact between the airbag and the friction plate.

Applied Bionics and Biomechanics
According to the structure of the airbag and its assembly relationship with the cage, the calculation process of S c refers to as follows: where S 1 refers to the surface area of the inner chamber of the airbag, R 1 refers to the radius of the inner chamber of the airbag, S 2 and S 3 refer to the upper and lower bottom areas of the inner surface of the airbag, respectively, h 1 and h 2 refer to the height from the center of the airbag to the upper and lower surfaces of its inner chamber, respectively, S 4 refers to the side area of the airbag, and β refers to the wrap angle corresponding to a single friction plate. Due to the existence of the cage, the airbag cannot completely contact the friction plate during deformation. Therefore, a correction factor ε is introduced.
Substituting Equations (15) and (16) into Equation (14), the positive pressure can be calculated as follows: The total braking torque produced by the friction is deduced as follows: where μ s ¼ 0:32 refers to the friction coefficient between the ball seat and the friction plate, and R 4 refers to the radius of the inner surface of the ball seat.

Experiment and Analysis of the Wrist
As the key parts of the wrist, the mechanical properties of the PAM and brake have a direct effect on its characteristics. The experimental system of the wrist is demonstrated in Figure 5.  Figure 6 indicates variations in elongation during the inflation and deflation process. The elongation increases nonlinearly with the increased air pressure. At 0.34 MPa, the maximum elongation is 44.18 mm. By reason of the hysteresis of the silicone tube, the elongation in the process of inflation is slightly smaller than that in the process of deflating.
The force transducer was utilized to acquire the output force curve change triggered by air pressure after artificial muscles contact with the target object at different positions, as shown in Figure 7. The specific experimental steps are as follows: (1) The artificial muscle-free elongation and contact with the limiting plane are controlled, and the air pressure is    Applied Bionics and Biomechanics gradually increased to achieve muscle extrusion limiting plane. (2) The output force data are measured through the force-measuring sensor fixed at the limiting plane. Figure 7 indicates that the output force of artificial muscle at different limiting planes increases linearly with the air pressure. Moreover, the driving ability of the artificial muscle to diverse limiting planes is different. The fundamental rule is that the closer the limiting plane is to the starting point of artificial muscle deformation, the stronger its driving ability is. When the air pressure is 0.34 MPa and the elongation is 0 mm, the maximum output force is 66.76 N.

Mechanical Properties Experiment of the Brake.
Under the action of air pressure, the radial expansion deformation propels the friction plate to contact the ball seat and generate positive pressure, generating friction torque to achieve braking. Figure 8 is the experimental schematic diagram of braking torque. The lower end of the brake is immobilized, the connecting rod and the top of the brake ball seat are fixed as a whole, and a groove is set at the axial position of 50 mm to hang the beaker. At the same time, the marker is fixed on the upper end of the connecting rod. During the experiment, the precision pressure-reducing valve was utilized to gradually increase the brake air pressure at an increment of 0.04 MPa. The water was continuously injected into the beaker, and the quality of the water in the beaker was tested. Water injection was immediately stopped when the 3D dynamic measurement system captured sudden changes in the space coordinate of the marking point. Measure and record the water weight in the beaker and use this as the maximum load the brake can bear at a given air pressure. Using the equation of torque calculation, the maximum braking torque provided by the brake under given pressure was obtained. Next, the structural brake parameters were substituted into Equation (18) to obtain the theoretical braking torque data. Lastly, the comparison between experimental data and the theoretical is illustrated in Figure 9.
As indicated in Figure 9, the following conclusions can be drawn: (1) The braking torque showed a linear increase with the air pressure. The maximum braking torque is (2) The braking torque is 0 at the air pressure of fewer than 0.05 MPa. The main reason is that the driving force generated by the airbag is mainly used to eliminate the gap between the airbag and the friction plate, as well as between the friction plate and the ball seat. (3) According to the theoretical equation of braking torque and the fitting curve equation, the theoretical value of braking torque coincides well with the experimental data when the deformation compatibility coefficient is 0.73 and the self-deformation resistance of the airbag is 9.32 N. Here, the maximum error between both is 2.78%.

Statics Performance Experimental of the Wrist.
Multidirectional wrist bending can be achieved using the experimental system shown in Figure 5 by controlling the ventilation combination of the four artificial muscles and the pressure gradient. During the experiment, the electric proportional valve was used to control the air pressure, gradually increasing at an increment of 0.02 MPa. Meanwhile, the pressure value was monitored by the pressure sensor to ensure the accuracy of the pressure value. The bending angle of the wrist was measured by a gyroscope under different bending directions. Figure 10 compares the theoretical and experimental values. Good agreement between the theoretical data and experimental data indicates the correctness of the established theoretical model for wrist bending angle. At 0.34 MPa, the bending angle is 20.72°. After the artificial muscle was extended under the action of air pressure, the spring gap became larger, which cannot completely limit the radial deformation of the silicone tube. The outer side of the silicone tube will expand outward along the spring gap, and the cross-sectional area S of the artificial muscle will increase. The increased cross-sectional area of the artificial muscle ΔS is related to the specifications and parameters of the silicone tube and spring, as well as the air pressure. Due to the difficulty in obtaining a specific value of ΔS, it was omitted in the modeling of wrist bending deformation. The result is that the first half of the theoretical curve is lower than the experimental curve. When the air pressure is greater than 0.24 MPa, axial contact between the restraint spring of the artificial muscle on the compression side of the wrist, as well as contact between the spring and the connecting rod ring, transferring the neutral layer, increasing the overall flexural stiffness of the wrist, and reducing the bending angle. This reason is not taken into account in the theoretical model, resulting the data in the later half of the theoretical curve being higher. Figure 11 demonstrates the curve of the bending angles with air pressure when two adjacent wrist muscles are separately ventilated. The following conclusions can be summarized from Figure 11: (1) The wrist bending angle of the wrist in all directions is consistent with the law of change and is approximately linear with the air pressure. (2) Due to manufacturing and assembly errors, there are differences in wrist bending angles in all directions, and the maximum difference is 2.85°. (3) There is a gap between the silicone tube and the constraint spring. When the air pressure is less than 0.04 MPa, the air pressure is mainly used to eliminate the gap, resulting in the bending angle of the wrist being less than 2°.
The experimental data of wrist bending deformation in different directions after 0.04 MPa were fitted, and Applied Bionics and Biomechanics corresponding empirical equations were obtained, which could provide a basis for subsequent research. When muscles 1 and 2 are simultaneously ventilated, the air pressure of muscles 3 and 4 is 0, and the fitting error is 1.945°. The bending deformation equation of the wrist around the positive direction of Y-axis can be expressed as follows: When muscles 2 and 3 are simultaneously ventilated, the air pressure of muscles 1 and 4 is 0, and the fitting error is 1.315°. The bending deformation equation of the wrist around the positive direction of Y-axis can be expressed as follows: When muscles 3 and 4 are ventilated simultaneously, the air pressure of muscles 1 and 2 is 0, and the fitting error is 2.282°. The bending deformation equation of the wrist around the negative direction of Y-axis can be expressed as follows: When muscles 1 and 4 are simultaneously ventilated, the air pressure of muscles 2 and 3 is 0, and the fitting error is 1.379°. The bending deformation equation of the wrist around the negative direction of X-axis can be expressed as follows: θ ¼ 63:49p − 0:81: ð23Þ Figure 12 indicates the spatial motion trajectories of the wrist under different ventilation combinations. It can be seen that the wrist can be bent in eight spatial directions by controlling different muscle ventilation combinations. Due to the manufacturing error of four artificial muscles, there was a certain torsion of the wrist while bending, as shown in Figure 12(b). Figure 13 indicates the effect of the load on the two bending states of the wrist when placed horizontally.
From Figure 13, it can be seen that under the same load, the wrist bending angle gradually increases with the air pressure. Under the same pressure, the wrist needs to overcome the load and self-weight when bending upward, while the bending angle decreases with the increased load. When the wrist bends downward, the load and self-weight promote the bending deformation, while the bending angle increases with an increase in load.

Experimental Dynamics
Performance of the Wrist. The dynamic model of the wrist is very complex and not conducive to accurate real-time control. The dynamic performance of the wrist was experimentally studied to facilitate the later motion control of the wrist. Using the experimental system shown in Figure 5, a single variable (whether the brake works or not) was used to conduct dynamic comparison experiments on the wrist under different excitation signals. The programmable logic controller (PLC) programing control system outputs an excitation signal. Then, it uses a 3D dynamic capture system to capture and track the marked points on the wrist to obtain dynamic data of the wrist at different times. Table 3 shows the specific experimental conditions.

Comparative Analysis of Time-Domain Response under
Step Excitation. Figure 14 shows the step time-domain response curve under different air pressure excitation without braking. According to Figure 14, when the wrist reaches a steady state, the overshoot is almost zero, which belongs to an overdamping system. During inflation, the higher the air pressure, the faster the bending angle increases.   According to Figure 15, the comparative analysis showed that the damping gradually increases with the working air pressure of the brake. Moreover, the bending angle gradually decreases when it reaches the steady state, while the response time when it reaches the steady state gradually increases.

Comparative Analysis of Time-Domain
Response under Impulse Excitation. The excitation signal with an impulse width of 1.5 s was adopted, and the driving air pressure was set to 0.10, 0.20, and 0.30 MPa, respectively. The influence of different damping on the dynamic performance of the wrist was analyzed by adjusting the working pressure of the brake, as indicated in Figure 16.
According to Figure 16, with an increase in the working pressure of the brake, the wrist bending angle gradually decreases once it reaches a steady state. In the process of pressure relief, the amplitude of the wrist returning to the balance position gradually increases with brake operating air pressure. Since the brake has been working, there is a certain deviation between the wrist's return to the balance position and the initial position, which is proportional to the working pressure value of the brake. excitation with a driving pressure of 0.30 MPa, obtaining the influence rule of braking pressure on the natural frequency of the wrist, as shown in Figure 17.
The following conclusions can be summarized from Figure 17: (1) The natural frequency of the wrist is independent of damping and is always 1 Hz. (2) The amplitude of the wrist after pressure relief gradually decreases with an increase in damping. It can be seen that increasing damping can effectively reduce wrist jitter, reduce the impact, and make it reach a steady state as soon as possible.

Application of the Flexible Wrist
The wrist was connected with the self-developed five-finger hand in series to facilitate grasping. The ventilation combination and pressure gradient of the artificial muscles of the wrist were adjusted by the pneumatic control system to complete the wrist posture and grasping experiment.

The Pose Experiment under no Load.
Under the control of the pneumatic system, the wrist has good flexibility and can achieve multidirectional bending movement through muscle coordination, as shown in Figure 18.

The
Pose Experiment under no Load. Choose ordinary objects for grasping to further verify the adaptability of the flexible wrists to grasp various shapes of objects, as demonstrated in Figure 19. Table 4 lists the specification of the grasped objects. Figure 19 indicates that the wrist has good adaptability and can cooperate with the hand to stably grasp various irregular objects in daily life.

Conclusion
In this paper, a 2-DOF pneumatic flexible wrist was designed, which is made up of axial elongation PAMs and a pneumatic spherical brake in parallel. The wrist can achieve multidirectional bending and adjust damping in real time as required. The structure and operating principle of the wrist were represented in detail, and the corresponding theoretical model was built. Lastly, a series of related experiments were conducted, and the findings are gained as follows: (1) An axially elongated PAM was designed, and its elongation and output force characteristics were experimentally analyzed. The experimental findings show that artificial muscle elongation increases nonlinearly with pressure. The axial elongation can reach 44.18% at a pressure of 0.34 MPa. The output forces of artificial muscles increase approximately linearly with the air pressure. At 0.34 MPa, the maximum output force of artificial muscle was 66.76 N. Moreover, the artificial muscle has different driving abilities on different limiting planes. The fundamental rule is that when the limit plane is closer to the deformation starting point of the artificial muscles, its driving ability is higher. (2) A type of pneumatic spherical brake was designed, and the corresponding theoretical model was built, followed by experimental verification. The experiment findings indicate that the braking torque increases approximately linearly with the pressure. At 0.35 MPa, the maximum braking torque is 1.4 N m. (3) The theoretical model of the wrist bending deformation under static conditions was built. Bending direction and bending angle change with air pressure were acquired, followed by the implementation of related experimental verification. The findings reveal that the bending angle of the wrist has a positive association with the air pressure, which is consistent with the trend of the theoretical curve. At 0.34 MPa, the maximum bending angle is 20.72°. The motion performance of the wrist in all directions is the same when the load is zero. When the external load is applied, the influence of the load on the bending angle is mainly related to the bending direction of the wrist. (4) The time and frequency characteristics of the wrist under different excitation signals and damping were obtained by dynamics experiments. The experimental results show that the wrist's natural frequency is independent of the damping and is always 1 Hz. However, with an increase in damping, the bending angle of the wrist decreases gradually, and the response time increases gradually once the wrist reaches a steady state.
The new pneumatic flexible wrist has the advantages of a high driving and braking force, ease of manufacture and maintenance, and low cost. The design is expected to be  14 Applied Bionics and Biomechanics applied in agriculture harvesting, rehabilitation robots, and the service industry.
In the next step, the wrist structure and its bending deformation ability will be further optimized and improved. Specific improvements can be made by developing a double-acting artificial muscle (artificial muscle can be axially extended or contracted according to different ventilation states) or prestretching to reduce spring resistance, achieving a wrist bend angle of 45°or greater.

Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
The authors declare that they have no conflicts of interest.