Hybrid Jamming for Bioinspired Soft Robotic Fingers

Introduction

The emerging soft robotics technology has changed the landscape of robotics field by offering robots with better adaptability in unstructured environments, conformability to different shaped objects, and safety during interactions with human.^1–3 Among a wide variety of soft robotic applications, soft grippers or hands have attracted lots of research interest.^4–6 Conventional rigid-bodied robotic end-effectors usually require complex sensing and control system, as well as sophisticated actuation mechanism, to perform dexterous grasping tasks or to be used in unknown environments.^7,8 In contrast, robotic grippers made of soft materials are inherently safe, easy to control, cost effective, and robust to unexpected impact benefited from its inherent compliance, which provide a promising alternative to broaden the application scenarios of robotic end-effectors such as in-home service robots where safety and adaptability are mainly concerned.

Even though soft robotic grippers have achieved rapid progress, their wider applications will require additional capabilities, including variable stiffness^9,10 and bending shape control capabilities.¹¹ The ability to control stiffness is essential for soft grippers since low stiffness state is capable of deformation and adaption with surroundings, while high stiffness state is required to exert force or maintain shape during heavy grasping. To address the problem of inherent low stiffness of soft robots, different variable stiffness methods have been investigated taking advantage of rigidity tunable materials such as shape memory polymers,^12–14 low melting point alloy,^15,16 polylactic acid (PLA),^17,18 electrorheological (ER) or magnetorheological (MR) fluids,^19,20 and jamming materials.^21,22 Among them, jamming transition phenomenon is widely used benefited from its simplicity, low cost, versatility, fast response, and possibility to customize.

Jamming phenomenon has been discussed and analyzed by physicists as a type of phase transition²³ and it was until 2010 that Brown et al. applied the particle jamming (also called “granular jamming”) process into a universal soft gripper, which can grasp lots of irregular shaped objects without the need of active feedback.²¹ Since then, various robotic applications have been reported using the particle jamming technology, for example, multifingered gripper,²⁴ highly articulated robotic manipulator,²⁵ ground rolling robot,²⁶ wearable joint support,²⁷ and prosthesis.²⁸ While particle jamming possesses high deformability in its fluid state and dramatic stiffness enhancement in its solid state, it usually requires a substantial volume for particle materials. Layer jamming (also called “laminar jamming”), by contrast, is more compact and lightweight, consisting of a laminate of flexible sheets. Utilizing layer jamming method, researchers have created robotic applications such as a flexible robotic manipulator,²⁹ soft fingers and grippers,^30,31 and wearable devices.³² However, the deformability of layer jamming is not as good as particle jamming since particles can flow like fluid in low stiffness state. The comparison of particle jamming and layer jamming indicating their different characteristics is listed in Table 1. We can see that both particle jamming and layer jamming methods can achieve considerable stiffness variation ratio. Their difference in passive deformation, required volume, and resistance to bending moments can be utilized to function as different parts of a bioinspired robotic finger, which will be explained in detail in the next section.

Shape control of soft fingers is also important for dexterous grasping and manipulation tasks. The finger shape should be different for a power grasp of a large object and a pinch grasp of a small object. Currently, most soft fingers or actuators are designed with single degree of freedom (DOF) for ease of fabrication and design,^33,34 significantly lower than rigid robotic fingers which often have multi-DOF for dexterous manipulation. Some researchers investigated multi-DOF soft finger enabled by multichamber design to realize soft finger shape control.³⁵ They have also fabricated a robotic hand with the fingers achieving good grasping capabilities and in-hand manipulation. However, this design complicates the fabrication process, and stiffness tuning has not been mentioned.

In this research, we propose a soft robotic finger based on hybrid jamming method to address the challenges of both variable stiffness and shape control. Hybrid jamming here refers to the integration of particle jamming and layer jamming in one structure. The finger has a soft actuator for actuation and a hybrid jamming structure for stiffness tuning and shape control. This study adopts soft pneumatic actuator for easy control. Of course, this hybrid jamming structure can be extended to other soft actuators such as shape memory alloys,³⁶ dielectric elastomers,³⁷ or motor/tendon mechanism. The design concept of proposed finger and its comparison with other two finger designs (pneumatic soft finger with particle jamming substrate only and pneumatic soft finger with layer jamming substrate only) are presented in Figure 1.

All three fingers can achieve variable stiffness when vacuum is applied caused by jamming phenomenon. The finger (as shown in Fig. 1a or b) will bend to a continuous curved shape when compressed air enters the air chamber of soft pneumatic actuator. At a given pressure, the finger curvature is always the same (except perturbed by obstacles). The proposed novel finger design (as shown in Fig. 1c) is different from the other two in that it's able to modulate its bending shape at a given pressure. Discretizing the jamming chamber with independent particle and layer chambers, the proposed finger in this study can achieve different bending shape by controlling the stiffness of each jamming chamber. As presented in Figure 1c, the layer chambers and particle chambers have overlapping regions so that they are interlocked to guarantee load transfer from finger end to fingertip.

Contributions of this study are concluded as follows:

The rest of this article is organized in the following manner. Materials and Methods section describes the bioinspired design and working principle of the proposed hybrid jamming finger. Theoretical modeling of finger stiffness and the fabrication process are also presented in this section. Experiments and Results section gives the detailed experimental studies of proposed finger, its comparison with other possible finger designs, and grasping demonstration of an assembled gripper. Finally, Conclusions and Future Work section concludes the article and discusses future work.

Materials and Methods

Design and working principle

The proposed soft robotic finger design and its bioinspiration are presented in Figure 2. Our human hand can handle different grasping and manipulation tasks regardless of object shapes or deformability, which provide us an ideal reference model. Figure 2a demonstrates the human index finger extensor mechanism. Muscle and tendon works cooperatively to extend and curl the finger. There are in total three joints in index finger, and here only two joints near fingertip are indicated: the distal interphalangeal joint between distal phalanx/middle phalanx and the proximal interphalangeal joint between middle phalanx/proximal phalanx.

For our proposed finger design shown in Figure 2b–d, it has two main components: a fiber-reinforced soft pneumatic actuator and a hybrid jamming substrate. The soft pneumatic actuator acts as muscle & tendon and generates bending motion when compressed air flows in and out while the hybrid jamming substrate mimics the function of finger bones and joints. The substrate in total has three bone parts connected by two joint parts. Compliant layers that become strongly coupled through friction when vacuum pressure is applied realize the bone part. Like the bone, the jammed layers exhibit high resistance to bending moments. Each joint part connects two bone parts and transfers stiffness from the fixed finger end to fingertip when high stiffness is expected. Therefore, an H-shape particle chamber as presented in Figure 2d is designed to enclose parts of the layer chambers for load transfer. When vacuum is not applied, the particles are in fluid state, and the joint is activated to bend freely during actuation. In this study, we take advantage of the merits of both layer and particle jamming. The layer structures functioning as bones are compact and lightweight, occupying most portions of the hybrid jamming substrate. The particles with good flowability (fluid state) but consuming large volume only function as connection parts between bones, acting as finger joints.

With the proposed novel finger design, bending shape control can be implemented at a given actuation pressure p, which is illustrated in Figure 3. When no vacuum is applied to all three layer (bone) chambers and two particle (joint) chambers, the finger bends to continuous curved shape with inlet pressure p just like particle jamming or layer jamming integrated soft fingers (Fig. 3a) in previous works.^24,31 When vacuum is only applied to all three layer chambers, the finger exhibits segmented bending at the two joint regions like our human finger (Fig. 3b). When vacuum is applied to all layer chambers and joint 2 particle chamber, the finger will tend to bend at joint 1, which is unjammed and at low stiffness state. In this study, only three bending shape examples are given for demonstration. In fact, by selectively stiffening different layer and particle chambers, a large variety of bending shapes can be achieved for different application scenarios.

Analysis

This section presents the stiffness modeling of the hybrid jamming structure. The analysis is divided into two parts: modeling of the particle jamming chamber at neutral position, modeling of the layer jamming chamber at neutral position, and analysis of the concatenated structure. Approximations and assumptions are made in the analysis to make the problem tractable.

Modeling of the particle jamming chamber

As shown in Figure 4, we approximate the positioning and packing of spherical particles with different levels of applied vacuum pressure as three statuses: random loose packing (RLP), random close packing (RCP),³⁹ and hexagonal close packing (HCP).⁴⁰ Initially, no vacuum is applied; the particles are stacked due to gravity force, when particle is free to move in a way similar to liquid. This state is called RLP. After small negative pressure is applied to the particle chamber, particles are jamming to form a RCP that can be interpreted as the ground state of the ensemble of jammed matter⁴⁰ and is with packing density of 64%. With the increase of the negative pressure, particles are squeezed further to form a packing called HCP with an extreme packing density of 74%.⁴¹ Note that there is another packing called face-center cubic (FCC), which has the same packing density to HCP and can be transformed to HCP by simply translating top layer of FCC.⁴¹ Therefore, we only study HCP in current work. For more details of packing phase transition of jammed matter, we recommend reference to refs.^40,42

Let the initial volume fraction be (determined by the volume left in the particle chamber during the particle filling operation in the fabrication process), radius of the particles be r, and length, width, and height of the chamber before vacuum application be L_p, W_p, and H_p. And after vacuum being applied, the packing density of the RCP and HCP in Figure 4b and c is and , respectively. Therefore, the volume of the chamber is when the formation of the particles is RCP. We can calculate the number of particles N_pand the volume of the compressed chamber V_h in HCP state as in Equation (1). Assume that the proportion of length, width, and height is kept constant during the shrinkage of the chamber, at the state in Figure 4c, we can also obtain the size of the chamber after vacuum is applied, as given in Equation (1):

(1)

where is the volume of each particle, and is the initial chamber volume.

Considering the large amount of particles in the chamber, we approximate the load condition as depicted in Figure 5. Every outermost particle on each face counterbalances force within the hexagon (marked as a red region in top view in Fig. 5b) applied due to the pressure difference between the two sides of the silicone rubber skin of the chamber. Let pressures of the atmosphere and the interior of the chamber be P_a and , we have the force applied by the skin from one face to each individual particle as follows:

(2)

where is the area of the hexagon marked in red in Figure 5a top view.

Each particle bears forces F_p induced by the pressure difference from six directions (along six faces' normal) as shown in Figure 5c, and the forces are propagated from the surrounding 12 particles. Since we are only interested in the resistance force in the Y direction (in Fig. 5a), here we calculate the resistance force F at the end point of the chamber by equalizing the works done by F and total work by frictional forces between particles. Since the relative displacement between the particle layers in the Y-Z planes is negligible compared to those in the other two dimensions, we only study the loading condition in Figure 5d within each layer as indicated by the brown plane in Figure 5a. Note that Figure 5d is obtained by taking only forces in Y_b–Z_b into consideration and performing resolution/combination of forces from Figure 5c. Similar interaction between particles and their surroundings was also presented in the previous work.⁴³ Assuming quasi-static motion between particles during the loading process, we obtain the forces from the surrounding particles , and the frictional forces f₁ and as follows:

(3)

where is the coefficient of friction between particles.

During the testing of stiffness, the deflection at the end point of the chamber is D, and we assume that the displacements of particles in the Z direction are comparatively negligible to that in the Y direction. Besides, we assume that the deflection is equally distributed to each particle layer parallel to the X–Y plane. Thus dD is calculated by dividing D by the number of layers N_l in Z direction. We have:

(4)

Combining Equations (3) and (4), and substituting Equations (1) and (2), we obtain the frictional work between particles:

(5)

Modeling of the layer jamming chamber

Modeling of layer jamming in this section takes sliding phenomenon between layers into account,³⁰ instead of simply treating multiple layers as a unified beam when compressed which was adopted in Zhu et al.³¹ that led to an unrealistically overestimated stiffness amplification factor. Ref.³⁰ gave highly detailed derivation of stiffness study of the laminar jamming structure, introducing phases, including preslip, transition, and full-slip regimes. Two-layer layer jamming was studied rigorously, and analytical results were compared to that from Finite Element method. However, more practically useful many-layer laminar structure was not given explicitly, but presented as an incomplete extension from the two-layer modeling, considering the significantly higher complexity when determining different regions of slipped and cohesive regions in layer interfaces and boundary conditions. Besides, in realistic fabrication, one usually needs a concise guideline to facilitate tuning of hardware parameters, including layer number, size, surface roughness (related to coefficient of friction), applied pressure, and so on. A simplified and more practical model is therefore required for many-layer structure.

Suppose that there is sliding and frictional work is generated between interfaces, let the friction coefficient be and length, width, and thickness of each sheet in the chamber be L_l, W_l, and H_l, and same as Modeling of the Particle Jamming Chamber section, pressure difference between the atmosphere and the interior be , the frictional forces between layers are:

(6)

We analyze the layer jamming with a cantilever beam structure with a clamped end and a free end as boundary conditions. For each sheet layer, with deflection D at the end point of the layer jamming chamber, and let the thickness of the sheet be h_l, the resistant force and work⁴⁴ due to the deformation of sheets are:

(7)

where is the elastic modulus of sheet, and is the number of sheets.

Following the assumption of small deflection, the deflection angle of the chamber and the relative sliding distance dL (Fig. 6a) are given by Equation (8), approximating the shape of the sheets by a circle. The frictional work dissipated between layers is also given in Equation (8).

(8)

Thus the total work generated during the loading with deflection of D is:

(9)

Stiffness of the hybrid jamming structure

Our design of the variable stiffness finger is sketched in Figure 6b, neglecting the inner structure and assuming that the attachments between adjacent chambers are firm. There are five sections with length L_i and deflection D_i at the end point for each section, as shown in Figure 6b. Similar to the approximations made in Modeling of the Layer Jamming Chamber section, we suppose that the shape of the whole fingers under external force is circular. Therefore, we obtain the deflections:

(10)

where is the vertical distance between the start and end of each section for the hybrid structure and when the deflections are small. Here R is the radius of the approximated circle curve that the finger forms when bended.

Substitute deflections into Equations (5) and (9), we have the total work during the bending test:

(11)

where g and h are works during the bending given deflection.

Since and , the stiffness of the structure with small deflection assumption is given by Equation (12) with W from Equation (11):

(12)

From the analytical model in Equations (11) and (12), we see that stiffness of the hybrid jamming structure is the summation of contributions from particle and layer jamming chambers. Note that stiffness of the particle chambers is a function of the filling volume fraction φ, RCP volume density , and HCP volume density and also proportional to the coefficient of friction between particles, width and height of the chamber, and pressure difference. This observation gives hints on how particle roughness, volume fraction, and size of chamber have effect on the stiffness of the particle chamber after negative pressure is applied. Similarly, we notice that for each layer jamming chamber, stiffness is affected by the number of layers, the coefficient of friction between layers, size of each layer, the elastic modulus of sheets, and negative pressure applied. Our model gives a more realistic amplification factor that is lower than n² as presented in Zhu et al.³¹ for the consideration of slippage in the layer interfaces instead of treating layers as a totally cohesive block. It suggests that increasing the number of layers, coefficient of friction, and area of sheets can enhance stiffness of the layer jamming chamber linearly. Whereas, different from that of particle chambers, stiffness of layer jamming chambers has a base component contributed by sheet stiffness before vacuum is applied, which leads to different behaviors, for example, having worse conformity to object's shape when making contact and being stiffer before vacuum application. Overall, the stiffness model of the hybrid jamming structure suggests how multiple design variables of the finger can be tuned to satisfy the requirements of different application scenarios.

Fabrication

As presented in Design and Working Principle section, the proposed soft finger is composed of two main components: the soft pneumatic actuator and the hybrid jamming substrate. The fabrication of actuator adopts previous works on soft fiber-reinforced bending actuator,^34,45 which include elastomeric rubber body, an inextensible layer, reinforcement fiber, and a port for air inlet. The inextensible layer guarantees bending toward one direction, while the reinforcement fiber restricts radial expansion and promotes better bending performance. The fabrication process of hybrid jamming substrate and the whole finger is illustrated in Figure 7a–e:

Experiments and Results

In this section, several experiments are conducted to evaluate the finger's bending shape control capability during bending motion, as well as its variable stiffness function. A gripper with two fingers is also developed in this study to further demonstrate the effectiveness of the proposed hybrid jamming principle.

Motion test

As stated in the Introduction section, the finger's shape control capability is important for many tasks, and most existing soft fingers or actuators are lacking this capability. In this work, bending shape control of the proposed finger is implemented by selectively applying vacuum to the particle and layer jamming chambers as depicted in Figure 3. To validate our design proposal, finger bending motion test is conducted. Figure 8 shows the experimental setup for motion test. The finger is mounted on a platform with 3D printed fixture. We attach three red markers on the tested finger: one on the fingertip and the other two each on the center of the finger's two joints, respectively, as shown in Figure 8a. A HD camera is used to capture the finger's bending motion. The inlet pressure of soft pneumatic actuator is controlled by a positive pressure regulator (IR1000-01BG; SMC Corporation), while vacuum pressure of jamming chambers is controlled using a vacuum pressure regulator (SMC IRV10-C06BG; SMC Corporation).

During the test, input air pressure for soft actuator increases from 0 to 50 kPa under three conditions of hybrid jamming substrate, respectively: (a) no vacuum is applied for both the layer and the particle chambers; (b) vacuum is only applied to the three layer chambers; and (c) vacuum is applied to the layer chambers and joint 2, same as Figure 3. In this test, vacuum pressures are all set to −80 kPa when vacuum is applied. The motion test results are presented in Figure 9 with captured finger shapes at actuation pressures of 50 kPa indicated. It can be seen that the experimental results are consistent with the design proposal given in Figure 3: the finger achieves continuous curved bending shape in Figure 8c and segmented bending shape in Figure 8d and tends to bend more at joint 1 in Figure 8e. The difference between real test results and design proposal is that the stiffened layer jamming structure (bone) and particle jamming structure (joint) will also be deformed a little bit under bending actuation of soft actuator. To better compare the finger's different bending shapes at p = 50 kPa, analysis is conducted to quantify the curvature variation of finger along its length based upon captured figures from Figure 8. A video of the finger's bending shape control can be accessed in the Supplementary Video S1.

From the snapshots of the finger under 3 configurations, 10 separated control points are acquired with approximately equal spacing, shown as black crosshairs in Figure 8c–e. For higher accuracy and consistency, control points are located on the visible blue curves (inextensible layer). Therefore, using these selected control points, the curves of the finger under different configurations are obtained based on piecewise polynomials of 3^rd order with the same smoothing parameters in curve-fitting function in MATLAB. With fitted curves illustrated by solid lines in Figure 9, multiple points are interpolated in consistent spacing (step size of 0.1 cm) with corresponding coordinates obtained, and thus, the curvature distributions on each interpolated point under different conditions can be calculated by the definition of curvature of discrete points which are accordingly depicted by dot lines in Figure 9. The length of dot line represents the magnitude of curvature, and the scale at the bottom right of Figure 9 denotes a unit of 0.5 cm⁻¹.

From observation on Figure 9, it can be noticed that the curve of the unconstrained finger in condition (a) is comparatively smoother with approximately uniform curvature distribution in the major body that possesses higher homogeneity of deformation along the length for the finger. Finger in this shape configuration shows better conformability and is more suitable for grasping larger objects strongly and robustly. In comparison, vacuum applied for three layer chambers in condition (b) changes the curvature uniformity of the body to the distribution that specific regions are with more distinguishable curvature values, indicating the positions of joints and stiffer bones. This finger morphing is commonly used in in-hand manipulation for human to move objects near the palm. Instead, under condition (c), it is apparent that the curvature in the vicinity of joint 1 is higher compared with the vicinity of joint 2, showing finger morphology for pinch grasping that can usually be observed during picking small objects from flat surfaces. In summary, by selectively controlling the vacuum conditions of the chambers, the finger is capable of adapting to significantly different scenarios of grasping tasks.

Stiffness test

In this test, we evaluate the finger's performance on stiffness variation. According to stiffness definition, here we measure the finger stiffness with the slope of force-displacement curve. Figure 11 presents the experimental setup for finger stiffness test. A digital force meter (range; 0–10 N, resolution: 0.001 N) is mounted on a stage, which can adjust height in the vertical direction. The tested finger is mounted on a screw linear guide that moves horizontally. During the test, the probe of force meter keeps in contact with the fingertip, and displacement at the fingertip ranges from 0 to 10 mm with an interval of 1 mm. At each displacement, the force meter measures the corresponding force. The finger stiffness is measured at three positions: Θ = 0°, 45°, and 90° (Θ indicates the finger's bending angle as shown in Fig. 10a). Θ is varied by inflating the pneumatic actuator. For each position, vacuum pressure of all five jamming chambers is controlled simultaneously within the range of 0 to −80 kPa with an interval of −20 kPa, and five sets of data are obtained. The angles were reset between each data collection. Under each vacuum condition, stiffness tests are repeated on three tested fingers, and five test samples are taken per finger. The average values are calculated as presented in Figure 11. Standard deviations of the test data are also presented.

It can be seen from Figure 11a–c that slopes of the force-displacement curves (solid lines) become larger as the vacuum levels increase from 0 to −80 kPa for all three positions. To make the comparison more intuitive, we perform linear fitting for the displacement interval 0–3 mm (force-displacement curves are almost linear within this interval in Fig. 11a–c), and slopes of the fitting lines indicating the finger stiffness are obtained. At 0° position (primary position), the finger stiffness increases from 0.006 N/mm when vacuum off to 0.0331 N/mm when vacuum pressure achieves −80 kPa with stiffness variation ratio of 5.52. The finger stiffness variation ratio is from 0 to −80 kPa at 45° position, and the ratio is from 0 to −80 kPa at 90° position. Hence, the finger's variable stiffness function is validated.

From Fig. 11d, the stiffness variation ratio contributed by jamming becomes smaller as the actuation pressure of soft actuator increases (bending angle changes from 0° to 90°). This could be explained as following: the soft pneumatic actuator's inherent stiffness is small when not actuated and only takes up a small proportion of the finger's overall stiffness; as inlet pressure of the actuator increases, its stiffness also increases dramatically and takes up a larger proportion of the finger's overall stiffness. Therefore, the finger stiffness variation ratio caused by proposed hybrid jamming substrate becomes smaller. It is also noticeable that the trends of stiffness increase with vacuum increase become more flat especially when vacuum exceeds −60 kPa.

Next, we compare the experimental values with analytical values at 0° position. According to the designed hybrid jamming soft finger, we set the parameters for our analytical model in Equations (11) and (12) as summarized in Table 2. In this study we set the kinetic coefficient of friction as 0.4 and as 0.33 according to test result from www.instron.us/-/media/literature-library/applications/2006/03/coefficient-of-friction-of-paper-used-in-a-copy-machine.pdf?la=en⁴⁶ Values of sizes are determined by the design of the finger. For layer jamming components, we select the elastic modulus to be 15 MPa,³⁰ number of layers to be 20. For particle jamming components, radius of glass ball is 1 mm; volume fraction, density of RCP, and density of HCP are 80%, 64%, and 74%, respectively.

Table 2. Parameters Setup for Analytical Modeling

Particle jamming chamber		Layer jamming chamber
Parameter (unit)	Value	Parameter (unit)	Value
	0.02		0.04
	0.02		0.02
	0.005		0.0001
r (m)	0.001		0.33
	0.4		15
	80%	n	20
	64%
	74%

The comparison results between experimental versus analytical values of the finger stiffness at 0° position are given in Figure 11e. We can see that the variation tendency of finger stiffness as the vacuum pressure increases is consistent for both experimental and analytical results. The difference may be attributed to assumptions made during analytical analysis and inaccurate value assignment for variables, for example, evaluation of coefficients of friction and . In the perspective of modeling inaccuracy, we list the following potential reasons for the overestimated stiffness by the analytical modeling. First, when integrating the frictional work dissipated between contacts for the layer chambers, we assume that the whole contacts have slip occurrence; however, for regions closer to the fixed end, there remain cohesive regions in the interfaces.³⁰ Similarly, for the particle chambers, certain region close to the fixed end, stable contacts are maintained. Finally, we made the assumption that particle and layer chambers have firm connections with each other, but this assumption does not necessarily hold for the interlocking structures (particle chambers squeeze and lock layer chambers' ends, as seen in Fig. 7c) transfer load with certain discount factor in the real soft finger and are not as strong as assumed, which results in a reduced total stiffness. In summary, the deviation of the experimental values from analytical results can be mitigated with better estimation of the coefficient of friction, new design of interlocking structure for interfacing two types of jamming chambers strongly, and modification of our model to take the cohesion and slippage transition into account, which may also lead to an overcomplicated model. However, for current work, our model is not yet integrated into predictive control of the finger, but serves as a guideline for hardware parameter iterations. Therefore, further improvements to narrow down the gap between experimental observations and analytical results can be saved for future work.

Comparative test

To further emphasize the unique functions and properties of the proposed hybrid jamming finger, comparative test is performed and described in this section. We compare the proposed hybrid design with similar physical designs in three cases: (1) with the jamming particles and sheets removed (soft actuator only); (2) with all chambers filled with particles (particle jamming finger, as shown in Fig. 1a); and (3) with all chambers filled with layers (layer jamming finger, as shown in Fig. 1b). For the particle and layer jamming cases, we set the chamber volume for these materials to be the same as the hybrid jamming case, that is:

(13)

Moreover, the volume fraction, diameter and material of particles for the particle jamming finger and number of layers, layer material for the layer jamming finger are also set as the same value with the hybrid jamming finger (volume fraction: 80%, diameter of particle: 2 mm, particle material: glass, number of layers: 20, layer material: copy paper). The material of particle jamming or layer jamming substrate membrane is also Ecoflex 0050, same as the hybrid jamming substrate. We compare the performance of these fingers with the proposed hybrid jamming finger through both motion test and stiffness test. The test setups are the same as the hybrid jamming finger, and test results are illustrated in Figures 12 and 13.

Figure 12 presents the fabricated finger designs for comparative test. Soft pneumatic actuator, layer jamming substrate, and particle jamming substrate are all shown in Figure 12a. Motion test results are given in Figure 12b–f with all fingers controlled to bend to Θ = 90°. The finger with actuator only in Figure 12b has no jamming substrate and bends to continuous curved shape when compressed air flows in. From Figure 12c–e, the particle jamming finger, layer jamming finger, and hybrid jamming finger all bend to smoothly curved shapes when air flows in and with jamming chambers vacuum off. For the particle jamming finger and layer jamming finger, applied vacuum generating the jamming phenomenon would not change the curved bending shape but only augments the fingers with stiffness tuning and shape-locking capability during motions. In contrast, the hybrid jamming finger shows segmented bending like human fingers in Figure 12f with vacuum on for three layer chambers. More bending shapes can be achieved by selectively controlling the jammed chambers of the hybrid jamming finger as discussed in Motion Test section. We also notice that the finger with soft actuator only needs lowest input pressure to bend to the given position. While the three jamming fingers need larger input pressure to achieve the given bending position, the pressure for the hybrid jamming finger falls in between the pressure values of the particle jamming finger and the layer jamming finger when vacuum off. The video showing the bending motion of different finger designs can also be viewed in the Supplementary Video S2.

The stiffness measurement result of this comparative test is given in Figure 13. Stiffness of the fingers is all measured at primary position (0° position) and at two vacuum conditions: 0 and −80 kPa. The stiffness test procedure is same as Stiffness Test section. Force-displacement curves of the soft actuator only finger, the particle jamming finger, and the layer jamming finger are presented in Figure 13a–c, respectively. Conducting linear fitting of the data in Figure 13a–c in the same way as for our hybrid jamming finger, the stiffness of the fingers is obtained. We compare the finger stiffness with the proposed hybrid jamming finger stiffness values in Figure 11d, and the comparison result is shown in Figure 13d. All three jamming fingers exhibit stiffness increase with vacuum on. The layer jamming finger achieves the largest stiffness 0.0361 N/mm after vacuum is applied. Stiffness of the proposed hybrid jamming finger is slightly smaller as 0.0331 N/mm after stiffening. For the particle jamming finger, its stiffness after stiffening is the smallest of the three jamming fingers as 0.0183 N/mm. From the stiffness test result, the layer jamming finger is stiffer than the particle jamming finger with materials and controlled variables such as layer numbers or particle volume fraction used in this study. We notice that the particles concentrate at the bottom of the particle jamming finger due to gravity and are not uniformly distributed. This could also have an impact on the finger stiffness. For our proposed hybrid jamming finger, most regions of its jamming substrate are layer regions with only two joint regions occupied by particles. Therefore, the stiffness of hybrid jamming finger is comparable with the layer jamming finger after stiffening. For the particle jamming finger, its jamming chamber needs to be carefully designed to make the particles uniformly distributed and have an ideal stiffness enhancement after stiffening.

Comparison of the proposed finger with other tested finger designs is summarized in Table 3 showing the unique characteristic of hybrid jamming finger. It is obvious that with more controllable pneumatic chambers, the proposed hybrid jamming finger can not only realize variable stiffness capability but also possess bending shape controllability, which is more versatile compared to the particle or layer jamming fingers.

Grasping demonstration

A two-fingered soft gripper based on the proposed finger design is fabricated as shown in Figure 14a to demonstrate the gripper's grasping capability with variable stiffness function. The gripper is assembled on a robotic arm (UR10; Universal Robot) with 3D printed fixtures. The grasping strategy is explained in Figure 14b and c, which mainly includes two steps. In the first step, the two fingers are soft with no vacuum applied and are pressurized to grasp the object with good conformability and adaptation due to their high compliance (shown in Fig. 14b). In the second step as shown in Figure 14c, vacuum pressure is applied to both of the fingers to increase their stiffness. As a result, the gripper demonstrates higher ability to bear the load of object for object lifting and other manipulation tasks.

In this test, we choose three objects with different geometries for grasping demonstration. These objects and their weights are: aluminum alloy work piece (334 g), 3M^™ Aluminum Foil Tape 425 (540 g), and water spray pot (400 g). Figure 15 shows snapshots of the whole grasping process of the gripper in two cases: with variable stiffness and without variable stiffness. Taking grasping of the aluminum alloy work piece for example (shown in Fig. 15a), the robotic arm locates the gripper and then soft pneumatic actuators are pressurized to bend the fingers for grasping first (p = 40 kPa). In the first case, the gripper lifts the work piece with vacuum off and the lifting fails due to large deflection at the fingertips under load (due to low stiffness). In the second case, vacuum pressure is applied (−80 kPa) for all the jamming chambers of the two fingers to realize stiffening of the gripper before lifting. Then, the robotic arm lifts the object successfully. From Figure 15, we can see that the deflection at the fingertip is quite small under load compared to the first case (vacuum off) due to the enhanced stiffness of the two fingers. A video of grasping demonstration can be viewed in the Supplementary Video S3.

Conclusions and Future Work

In summary, we have proposed a novel soft robotic finger that is capable of both bending shape control and stiffness modulation in this study. The finger design adopts a new hybrid jamming structure and takes inspiration from our human finger using compact layer jamming structures as bones and highly deformable particle jamming structures as joints. By controlling the vacuum level of the layer jamming and the particle jamming chambers, stiffness of the whole finger can be tuned and bending shape can be controlled during actuation. Theoretical model is also established to predict the stiffness change when different vacuum pressure is applied. Experimental section validates the proposed finger's bending shape control and variable stiffness capabilities through motion test and stiffness test. Theoretical analysis of the finger's stiffness tuning property is also experimentally verified. Finally, a two-fingered gripper is fabricated, and grasping tasks are performed for demonstration.

It is expected that this study would provide some insights for other researchers to address current challenges of soft robots through bioinspired hybrid jamming design. In future studies, the shapes and dimensions of hybrid jamming substrate can be optimized to improve the finger's performance. We also plan to add soft sensors to this finger to provide joint bending angle feedback and realize close loop control so that more sophisticated manipulation tasks could be carried out. Besides, an anthropomorphic robotic hand utilizing proposed finger design will be developed for dexterous grasping tests. Another direction of our future work is to extend this hybrid jamming design to leg design of quadruped robot.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This research is supported by the Hong Kong Innovation and Technology Fund (ITF) ITS-018-17FP.

Supplementary Material

Supplementary Video S1

Supplementary Video S2

Supplementary Video S3