Robotic grippers, which act as the end effector and contact the objects directly, play a crucial role in the performance of the robots. In this paper, we design and analyze a new robotic gripper based on the braided tube. Apart from deployability, a self-forcing mechanism, i.e., the holding force increases with load/object weight, facilitates the braided tube as a robotic gripper to grasp objects with different shapes, weights, and rigidities. First, taking a cylindrical object as an example, the self-forcing mechanism is theoretically analyzed, and explicit formulas are derived to estimate the holding force. Second, experimental and numerical analyses are also conducted for a more detailed understanding of the mechanism. The results show that a holding force increment by 120% is achieved due to self-forcing, and the effects of design parameters on the holding force are obtained. Finally, a braided gripper is fabricated and operated on a KUKA robot arm, which successfully grasps a family of objects with varying shapes, weights, and rigidities. To summarize, the new device shows great potentials for a wide range of engineering applications where properties of the objects are varied and unpredictable.

Introduction

The gripper is an important kind of end effector mounted on the end of the manipulator to provide robots with the capability of accomplishing a wide variety of manipulative assignments [1]. Contacting the objects directly, it greatly affects the functionalities of the robots [2]. Conventional rigid-bodied grippers cannot adapt to objects with varying shapes and rigidities, making it easy for them to drop or crush the objects [3]. In recent years, soft grippers have drawn increasing attention from researchers due to their great adaptability to objects. Considering the unpredictable or inconsistent properties of the objects, an effective soft gripper is required to be able to grasp objects with various shapes, weights, rigidities, and so on [2,4].

To achieve universal grasping, various grippers have been designed. One popular group is the anthropomorphic hand with two or more articulated fingers [5,6]. This gripper mimics human hand, which exerts great dexterity to grasp objects with different shapes and volumes. However, the high mechanical and control complexity and difficulties in handling soft and deformable objects limit its practical applications [4,7]. Recently, grippers with soft fingers have also been studied [8,9]. With the soft contact, the fingers can bend around the object to pick it up with little damage. However, it is difficult to provide sufficient force in a controllable manner [4]. To tackle this problem, underactuation has been adopted to make the hand fingers adaptive yet powerful [10,11]. Another type of grippers use controlled adhesion realized by electroadhesion or dry adhesive [12,13]. They demonstrate excellent dexterity and versatility for its special grasping mechanism, allowing them to grasp fragile, flat, soft, and deformable objects. The limitations of those grippers include requirements for clean, relatively smooth, and dry surfaces [4]. The granular jamming gripper based on a bag containing granular coffee beans is also a famous one for its high compliance [14,15]. It is soft at normal state and becomes rigid when negative pressure is applied. It can grasp various objects through static friction, geometric constraints, vacuum suction, or the combination of them [14] through simple control. Nevertheless, it needs to partially envelop the object for grasping, and the holding force may be insufficient at a small gripper volume.

Braided tube is a kind of deployable structure, which is made of fibers interwoven in a crisscross pattern to form a tubular mesh configuration [16]. It shows desirable features including light weight, excellent flexibility, fatigue resistance, and dimensional stability [17] and has been applied in various areas such as piping industry [18,19], soft robotics [20,21], smart materials [22,23], and medicine [24,25]. The mechanical behaviors of the braided tube are of great importance and have been extensively studied. With the open-coiled spring theory [26], Jedwab and Clerc [27] analyzed the deployability and radial stiffness of the braided tube and derived theoretical formulas to determine them. The radial stiffness of the braided tube was also experimentally investigated by Wang and Ravichandar [28] and numerically studied by Ni et al. [29], who provided more validation for the theoretical analysis. Besides, Kim et al. [30] studied the bending behavior of the braided tube with numerical methods, and the results demonstrated the excellent flexibility of the structure. Li et al. [31] designed a novel surgical instrument based on the braided tube and proposed a simplified model to describe its binding capability.

In this paper, we design and analyze a new gripper based on the braided tube. The superior deployability helps it to contain objects with a wide range of sizes and shapes, thereby enabling universal grasping. The self-forcing mechanism, which increases the holding force with load, makes it possible for the holding force to passively adjust according to the weight of the objects to avoid dropping and crushing. With the design tailorability, light weight, easy fabrication, and simple control system, the gripper shows great promise especially in repetitively grasping objects with unpredictable properties. This paper focuses on the analysis of the self-forcing mechanism of the braided gripper and showing its feasibility, and it is organized as follows. In Sec. 2, a cylindrical object is taken as the example to theoretically explain the self-forcing mechanism of the braided gripper, and explicit formulas are derived to calculate the range of holding force. The deployability of the gripper is also discussed in this section. Next, experimental setup and finite element modeling for the mechanism of the gripper are presented in Sec. 3. Subsequently, the results and discussions are presented in Sec. 4. Finally, conclusion is given in Sec. 5, which ends the paper.

Theoretical Analysis

Mechanism of the Grasping.

The braided gripper is made of spiral fibers interwoven in a crisscross pattern to form a tubular mesh configuration. The geometry of the braided gripper is shown in Fig. 1, which is determined by d, n, β, D, and L. Parameters p, c, Di and Do can be calculated through the following equation: 
{p=πDtanβc=L/pDi=D2dDo=D+2d
(1)

The grasping mechanism of the braided gripper is illustrated in Fig. 2. First, the gripper stays at a smaller diameter compared to the grasped object. Second, the gripper is deployed (details in Sec. 2.2) to a larger profile with transmission wires. Third, the gripper is moved to contain the object. Finally, the transmission wires are relaxed, and the gripper grasps and lifts the object due to the self-forcing mechanism (details in Sec. 2.3).

Deployability.

Each fiber of the braided gripper is a helix, and the spreading of one fiber in a plane is shown in Fig. 3. For its large β, L and D will change upon longitudinal load, leading to folding and deployment of the gripper. Since the fiber is nearly inextensible, the fiber length can be considered as unchanged during deformation and calculated by 
l=cπD/cosβ=cπD/cosβ
(2)
where the parameters of the deformed gripper are denoted with a prime. Simplifying Eq. (2), the diameter of the deformed gripper can be acquired as 
D=Dcosβ/cosβ
(3)
where β′ theoretically ranges between 0 deg and 90 deg during deformation. A braided gripper can be fabricated at a slim state with a large β′ approximate to 90 deg. In this state, the fibers huddle together, and the gripper diameter is about 2d. When β′ tends to 0 deg, the diameter of the gripper comes to its upper limit D/cos β, which helps to form a large profile to contain objects with various shapes.

Self-Forcing Mechanism.

Li et al. [31] proposed a simplified model to describe the binding capability of the braided tube as a surgical instrument, i.e., the maximum holding force here. However, the friction distribution between the tube and the object was ignored, making the analysis less accurate and even out of work in some situations. Here, assuming the braided gripper as a combination of independent helical springs, the friction distribution is analyzed with infinitesimal calculus. According to Jedwab and Clerc [27], when the gripper is tensioned longitudinally (shown in Fig. 4(a)), the tension force on the gripper can be calculated as follows: 
T=2n[2GIK3(2sinβK3K1)EItanβK3(2cosβK3K2)]
(4)
where K1=sin2β/D,K2=cos2β/D,K3=D/cosβ. The tension force and the radial pressure (shown in Fig. 4(b)) loaded on the braided gripper are equivalent. Both forces can elongate the gripper, and the relationship between them was also given by Jedwab and Clerc [27]: 
P=2TcDLtanβ=2πp2T
(5)

The grasping force is provided by the friction between the gripper and the object caused by compression. Here, a cylindrical object is taken as an example to explain the self-forcing mechanism. As shown in Fig. 5(a), the cylindrical object is contained in the braided gripper. The left end of the gripper is fixed, and the object is forced rightward with load F. The compression of the gripper to the object includes two components. One is caused by the deployment of the braided gripper and denoted by P0. The diameter of the gripper becomes larger to contain the object, and the elastic deformation needs to be sustained and causes the compression. The other arises from the self-forcing mechanism and denoted by Ps. The gripper is tensioned longitudinally due to the frictional force, and the tension force on the gripper is partly equilibrated with the increased radial force provided by the object. The increased radial force will also improve the friction in turn.

The force loaded on the object is described in Fig. 5(b). First, with Eqs. (3)(5), the pressure caused by the elastic deformation of the braided gripper, i.e., the first component of the compression mentioned above P0, can be calculated. Next, the tension force on the braided gripper is studied to analyze the self-forcing mechanism. The force at x = 0 is equal to the load F since the left end of the gripper is fixed and that at x = L is zero since the right end is hanging. Due to the existence of friction, the force on the gripper damps gradually to zero from x = 0 to x = L. A differential equation of the force on the gripper in the longitudinal direction can be established as follows: 
dT=μ(Ps+P0)πDdx
(6)
It is assumed that the deformation of the gripper at the tension force does not change, with which Eq. (5) still works, and Eq. (6) can be expressed as follows: 
dT=(μ2π2Dp2TP0μπD)dx
(7)
Integrating Eq. (7), an explicit formula of the force distribution in the longitudinal direction can be acquired as follows: 
T=P0p22π[(1+2πFP0p2)eμ2π2Dp2x1]
(8)
According to Eq. (8), T damps to 0 along the longitudinal direction. When the object is to slide, the force at x = L is just to exceed 0. As a result, the holding force when the object is to slide can be determined as follows: 
Fmax=P0p22π(e2π2μDLobjp21)
(9)
The large range of holding force is achieved due to the compression Ps caused by the self-forcing mechanism. When the load is small, the self-forcing does not function, and only P0 constrains the object. As a result, light and fragile/deformable objects are likely to be grasped with little damage. In this situation, the holding force on the object is the minimum and can be determined as follows: 
Fmin=πDobjLobjP0μ
(10)
When releasing the object, the release force can be applied to the right end of the braided gripper to force it to deploy. When the diameter of the braided gripper is larger than that of the object, the object can be removed easily. During this process, the force is only used to overcome P0, guaranteeing an easy release. The release force can be calculated as follows: 
Frelease=P0p2/2π
(11)

Experimental Setup and Finite Element Modeling

Holding Force Tests.

To evaluate the self-forcing mechanism of the braided gripper, holding force tests were conducted on an Instron 5982 testing machine. Nylon PA66 fiber, whose Young's modulus was tested to be 3498.6 Mpa through tensile tests, was selected for the fabrication of the braided gripper with the 3D braiding machine. Cylindrical objects were fabricated with ABS by 3D printing. The experimental setup is illustrated in Fig. 6. The cylindrical object with a slim handle for clamping was put in the gripper previously. Compared with the inner diameter of the braided gripper, the handle was smaller in size and had no effects on the experimental results. One end of the braided gripper was fixed with a clamp, and the other was free. The object was forced upward by the other clamp connected to a load cell. Displacement control was applied in the experiments, and the loading rate was set as 4 mm/min to avoid dynamic effects. A braided gripper grasping objects with different sizes was tested, and the parameters are listed in Table 1.

Universal Grasping Tests.

A braided gripper was fabricated and mounted on a KUKA robot arm to test the universal grasping capability, as shown in Fig. 7(a). The gripper was actuated with four tension wires tied to the gripper's free end to achieve its deployment and bending. The actuation system is illustrated in Fig. 7(b), which contains a four-axis controller, four actuators, and four stepping motors to control the wires' stressing and relaxing. The gripper bent when only one wire was tensioned and deployed when all four wires were stressed. Objects with different properties were grasped with the gripper to test the capacity of universal grasping.

Finite Element Modelling.

To understand the self-forcing mechanism of the braided gripper in more detail, the holding force tests were numerically simulated using commercial finite element code abaqus/explicit [32]. The numerical model is shown in Fig. 8(a), in which three parts were established, including a braided gripper, twelve arc opening plates, and a cylindrical object, to model the tests. To stagger the helical track of the fibers at the intersections, sinusoidal disturbances were added in the radial direction to the helixes as introduced by Alpyildiz [33]. In this study, matlab was used as a preprocessor to build the geometrical models of the braided gripper. The element length was set with matlab codes, after which nodes and element numbers of the braided gripper could be obtained. Thus, an orphan mesh part was built and imported into abaqus. Beam element, B31, was used to mesh the gripper. Both the opening plates and the objects were modeled with shell elements and set as rigid bodies. The objects were partitioned and set with different surface properties. The first part was frictional with a coefficient of 0.2, whereas the last one was frictionless, which had no effects on the holding force, and was only used as a guiding part to guarantee the convergence of the numerical analysis.

Two analysis steps were defined to model the testing process. The first step (shown in Fig. 8(b)) was to deploy the gripper. In this step, the object was inactive, and the arc opening plates moved in the radial direction to deploy the braided gripper to contain the object. The second step (shown in Fig. 8(c)) was to test the maximum holding force, in which the opening plates were removed, and the object was activated. A prescribed displacement was assigned to the free degree of freedom of the object to control its movement in the longitudinal direction, and smooth amplitude definition built in abaqus was assigned to control the rate.

According to convergence tests prior to the analysis, a mesh size of 0.2 mm for the braided gripper and step times of 0.02 s and 0.1 s for the two steps yielded satisfactory results. Displacement and reaction force of the object were recorded during the analysis.

Results and Discussion

Self-Forcing Mechanism of the Braided Gripper.

Experiments and numerical simulations of a gripper grasping objects with three different sizes were studied to demonstrate the self-forcing mechanism. The experiments were conducted three times for each object, and the repeated results showed good consistence. The experimental force versus displacement curves are presented in Figs. 9(a)9(c). Comparing the curves for the three objects, the maximum holding force is found to increase with the size of the object. Besides, the reaction force increases quickly at first and then fluctuates periodically. In the first step, no sliding between the gripper and the object appears, and the displacement is caused by the elongation of the gripper. When the force exceeds the holding capacity of the gripper, sliding occurs. Due to the waved inner surface of the braided gripper, the force drops sharply and then increases gradually. The regular mesh configuration of the braided gripper leads to a periodical fluctuation of the curve. Numerical results are also drawn in the same figure and show the same tendency with the experimental ones. The forces at the crests are recorded, and the error bars representing the extrema are shown in Fig. 9(d). The average of the forces are calculated as the maximum holding force and listed in Table 2. The average error between the experimental and the numerical results is 14.38%. Also, theoretical results calculated with Eq. (9) are obtained, and the error between the experimental and the theoretical results is 14.82%. The minimum holding forces of the three objects are theoretically calculated to be 1.18 N, 3.32 N, and 4.98 N, which are, respectively, only 67.8%, 57.8%, and 45.1% of their theoretical maximum holding force, validating the large range of the holding force.

Effects of Design Parameters on the Maximum Holding Force.

The maximum holding force is derived from the self-forcing mechanism. To investigate the effects of the parameters on the maximum holding force, a set of numerical models were built and analyzed. All the grippers had the same length of 120 mm and diameter of 20 mm. Nylon material with the Young's modulus of 3498.6 Mpa was still adopted. Other design parameters were varied and divided into two groups. One was the properties of the gripper, including d, n, and β. The other was the properties of the object, including Lobj, Dobj, and μ. The varied parameters of the models are listed in Table 3. The maximum holding forces were numerically analyzed and theoretically calculated with Eq. (9), and the results are presented in Figs. 10 and 11.

First, the effects of the gripper's properties are numerically analyzed with models in group A, B, and C, respectively, for d, n, and β, and the results are shown in Fig. 10. It can be seen that the force increases sharply with d. The force is 0.44 N at d = 0.6 mm and 14.4 N at d = 1.2 mm. This is caused by the improvement of the strength of the gripper, which is linear with I=πd4/64 according to Eq. (4). A larger gripper strength guarantees a higher compression at the same deformation, also a higher holding force. The other two parameters affect the holding capability in the same manner. According to Eq. (4), the strength of the gripper is positively correlated with n, whereas negatively correlated with β within the range studied here. This is also the case of the holding capability as shown in Figs. 10(b) and 10(c). Theoretical results calculated with Eq. (9) are also drawn in Fig. 10, which show great consistence with the numerical results.

Subsequently, the effects of the properties of the object are numerically investigated with models in group D, E, and F, respectively, for Dobj, Lobj, and μ, and the results are presented in Fig. 11. As can be seen from Fig. 11(a), the force increases sharply with Dobj. This is mainly caused by the higher compression at larger deformation of the gripper. Besides, the results in Figs. 11(b) and 11(c) show that the force increases with Lobj and μ, and the tendency is nearly the same. This is owing to the increase in friction and consistent with Eq. (9). Theoretical results are also obtained with Eq. (9) and presented in Fig. 11, and a good match between numerical and theoretical results is obtained.

Grasping Objects With Different Properties.

To demonstrate the feasibility of the new design, a braided gripper with a length of 200 mm and an inner diameter of 18 mm was fabricated and mounted on a KUKA robot arm to grasp different objects. The gripper was made of 22 nylon fibers and only weighed 7 g. According to Eqs. (9)(11), the maximum holding force, the minimum holding force, and the release force on each wire are 4.78 N, 2.76 N, and 0.76 N, respectively, when the gripper grasps a tubular object with a length of 50 mm and a diameter of 50 mm at a friction coefficient of 0.3. It shows a powerful grasping, a great force adaptivity, and an easy release. The grasping procedure is described in Figs. 12(a)12(d). Its normal state is shown in Fig. 12(a). To contain the object, it deploys at the action of the four transmission wires (see Fig. 12(b)). Next, the robot arm is moved to contain the object as shown in Fig. 12(c). Relaxing the transmission wires, the gripper covers the surface of the object and grasps it tightly, achieving grasping. Finally, the robot arm is moved again to lift the object as shown in Fig. 12(d).

Grasping fragile and deformable objects has always been a challenge. Grasping tests are conducted on a fragile grape and a deformable jelly, and the results are presented in Figs. 12(e) and 12(f), respectively. For the self-forcing mechanism, the two objects were successfully grasped without damage. In addition, the gripper forms a circular profile with a diameter of 60 mm, facilitating grasping of the objects no matter the contacting surface is smooth or angular, and the maximum weight among the grasped objects reaches 350 g. The grasping tests indicate that the braided gripper has great potentials as an effective soft gripper.

Discussion.

The analysis above validates the self-forcing mechanism of the braided gripper, in which the holding force increases with the load. As a result, a larger holding force can be exerted on heavy objects, whereas no excessive force is generated for fragile and deformable objects. This property makes the braided gripper a universal soft end effector that is able to deal with a wide range of objects with varying properties. Besides, the large deployable ratio helps to grasp objects of various shapes and sizes. The braided gripper has a great design tailorability due to the large number of design parameters, light weight, and low cost. All of these facilitate engineering application of the new device. However, similar to other grippers, the braided gripper may be less functional in certain occasions, such as grasping sheet objects, tiny granular objects, or objects with smooth surface.

Conclusion

In this paper, a new robotic gripper based on the braided tube, which shows great deployability and self-forcing mechanism, is developed. Taking the cylindrical object as an example, the self-forcing mechanism, in which the holding force increases with load, has been theoretically analyzed and explicit formulas have been established to determine the holding force range based on the open-coiled spring theory. Experimental tests and numerical simulations have also been conducted to understand the self-forcing mechanism. The results show that a holding force increase by 120% is obtained due to self-forcing. Furthermore, a parametric analysis has been conducted with both numerical and theoretical methods. It has been found that a stronger gripper with larger fiber number, larger fiber diameter, and smaller braiding angle, and a rough object with larger size, lead to a higher grasping force. Finally, a braided gripper has been fabricated and mounted on a KUKA robot arm and successfully grasped a fragile grape and a deformable jelly. Altogether this work shows that the braided tube has great potential as a robotic gripper. In the future, improving the adaptability of the braided gripper in some special occasions, such as the grasping of sheet objects and smooth objects, will be the focus. Besides, the transmission system will also be improved for easy grasping at a bent configuration.

Funding Data

  • National Natural Science Foundation of China (Grant No. 51475323)

  • National Key R&D Program of China (Grant No. 2017YFC0110401)

  • National Natural Science Foundation of China (Grant Nos. 51575377, 51721003, and 51520105006)

Nomenclature

     
  • c =

    number of the coils of the gripper

  •  
  • d =

    diameter of the fiber

  •  
  • l =

    fiber length

  •  
  • n =

    number of the fiber

  •  
  • p =

    pitch of the gripper

  •  
  • D =

    diameter of the gripper

  •  
  • E =

    Young's modulus of the fiber

  •  
  • F =

    longitudinal load

  •  
  • G =

    rigidity modulus of the fiber

  •  
  • I =

    moment of inertia of the fiber

  •  
  • L =

    length of the gripper

  •  
  • P =

    radial pressure on the gripper

  •  
  • T =

    tension force on the gripper

  •  
  • Di =

    inner diameter of the gripper

  •  
  • Do =

    outer diameter of the gripper

  •  
  • Dobj =

    diameter of the object

  •  
  • Fmax =

    maximum of the holding force

  •  
  • Fmin =

    minimum of the holding force

  •  
  • Frelease =

    release force

  •  
  • Lobj =

    length of the object

  •  
  • P0 =

    radial pressure caused by the elastic deformation

  •  
  • Ps =

    radial pressure caused by the self-forcing mechanism

  •  
  • β =

    braiding angle

  •  
  • μ =

    friction coefficient

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