Endoskeleton Soft Multi-Fingered Hand with Variable Stiffness

Abstract

The use of a soft multi-fingered hand in handling fragile objects has been widely acknowledged. Nevertheless, high flexibility often results in decreased load capacity, necessitating the need for variable stiffness. This article introduces a new soft multi-fingered hand featuring variable stiffness. The finger of the hand has three chambers and an endoskeleton mechanism. Two chambers facilitate bending and swinging motions, whereas the third adjusts stiffness. An endoskeleton mechanism is embedded in the third chamber, and the friction between its moving parts increases as negative air pressure rises, causing the finger's stiffness to increase. This mechanism can alter its stiffness in any configuration, which is particularly useful in manipulating irregular-shaped fragile objects post-grasping. The effectiveness of the proposed soft multi-fingered hand is validated through five experiments: stiffness adjustment, finger stiffening under a specific orientation, bulb screwing, heavy object lifting, and bean curd grasping. The results demonstrate that the proposed soft multi-fingered hand exhibits robust grasping capabilities for various fragile objects.

Introduction

The emergence of soft robotics has led to the development of various soft multi-fingered hands by researchers.^1–6 These soft hands are typically constructed using flexible materials, providing increased degrees of freedom (DOFs) and passive compliance compared with conventional rigid robotic hands, which can be highly adaptable to the uncertainties associated with the shape, size, and pose of objects being grasped and, therefore, have broad applications in various fields such as rescue operations,⁷ medical procedures,⁸ rehabilitation,^9,10 human-machine interaction,¹¹ and fragile object handling.¹²

For various tasks, soft hands must exhibit not only adequate flexibility to conform to the shape of the object but also sufficient rigidity to maintain their attitude while holding the object. However, the flexibility of the soft hands does not always generate variable grasping force for a given attitude,^13,14 and the alteration of grasping force is often coupled with finger deformation. Consequently, when dealing with large and heavy fragile objects, it becomes necessary to adjust the hand's postgrasping stiffness while maintaining its attitude, thus emphasizing the significance of variable stiffness for complex grasping tasks.^15,16 To address the problem of inherent low stiffness in soft hands, researchers have used several methods to adjust the stiffness of soft hands. Among these methods, the insertion of additional structures into the soft hand has been proven effective in adjusting the stiffness, and these structures can be primarily categorized into three classical types: jamming technology, mechanical constructions, and biomimetic mechanisms.

Jamming technology¹⁷ offers numerous advantages in designing the variable stiffness soft hands, including simple structure, quick response, and a wide range of stiffness variation. This approach involves loosely packing friction fillers within an enclosed membrane of the soft hand, enabling the system to conform to contact surfaces with compliance and flexibility. By reducing pressure using a vacuum pump, the particles tightly jam together, resulting in high stiffness. Particles,^18–20 layers,^21,22 and fibers²³ are widely utilized as inner fillings. In a notable study by Yang et al.,²⁴ a soft robotic finger was developed, integrating particle jamming and layer jamming to imitate finger joints and bonds, respectively. This innovative approach achieved an impressive 5.52 times enhancement in stiffness at the primary position. Kim et al.²⁵ developed a layer jamming mechanism to realize stiffness modulation by exploiting the friction present between layers of thin material.

Gao et al.²⁶ introduced a cable-driven gripper with three fingers incorporating layer jamming, resulting in significant load capacity enhancement. Zeng and Su²⁷ presented a variable stiffness soft hand utilizing layer jamming technology. The stiffness of the soft hand is adjusted by sealing layers of jamming sheets within a vacuum bag. This innovative soft hand design demonstrates the capability to grasp heavy objects weighing 6–10 kg.

The second type is the use of specifically designed mechanical constructions to alter the stiffness of soft hands. Hybrid-driven or stiffness-enhancing mechanisms are typically incorporated into soft grasping hands to enhance the stiffness. Cui et al.²⁸ added a rigid slider to the soft actuator to enhance rigidity, which can grasp with diameters ranging from 0.5 to 180 mm and 5.5 times the gripper's weight. Zhang et al.²⁹ combined pneumatic and ribbon actuation to increase the gripper's stiffness. The bending deformation and the stiffness modulation of the soft finger are uncoupled, resulting in both high flexibility and good variable stiffness. Based on McKibben muscles, Al Abeach et al.³⁰ proposed a variable stiffness soft gripper in which the fingers' bending stiffness can be increased by >150%. The proposed soft gripper can adjust its stiffness without a resulting change in finger position.

The third type is the biomimetic mechanism that is inspired by bionic behavior. Many creatures in nature have an ingenious variable stiffness mechanism, and this biomimetic mechanism was introduced into the design of the variable stiffness soft hand by researchers. Shiva et al.³¹ designed a soft actuator inspired by octopus muscles, which had tendons and three inner chambers to control motion and change the overall stiffness, respectively. Chellattoan and Lubineau³² manufactured a novel stretchable fiber with variable stiffness inspired by the longitudinal muscle fibers present in the skins of worms. Sun et al.³³ proposed a pangolin scales-inspired endoskeleton soft gripper with variable stiffness. The proposed gripper adjusts its stiffness by utilizing the frictional force generated through negative pressure on the endoskeleton.

Inspired by the human finger, Yan et al.³⁴ developed a highly innovative soft finger with variable stiffness and dual-mode morphing. This remarkable finger incorporates conductive thermoplastic starch polymers into segmented pneumatic soft actuators, mimicking the structure of biological phalanges. The stiffness of these actuators can be independently adjusted by utilizing their customized thermomechanical properties. The proposed soft gripper successfully lifts a dumbbell weighing 1460 g with an impressive load/weight ratio of 7.6.

In previous research works, some soft hands can only achieve bending motion and adjust bending stiffness for simple grasping tasks. On the contrary, some mechanisms were capable of swinging motion but lacked the ability to adjust stiffness. This limitation restricted their application to screw fragile objects under variable stiffness. This article introduces a new soft multi-fingered hand that takes inspiration from the biological structure of the human hand to overcome its limitations. It incorporates an endoskeleton design to adjust the stiffness. The endoskeleton mechanism is embedded into each finger, increasing friction and stiffness of the finger as negative air pressure rises.

The proposed soft multi-fingered hand not only has the ability to actively realize bending and swinging motions but also allows for adjusting bending and swinging stiffness simultaneously. This feature provides high dexterity and allows for stiffness adjustments in any hand configuration, making it suitable for grasping and screwing fragile and irregular-shaped objects. Our article makes the following contributions to the research in variable stiffness soft multi-fingered hands: (1)

Design and Fabrication: Each finger of the hand features three chambers that can realize both bending and swinging motions. The specially designed endoskeleton mechanism in the vacuum chamber is used to adjust the finger's stiffness. The fingers are fabricated using injection molding, whereas the endoskeleton mechanism is printed in three-dimensional form.

(2)

Theoretical analysis: The bending and swinging angle models are derivate, the frictional torque model of the endoskeleton mechanism unit is established, and the stiffness of the finger is analyzed.

(3)

Experiment varication: The performance of the proposed soft multi-fingered hand is evaluated through various experiments.

Design and Fabrication of Soft Multi-Fingered Hand with Variable Stiffness

Design of the soft finger

The human hand can be considered as a rigid-flexible coupling mechanism, where the endoskeleton and joints form a rigid mechanism, whereas the muscles and skin make up flexible tissues that wrap the skeleton (Fig. 1A). According to the positional relationship between the skeletal elements, the finger joints primarily consist of the distal interphalangeal (DIP) joint, proximal interphalangeal (PIP) joint, and metacarpophalangeal (MCP) joint. The DIP joint and PIP joint only have one rotational DOF, whereas the MCP joint has two rotational DOFs.³⁵ Based on this definition, the finger can achieve bending motion in the direction where the three joints share the same DOF. In addition, in the other DOF of the MCP joint, the finger can perform the swinging motion. This coupling mechanism not only provides good flexibility but also has a high load capacity. The human hand can flexibly interact with the outside world while ensuring structural strength and load capacity.

FIG. 1.

The proposed endoskeleton multi-fingered hand with variable stiffness. (A) Muscle-endoskeleton structure of the human hand. (B) The structure of the proposed endoskeleton soft finger with variable stiffness. (C) The variable stiffness endoskeleton mechanism chain. (D) Endoskeleton mechanism unit in the free state. (E) Motion types of the mechanism unit. (F) Mechanism unit in the compressed state.

In this article, an endoskeleton soft multi-fingered hand that adopts a similar rigid-flexible coupling structure was designed, and the fabrication of the endoskeleton soft hand was conducted (Supplementary Note S1 in the Supplementary Data and Supplementary Fig. S1). The structure of the endoskeleton soft finger with variable stiffness was designed (Fig. 1B). It comprises three parallel chambers. The left and right air chambers are two typical elbow pneumatic actuators used for generating bending and swinging motions under positive air pressure. When the positive pressure input is the same in both chambers of the soft finger, the soft finger undergoes expansion and deformation to an equal extent. In each positive pressure chamber, the upper inflatable chamber inflates and expands, whereas the outer walls between the inflatable chambers mutually compress each other, resulting in the finger achieving bending motion.

In addition, when there is a difference in the positive pressure input, the expansion and deformation of the left and right positive air chambers of the soft finger are inconsistent, enabling the soft finger to perform a swinging motion.

The negative pressure chamber, which contains an embedded endoskeleton variable stiffness mechanism, is used for stiffness adjustment. The adjustment of stiffness in the soft finger is accomplished through the utilization of friction principles. The variable stiffness endoskeleton mechanism comprises a series of 2-DOFs mechanism units (Fig. 1C). Each mechanism unit has two revolute joints, C1 and C2, where axis 1 of C1 is fixed with link 1, and axis 2 of C2 is fixed with link 2. A soft sleeve holder is used to connect all parts of the unit (Fig. 1D). When the mechanism is in the free state, the two separated axle sleeves are not compressed with axis 1, and axle sleeves 1 and 2 are not compressed with the two contact planes of link 2.

In this case, the mechanism is free to rotate around these two revolute joints, which can be adaptive to the bending and swinging motion of the soft finger (Fig. 1E), and the soft finger exhibits the lowest stiffness. When the third chamber uses negative pressure, the compressive force provided by the negative pressure chamber to the two separated axle sleeves and axis 1, as well as the two contact planes of link 2, causes the friction between the two separated axle sleeves and axis 1, and the friction between the two contact planes of the two separated axle sleeves with respect to link 2 to increase. This enables the mechanism unit to be securely locked in this state (Fig. 1F). Moreover, the soft finger exhibits maximum stiffness.

Theoretical Modeling of the Endoskeleton Soft Multi-Fingered Hand

To analyze the proposed endoskeleton multi-fingered hand's bending and swinging motion under the action of the two position pressure air chambers, in this part, the bending and swinging angle modeling are established based on the Euler–Bernoulli equation.^36–39 Furthermore, to analyze the variable stiffness ability in the bending and swing direction, we first establish the friction torque model of the endoskeleton mechanism and then establish the stiffness model of the proposed endoskeleton multi-fingered hand by simplifying the soft finger as a cantilever beam.⁴⁰

Finger's bending and swinging angle modeling

As for the proposed endoskeleton soft multi-fingered hand, when the two positive pressure chambers in each finger are subjected to equal input pressure, the fingers will bend without any swinging motions. Based on the derivation process in Supplementary Note S3 in the Supplementary Data, the analytical model for the steady-state bending angle of the finger $θ_{b}$ can be obtained as follows:

where n is the number of the chambers, $A_{b w i}$ ( $A_{b w 1}$ and $A_{b w 2}$ ) is the solid cross-sectional area, $A_{b i}$ ( $A_{b 1}$ and $A_{b 2}$ ) is the cross-sectional area of the airflow area. The point $Q_{b i}$ ( $Q_{b 1}$ and $Q_{b 2}$ ) is the center of pressure, the point $N_{b i}$ ( $N_{b 1}$ and $N_{b 2}$ ) is in the plane where the neutral axis of the cross-section is located, and $e_{b i}$ ( $e_{b 1}$ and $e_{b 2}$ ) is the effective distance between points $Q_{b i}$ and $N_{b i}$ . ${M_{b}}_{i}$ ( $M_{b 1}$ and $M_{b 2}$ ), E, and $I_{b i}$ ( $I_{b 1}$ and $I_{b 2}$ ) are bending moment, modulus of elasticity, and area moment of inertia of the deflected finger, respectively.

As for the proposed endoskeleton soft multi-fingered hand, when the two positive pressure chambers of each finger have different input pressure, that is, $P = P_{1} - P_{2} > 0$ , the fingers will swing toward the side where P₂ is input. Based on the derivation process in Supplementary Note S3 in the Supplementary Data, the analytical model for the steady-state swinging angle θ_s of the finger can be obtained as follows:

where n is the number of the chambers, $A_{s w i}$ ( $A_{s w 1}$ and $A_{s w 2}$ ) is the solid cross-sectional area, A_s( $A_{s 1}$ and $A_{s 2}$ ) represents the cross-sectional area of the side through which a pressure of P (kPa) is applied. The point $Q_{s i}$ ( $Q_{s 1}$ and $Q_{s 2}$ ) is the center of pressure, the point $N_{s i}$ ( $N_{s 1}$ and $N_{s 2}$ ) is in the plane where the neutral axis of the cross-section is located, and $e_{s i}$ ( $e_{s 1}$ and $e_{s 2}$ ) is the effective distance between points $Q_{s i}$ and $N_{s i}$ . $M_{s i}$ ( $M_{s 1}$ and $M_{s 2}$ ), E, and $I_{s i}$ ( $I_{s 1}$ and $I_{s 2}$ ) are swinging moment, modulus of elasticity, and area moment of inertia of the deflected finger, respectively.

Based on the measuring method in Supplementary Note S9 in the Supplementary Data, the experimental and theoretical results of the bending and swinging angles under different input pressures can be obtained (Supplementary Fig. S2D.i, D.ii). The experimental results indicate that the developed finger's bending and swinging angle modeling can successfully predicate the finger's bending and shaking angles during inflating and deflating processes.

Frictional torque modeling of the endoskeleton mechanism

The chamber containing the endoskeleton mechanism is designed (Fig. 2A.i) with a soft chamber made of silicone material. In its free state, the air pressure in the negative pressure chamber is at atmospheric pressure, and there is no compressive force acting on the axle sleeves. As a result, there is no frictional force on the contact surface of the endoskeleton mechanism, making the endoskeleton mechanism as soft as the chamber. However, as the air pressure in the negative pressure chamber decreases, a compressive force acts on the axle sleeves, generating a sliding friction force on the contact surface of the endoskeleton mechanism. This enables the device to change its stiffness by controlling the negative air pressure in the negative pressure chamber.

FIG. 2.

Variable stiffness principle of the finger. (A) The variable stiffness endoskeleton mechanism. (A.i) The negative pressure chamber. (A.ii) Frictional torques for a variable stiffness unit. (A.iii) The geometry of an axle sleeve. (B) Stiffness analysis of the finger. (B.i) Bending stiffness analysis. (B.ii) Swinging stiffness analysis.

Based on the bending and swinging mobility and the contact surface of the variable stiffness of the endoskeleton mechanism, each variable stiffness mechanism unit has a bending frictional torque $M_{f b}$ and a swinging frictional torque $M_{f s}$ (Fig. 2A.ii). The bending frictional torque $M_{f b}$ of a variable stiffness unit is generated in the cylindrical axle surface and the two axle sleeves. The swinging frictional torque $M_{f s}$ is generated on the contact planes of link 2 with the two-axle sleeves. According to the derivation process in Supplementary Note S4 in the Supplementary Data, the bending friction torque $M_{f b}$ can be obtained as follows: $M_{f b} = 2 c μ θ_{k} R_{_{1}}^{2} L_{1} Δ P$ (3)

where $Δ P$ is the pressure difference between the inner and outer of the negative pressure chamber, c is the factor used for calculating the contact area, μ is the surface friction coefficient of the mechanism unit. θ_k, R₁, and L₁ are the geometrical parameters (Supplementary Table S1).

Since the rotational scope is small for the mobility of the swinging frictional torque $M_{f s}$ , it is approximatively assumed that the contact area of one axle sleeve with respect to link 2 is constant, which is a red color area (Fig. 2A.iii). Based on the deviation process in Supplementary Note S4 in the Supplementary Data, the swinging frictional torque M₂ can be given as: $M_{f s} = 8 (\int_{0}^{γ} \int_{R_{2}}^{\frac{L_{3}}{2 sin α}} μ Δ P ρ^{2} d α d ρ + \int_{γ}^{\frac{π}{2}} \int_{R_{2}}^{\frac{L_{2}}{2 cos α}} μ Δ P ρ^{2} d α d ρ)$ (4)

where , $α$ is the polar angle ρ with respect to the x axis, and the friction coefficient of the sliding surface of variable stiffness units is μ.

The revolute joints C1 and C2 of each endoskeleton mechanism unit have different maximum static friction torque thresholds depending on the level of contact pressure. If the torque generated by the outer load force exceeds this friction torque threshold, the mechanism begins to rotate. Therefore, the maximum static friction torque threshold represents the stiffness of the variable stiffness unit, and the stiffness is adjustable by changing the contact pressure through the air pressure difference $Δ P$ between the inner and outer parts of the negative pressure chamber. To determine the stiffness property of the variable stiffness unit at different air pressures, simulations were conducted using ABAQUS software (Supplementary Fig. S3 and Supplementary Note S6 in the Supplementary Data).

Stiffness analysis for the soft fingers

The frictional torques $M_{f b}$ and $M_{f s}$ are proportional to the pressure difference $Δ P$ and directly affect the stiffness of the endoskeleton mechanism. In other words, if the bending torque generated by load force is smaller than $M_{f b}$ , or the swinging torque generated by the load force is smaller than $M_{f s}$ , the endoskeleton mechanism will work in the rigid status, and no bending and swinging mobility can be generated. The stiffness of the endoskeleton mechanism refers to the structural stiffness, which enables it to resist deformation and maintain its shape. Without this structural stiffness, the endoskeleton mechanism would only function in a soft state and would be prone to bending or swinging.

When a load $F_{T b}$ is applied to the finger trip, if $F_{T b}$ is large than the blocked force of the soft finger, the soft will generate deformation $Δ d_{b}$ in the bending direction (Fig. 2B.i). Based on the deviation process in Supplementary Note S5 in the Supplementary Data, the analytical model of the finger's bending stiffness can be deviated as follows: $K_{b} = \frac{F_{T b}}{Δ d_{b}} = \frac{3 E I_{b}}{L_{b}^{3}}$ (5)

where L_b represents the length of the finger, and I_b represents the area moment of inertia of the bending finger.

Similarly, when a load $F_{T s}$ is applied to the finger trip, if $F_{T s}$ is large than the blocked force of the soft finger, the soft will generate deformation $Δ d_{s}$ in the swinging direction (Fig. 2B.ii). Based on the deviation process in Supplementary Note S5 in the Supplementary Data, the analytical model of the finger's swinging stiffness can be deviated as follows: $K_{s} = \frac{F_{T s}}{Δ d_{s}} = \frac{3 E I_{s}}{L_{s}^{3}}$ (6)

where L_s represents the length of the finger, and I_s represents the area moment of inertia of the swinging finger.

Experiments and Analysis

Stiffness adjustment experiment

The proposed soft hand was fabricated based on the manufacturing processes in Supplementary Note S1 in the Supplementary Data and installed on the UR5 robot arm (Fig. 3). The experimental setup was installed as given in Supplementary Figure S4A and described in Supplementary Note S7 in the Supplementary Data. One of the key features of the proposed endoskeleton soft hand is its ability to adjust both bending and swinging stiffness. To verify the soft finger's bending and swinging stiffness adjustment ability, various experiments were carried out to measure the load force at a particular displacement. Before conducting various experiments, the fatigue test was performed on the soft fingers (Supplementary Note S8 in the Supplementary Data). The fatigue test involved repeating inflation and deflation cycles a total of 2750 times. This test result illustrates the relatively high durability of the proposed soft finger, as it endured a significant number of actuation cycles before failure.

FIG. 3.

The prototype of the endoskeleton soft multi-fingered hand with maximum grasping diameter of 160 mm.

The bending and swinging stiffness adjustment experiment of a single finger is first carried out to demonstrate the finger's stiffness adjustment ability (Supplementary Note S10 in the Supplementary Data). The single finger's bending stiffness adjustment experimental setup is given in Supplementary Figure S4D.i. The soft finger was placed horizontally, and the rigid hub was fixed to a vertically placed linear guide, whereas the fingertip was connected to a tensiometer via a metal wire. The experimental and theoretical load-displacement curve results of the bending stiffness adjustment experiment are given in Figures 4A.i and A.ii, respectively, and Figure 4A.iii shows the experimental and theoretical bending stiffness adjustment range of the soft finger. The maximum stiffness of the soft finger is 0.0817 N/mm, which is 1.70 times greater than its original value.

FIG. 4.

Stiffness adjustment experiment. (A) Experiment and theoretical load-displacement curve under different negative pressure inputs when finger bending. (A.i) Experiment results. (A.ii) Theoretical results. (A.iii) Experiment and theoretical results of the stiffness adjustment range. (B) Experiment and theoretical load-displacement curve under different negative pressure inputs when finger swinging. (B.i) Experiment results. (B.ii) Theoretical results. (B.iii) Experiment and theoretical results of the stiffness adjustment range. (C) The stiffness adjustment ability of the proposed soft hand. (C.i) The swinging stiffness adjustment experiment results of the two-fingered hand. (C.ii) The bending stiffness adjustment experiment results of the four-fingered hand.

The single finger's swinging stiffness adjustment experimental setup is given in Supplementary Figure S4D.ii. The soft finger was placed horizontally, and the rigid hub was fixed to a vertically placed linear guide, whereas the fingertip was connected to a tensiometer via a metal wire. Figures 4Bi and Bii demonstrate the experimental and theoretical load-displacement curve results of the swinging stiffness adjustment experiment, and Figure 4B.iii shows the experimental and theoretical swinging stiffness adjustment range of the soft finger. The maximum swinging stiffness of the soft finger is 0.0393 N/mm, which is 1.5 times greater than its original value.

Subsequently, experiments were conducted to evaluate the stiffness adjustment ability of the proposed soft hand through two-fingered and four-fingered configurations (Supplementary Notes S11 and S12 in the Supplementary Data). The experimental setups for adjusting the hand stiffness of the two-fingered and four-fingered hands are illustrated in Supplementary Figure S4D.iii and D.iv, respectively. In the case of the two-fingered hand, the soft finger was positioned horizontally and secured in place using the UR5 robot arm. To measure the swinging stiffness, a foam cube was attached to a tensiometer via a metal wire. For the four-fingered hand, the soft finger was oriented vertically and also fixed using the UR5 robot arm.

Similarly, a foam cube was connected to a tensiometer using a metal wire to assess the bending stiffness. The experimental outcomes revealed that the two-fingered hand achieved a maximum swinging stiffness of 0.0776 N/mm (Fig. 4C.i), whereas the four-finger hand exhibited a maximum bending stiffness of 0.7226 N/mm (Fig. 4C.ii). Hence, it can be concluded that the proposed soft hand effectively enhances the rigidity of its fingers in both bending and swinging directions.

The results show that the stiffness characteristics of the soft finger are improved with an increasing pressure difference between the inner and outer of the negative pressure chamber. This suggests that the proposed soft multi-fingered hand not only has the ability to actively realize bending and swinging motions but also allows for adjusting the finger's bending and swinging stiffness.

Finger stiffening experiment

The variable stiffness of the endoskeleton soft hand is achieved through the adjustable sliding friction, allowing the soft hand to attain a “self-locking” effect when negative pressure is applied to the negative pressure chamber. Therefore, the soft fingers can maintain their shape under some negative pressure input, effectively transitioning from a “soft” status to a “rigid” status. In this experiment, a single finger was used to demonstrate the self-locking ability of the finger under constant curvature and varying curvature configurations. When the negative pressure input was applied to the negative pressure chamber, the finger can successfully keep its shapes under constant and varying curvature configurations when the finger is bending (Fig. 5A–C and Supplementary Movie S1) or swinging (Fig. 5D–F and Supplementary Movie S1). The “self-locking” characteristic enables the soft fingers to be maintained in a fixed shape by applying a given negative pressure input to the negative pressure chamber, hence allowing us to adjust the stiffness of the soft finger in any posture. This feature is particularly useful for manipulating irregular-shaped objects.

FIG. 5.

Finger stiffening under the given attitude. (A, B) The soft finger maintains constant curvature in bending posture. (C) The soft finger maintains varying curvature in a bending posture. (D, E) The soft finger maintains constant curvature in a swinging posture. (F) The soft finger maintains varying curvature in a swinging posture.

Heavy objects lifting experiment

Grasping experiments were performed to evaluate the load capacity of the endoskeleton soft hand. Objects of different weights were used, and their weight and dimensions are given in Supplementary Table S2. The proposed hand successfully grasped a vitamin sports drink of 963 g and a coconut of 1004 g using the high stiffness grasping mode. A comparison was also made, which showed that the hand was unable to lift these two heavy objects without any negative pressure input in the variable stiffness negative pressure chamber (Fig. 6A.i, A.iii). However, when the maximum negative pressure (−99 kPa) was applied to the variable stiffness negative pressure chamber, the heavy objects could be lifted successfully (Fig. 6A.ii, A.iv and Supplementary Movie S2), indicating a significant improvement in the load capacity of the soft hand. By changing its stiffness, the soft hand was able to successfully grasp heavy objects.

FIG. 6.

Grasping experiment. (A) Heavy objects lifting experiments. (A.i) Unsuccessful grasping of vitamin sports drink. (A.ii) Successful grasping of vitamin sports drink. (A.iii) Unsuccessful grasping of coconut. (A.iv) Successful grasping of coconut. (B) Bean curd grasping experiments. (B.i) Four-fingered hand grasps bean curd failed. (B.ii) Four-fingered hand grasps bean curd successfully based on the bending stiffness adjustment. (B.iii) Two-fingered hand grasps bean curd failed. (B.iv) Two-fingered hand grasps bean curd successfully based on the swinging stiffness adjustment. (C) Bulb screwing experiment. (C.i) Two soft fingers 1 and 2 contact the bulb. (C.ii) The bulb is screwed by 20°. (C.iii) Another two soft fingers 3 and 4 contact the bulb. (C.iv) The bulb is light.

Furthermore, the grasping experiment demonstrates that the endoskeleton soft hand exhibits excellent flexibility and adaptability in gripping objects of varying sizes and shapes (Supplementary Fig. S4E.i–vi and Supplementary Note S13 in the Supplementary Data). The grasping method of the soft hand was diverse in this process. For example, when grasping small-shaped objects like mangoes, the soft hand adopted the fingertip grasping method, whereas for larger-shaped objects like coconuts, the envelope grasping method was used.

Bean curd grasping

The traditional rigid gripper is known for its ability to grasp objects stably; however, its rigid structure can potentially damage fragile and complex irregular-shaped objects during the grasping process. The endoskeleton soft hand proposed in this article overcomes this issue by combining rigid and flexible materials, resulting in both good flexibility and high load capacity. This unique rigid-flexible coupling feature of the soft hand allows for successfully grasping heavy and fragile objects such as bean curd. In the grasping experiment, the two-fingered soft hand successfully grasped a bean curd weighing 178 g, whereas the four-fingered soft hand demonstrated its capability by grasping a bean curd weighing 382 g. Initially, without negative pressure input, the soft hand failed to grasp the bean curd in both bending and swinging configurations (Fig. 6B.i, B.iii).

However, upon introducing negative pressure, the proposed soft hand can adjust the finger's bending and swinging stiffness effectively, resulting in the bean curd being grasped successfully without damage and remaining intact during the grasping process (Fig. 6B.ii, B.iv and Supplementary Movie S3). This experiment demonstrates that the proposed endoskeleton soft hand maintains its flexible grasping feature while also possessing excellent load performance through the variable stiffness endoskeleton mechanism.

Consequently, we anticipate that the endoskeleton soft hand with variable stiffness can be applied in various fields such as food processing, biomedical applications, and human–machine interaction for the successful grasping of both fragile and heavy objects.

Bulb screwing experiment

Each finger of the variable-stiffness endoskeleton soft hand possesses two DOFs, allowing the hand to perform screwing manipulations of objects through the alternate use of the bending and swinging motions of the soft fingers. The changeable stiffness of the hand enables it to have a large screwing capacity, making it especially useful for screwing fragile objects such as light bulbs.

In this experiment, a light bulb with a diameter of 100 mm is screwed by the endoskeleton soft hand (Fig. 6C). First, 80 kPa of air pressure was introduced to the left and right chambers of the two oppositely distributed soft fingers 1 and 2 to generate the bending motion required for grasping the light bulb, and negative pressure was also applied to the negative pressure chambers of these fingers 1 and 2 to ensure firm grasping of the light bulb (Fig. 6C.i). Second, the air pressure in the left chambers of the two fingers 1 and 2 was increased to 120 kPa, whereas the air pressure in the right chambers was set to atmospheric pressure. The negative pressure of the negative pressure chambers of fingers 1 and 2 was kept unchanged to provide great tangent screwing force. The light bulb was then rotated by 20° (Fig. 6C.ii). Third, fingers 1 and 2 were released by setting the air pressure to atmospheric pressure, and fingers 3 and 4 were kept in the operating state to hold the bulb firmly (Fig. 6C.iii). The other two fingers repeat the previous steps of fingers 1 and 2, and the light bulb is continuously screwed. After several operating cycles, the bulb is screwed into light up (Fig. 6C.iv and Supplementary Movie S4).

Supplementary Table S3 lists the characteristics of some typical soft variable stiffness soft hands developed in recent research. Our proposed soft hand is capable of continuously rotating fragile objects, making it particularly useful when the normal grasping force should not be too large to break the object, but the tangent grasping force should be large enough to rotate the object. Therefore, soft hands can be well applied in various flexible grasping and rotating tasks.

Conclusion and Future Works

This article presents a novel soft multi-fingered hand that uses variable stiffness to achieve high load capacity while maintaining flexibility. The finger of this hand consists of three chambers and an endoskeleton mechanism that uses the sliding friction principle to adjust stiffness. A theoretical model for stiffness was developed, and simulations were conducted to show the relationship between negative pressure and stiffness. Five experiments were conducted to demonstrate the hand's capabilities, including stiffness adjustment, finger stiffening under a given attitude, heavy object lifting, bean curd grasping, and bulb screwing. The results showed that the proposed soft multi-fingered hand significantly improves load capacity by adjusting the stiffness of the endoskeleton mechanism while maintaining flexibility. The soft hand can thus be applied in various flexible grasping and rotating tasks involving fragile objects.

Our proposed endoskeleton soft multi-fingered hand does have certain limitations. The proposed endoskeleton multi-fingered hand exists coupling between the swinging and bending motions. To maintain an effective grasping force, the bending and swinging chambers were designed with larger volumes compared with the vacuum chamber, resulting in a smaller volume for the endoskeleton mechanism itself. In addition, the low friction coefficients of the contact area in the endoskeleton mechanism units restrict the range of stiffness adjustment in our hand, which is comparatively smaller than that of some other soft multi-fingered hands. To address this challenge, our future work will focus on achieving complete decoupling of the swinging and bending motions of the soft fingers. We will actively explore materials with higher friction coefficients for constructing the endoskeleton mechanism. Simultaneously, we will optimize the volume of the three chambers in the soft hand.

Footnotes

Author Disclosure Statement

The authors declare no competing financial interests exist.

Funding Information

This work was supported by the National Key R&D Program of China (Grant No. 2022YFB4701200), National Natural Science Foundation of China (Grant No. 52335003 and No. 52075113), the Guangdong Science and Technology Research Council (Grant No. 2020B1515120064), the Shenzhen Peacock Innovation Team Project (Grant No. KQTD20210811090146075), the Shenzhen Science and Technology Program (Grant No. JCYJ20210324115811033), and the Shenzhen Natural Science Fund (Grant No. GXWD20220811151529003).

Supplementary Material

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