Honeycomb Jamming: An Enabling Technology of Variable Stiffness Reconfiguration

Abstract

Jamming technologies are one of the promising approaches of variable stiffness mechanisms. However, there are problems limiting the broad application of jamming-based approaches such as a limited stiffening capacity and restricted stiffening position. This article presents a variable stiffness mechanism to achieve a rapid flexible to rigid state transition with biocompatibility, fail-safe design, and enhanced stiffening capacity. A novel strategy of reconfiguration of stiffening regions, which is entitled variable stiffness reconfiguration, is exploited to control not only the stiffnesses but also the positions and areas of the stiffening regions. At first, this article provides a new approach to the variable stiffness soft robotics community to enable both stiffness control and stiffening region adjustment. In this way, additional functions of the variable stiffness mechanisms including reproducing complex manipulator postures or customizing the soft gripper, through delivering functional units into or out of the devices, are demonstrated. Through reconfiguration, our design provides a generally applicable solution for a wide range of complex manipulator postures reproduced and objects grasped by reconfiguration of the stiffening regions. The variable stiffness mechanism is empirically evaluated with a comparison with other variable stiffness strategies in which the proposed solution shows greater stiffening capability, and an experimental search of optimal parameters of the honeycomb structure is presented. Finite element models, which have shown reasonable agreement with the empirical results, are constructed to model the stiffnesses, and an analytic model of the manipulator is derived to predict the posture.

Introduction

Soft robots have been investigated by researchers due to their unique advantages: inherent compliance, adaptability to the unstructured environment, enhanced safety, high dexterity, and the obstacle avoidance capability.^1,2 Several applications including medical and industrial uses have been developed.^3,4 However, the high flexibility of soft robots can limit their payloads, which can result in large deformation and torsion under high loading conditions. The unfavorable deformation can, thus, lead to failures in the model prediction, and even fractures of the structures.

For some operations such as grasping⁴ or traversing a tortuous path,⁵ they can be broken down into two states: a flexible state to explore and adapt to the environment and a rigid state of load carrying. Addressing that scenario, recent research has focused on the utilization of variable stiffness mechanisms, which can alter the stiffnesses of the robots for different needs.^6,7 One possible solution to achieve a variable stiffness is to through the embedment of smart materials. Field-activated materials such as magnetorheological fluids^8,9 or the electrorheological fluids,¹⁰ thermoplastics,^11,12 and low-melting point alloys¹³ can be used to change the stiffness through the application of external fields or thermal simulations. However, those methods suffer from the problems of biocompatibility, unsuitable stiffnesses of flexible or rigid states, and leakage problems⁷ when used for medical uses. Some methods also rely on active elements, such as shape memory materials,¹⁴ electroactive polymers,¹⁵ dielectric elastomer actuators,¹⁶ or fluid actuators¹⁷ to respond against the load. By changing the response of the actuators to the load, different stiffnesses can be realized. Researchers have also exploited a method to magnify the stiffening capacity of those variable stiffness approaches by the incorporation of the honeycomb core.^18,19 However, active elements usually have a higher power requirement, biocompatibility, and leakage problems.²⁰ Methods relying on the structural interaction between elements including segments,^21,22 wires,^23,24 granules,^25,26 and layers of sheets^27,28 were reported. The interaction forces may be induced by friction forces and interlocking geometries,^6,7 and the stiffness of the device can be altering by manipulating the structural interactions.

Jamming-based technologies, as one of the structural interaction approaches, have demonstrated their promising performance for fail-safe, fast response speed operation. It is characterized by an air-tight envelope filled with granular matters^25,26 or layers of sheets,^27,28 which can be stiffened through applying negative pressure. It can be fluid-liked or flexible in the flexible state, while after applying negative pressure, it can leverage friction and interlocking forces between the granules or layers, induced from the isotropic pressure, to rigidify the devices. Analyses of the design parameters including the geometry of granules,^29,30,31 and membrane^32,33 were reported. Several applications of medical uses,^25–27 haptics,³⁴ and industrial uses⁴ were also reported. One problem of this approach is its large device size to achieve sufficient stiffness changing ratio due to its limited stiffening capacity. More importantly, existing solutions can only achieve stiffening in a fixed, discrete region, and control of positions and areas of stiffening regions cannot be made. In other words, the geometrical size of the variable stiffness region and the location of the region cannot be controlled. It imposes a great limitation to stiffening-enabled operations,^35–37 as one set of stiffening regions can only serve specific targets and objects.

Objective

In this article, we introduce a variable stiffness mechanism, entitled the honeycomb jamming mechanism, and a module to control the positions of stiffening regions, entitled the sliding layer module. The honeycomb mechanism has been briefly introduced in our previous work³⁷ and shown its potential for robot application. We present an in-depth study of the honeycomb jamming mechanism with the incorporation of an extra module to further extend the reconfigurability in this article. To the best of the authors' knowledge, this is the first reported work that can achieve a full reconfiguration on both the position and the area of the stiffening regions, which we named variable stiffness reconfiguration.

Previous efforts of variable stiffness mechanisms focus on the exploitation of mechanisms, which can vary the stiffness of fixed area and position stiffening regions. In contrast, our design enables control over the positions and areas of the stiffening regions meaning that we can achieve a varying stiffening region in one single envelope, through variable stiffness reconfiguration. Besides, for conventional variable stiffness mechanisms, the connections of smart materials or mechanisms with the structural component, which have different stiffnesses, are required. As reported in a article,³⁸ the connection between rigid and flexible materials can be challenging and prone to failures, especially for devices with multiple separated variable stiffness mechanisms. Our design also circumvents the needs of connections, as our design contains the honeycomb core that can act as both mechanisms and structural components, and the stiffening can directly take place on the honeycomb core. Thus, the failure rate induced by the connection points can be minimized.

Researchers have explored the possibilities of reducing the number of actuators and the actuator requirements by the incorporation of the variable stiffness mechanisms. A soft actuator and a spherical mobile robot were reported³⁹ to demonstrate the ability of granular jamming incorporated with omnidirectional actuation to minimize the number of actuators and the power requirement. Applications such as grasping,³⁵ achieving complex robot postures by configurations matching,³⁶ the exploitation of robotics kinematic⁴⁰ were also reported. However, the above-mentioned works suffer from a fixed position of stiffening regions, which means one single design can only serve a narrow range of objects or configurations. Grasping different objects or achieving configuration matching from the original design entails another design iteration and fabrication. In contrast, our design offers a generally applicable solution for a wide variety of target objects or configurations by reconfiguration of stiffening regions.

To achieve the variable stiffness reconfiguration, the jamming layers in this article are reversibly slided from the backend module to the manipulator to change the stiffnesses, positions, and areas of the stiffening regions. In other words, functional units or materials are delivered from the backend system or removed from the manipulator to modify the properties of the robotic manipulator. This paradigm differs from the reconfiguration of the robots,³⁷ of which the overall amount of materials or the number of functional units remains constant. While in the proposed solution, the potential of reconfiguration is unleashed, and full control over the properties of the robot is enabled by delivering or removing necessary functional units and materials.

We illustrate our proposed mechanism and modules by a robotic manipulator first in the Materials and Methods section, followed by an evaluation of the mechanism in the Comparison with Existing Methods section, the Pattern Design Evaluation section, the Design Parameter Evaluation section, and the Finite Element Model section. The application of replicating desired configurations by the manipulator is presented in the Configuration Matching section. Then, we introduce another application of a reconfigurable gripper using the proposed mechanism.

Materials and Methods

Honeycomb jamming mechanism

As illustrated in Figure 1b and c, the key components of the manipulator include a honeycomb core sandwiched by jamming layers and enclosed by an airtight envelope. The basic working principle of the variable stiffness mechanism, entitled the honeycomb jamming mechanism, is the utilization of a phenomenon observed from the honeycomb core structure, as shown in Figure 1a. The honeycomb core alone can be flexible, while if it is bonded with flexible, but inextensible sheets on its top and under it, the composite becomes rigid. To achieve a reversible fast bonding between the sheets, which we named jamming layers in this article and the honeycomb core, the jamming technology is adopted. Before activating the jamming, the envelope is under ambient pressure, and the friction force between the jamming layers and honeycomb core is low enough to allow relative motion between the honeycomb core and jamming layers resulting in a flexible composite. Through applying negative pressure, the isotropic pressure force leads to a high normal force and friction force exerted by the jamming layers on the honeycomb core. The friction force can interlock the honeycomb core with the jamming layers converting the whole composite into a rigid one.

FIG. 1.

(a) A commercial honeycomb core which is the inspiration of the honeycomb mechanism. (b) The internal structure of the manipulator is illustrated. The honeycomb core and jamming layers compose the honeycomb jamming mechanism, and the sliding tendons compose the sliding layer module. Schematic illustration of the (c) cross-sectional view of the manipulator and (d) longitudinal section view of the manipulator. The details for the working principle of the (c) honeycomb jamming mechanism and (d) sliding layer module are shown. (d) The sliding direction refers to the movable direction of jamming layers in the sliding layer module. Rigid regions and flexible regions refer to the region stiffened or remaining flexible after the application of vacuum pressure.

The honeycomb core is sandwiched by a top and bottom jamming layer. To fabricate the honeycomb core with different parameters for subsequent analysis, the honeycomb core was fabricated by stereolithography (SLA) 3D printing (Form2; Formlabs). Eighty grit silicon carbide grit papers (Starcke Abrasives UK Ltd.) are selected to maximize the friction force between jamming layers and the honeycomb core.

Sliding layer module

Stiffening requires three elements: a vacuum environment, a honeycomb core, and jamming layers. It also implies that under the condition that a region of the honeycomb core without the coverage of jamming layers remains flexible in a vacuum environment, which leads to the development of the sliding layer module. The sliding layer module enables control over the position of the stiffening regions based on the honeycomb jamming mechanism. Rather than full coverage of the honeycomb core by jamming layers as described in the previous section, the jamming layers that are cut into strips make partial coverage of the honeycomb core. The strips are connected by a sliding cable that can drive the strips along the longitudinal direction of the manipulator, as indicated by the sliding direction in Figure 1d. As jamming only occurs in the regions of the honeycomb core with the jamming layers' coverage, the regions with jamming layers will be stiffened, whereas the regions without jamming layers will remain flexible, as shown in Figure 1d.

Jamming layer strips are fabricated by laser cutting silicon carbide grit papers (Starcke Abrasives UK Ltd.). A 1-mm-thick layer of ethylene-vinyl acetate is then laid on the back of the jamming layer to act as an adhesion layer for subsequent attachment with the sliding cable. Polyethylene fishing lines are used as the sliding cables due to its high durability and toughness. The jamming layer can then be attached to the sliding cable through the melting and rigidifying of the adhesion layer, which is further explained in the Reconfiguration Module section, along the longitudinal direction. A tendon for active bending was further bonded on the surface of the envelope, and the whole manipulator was then enclosed by a heat-shrinkable sleeve, as illustrated in Figure 1b.

Reconfiguration module

The sliding layer module can only shift the positions, whereas the overall area of the stiffening regions remains the same. The reconfiguration module serves as a solution to the mentioned problem of the sliding layer module to extend the reconfigurability. The module, shown in Figure 2, is aimed to enable variable stiffness reconfiguration meaning that the positions and areas of the stiffening regions can be controlled. As mentioned in the previous section, the regions covered with the jamming layers represent the stiffening regions. The number of jamming layer strips should be controlled to alter the overall area of stiffening regions. In other words, the overall area of stiffening regions can be increased or decreased by sliding the jamming layer into or out of the manipulator.

FIG. 2.

(a) The backend reconfiguration module is shown, which is composed of a movable jamming layer stock, a heating system, and a sealer. The orange arrow represents the moving direction of jamming layers to slide into the manipulator during reconfiguration. (b) Demonstration of the prototype of the manipulator. The manipulator (white) is mounted on the backend reconfiguration module. The manipulator is enclosed by a sleeve (white) and a 3D printed end cap (black).

As illustrated by Figure 3 and Supplementary Videos S1, we herein propose a pipeline-like workflow to slide the additional jamming layers into the manipulator, of which the procedures are listed below:

FIG. 3.

Conceptual illustration of proposed procedures of the variable stiffness reconfiguration. The conventions on the illustration are displayed on the right, and details of the structure are simplified or omitted for brevity. For procedures 1–3, the side view of the jamming layers is adopted, whereas for procedure 4, the top view of the jamming layers is adopted.

(1)

Select extra jamming layers;

(2)

attach the jamming layer to the sliding tendon;

(3)

slide the extra jamming layers into the manipulator;

(4)

seal the manipulator and apply negative pressure.

In procedure 1, a suitable jamming layer is selected for sliding into the manipulator. A movable jamming layer stock was designed to store multiple jamming layers, deliver suitable jamming layers, and engage them to the sliding cable for subsequent operations. As shown in Figure 4, procedure 2, an adhesion layer is laid on the back of jamming layers. The targeted jamming layer is then heated to melt the adhesion layer laid behind the jamming layer in procedure 2. As the tension of the sliding layers is kept, the sliding cable can cut into the molten adhesion layer, which ensures firm adhesion between the sliding tendon and the jamming layer. After cooling by natural convection, the adhesion layer is solidified and bonded between the sliding cable and the jamming layer. As each jamming paper strip is fixed in length, longer jamming layer segments can be achieved by repeated attachment of jamming layers on the sliding tendon. Procedures 1–2 are repeated until suitable lengths of jamming layer segments from jamming layer strips are formed. Noted that the jamming layer segment can also be formed by overlapping of jamming layer strips to achieve different lengths of segments.

FIG. 4.

Illustration of the details in procedure 2. The conventions of the illustration are also displayed on the right, and the side view of the jamming layer is adopted for all processes.

In procedure 3, all the jamming layer segments, driven by the sliding cable, can slide into the manipulator. To prevent buckling of the manipulator during sliding, a retractable supporter was designed to hold the manipulator in place. Then, an air-tight environment should be created by sealing the manipulator for applying negative pressure. Therefore, in procedure 4, a pneumatic actuator is adopted to provide the pressing force and mechanically seal the inlet of the manipulator, and the jamming can be activated by applying negative pressure. As a result, a manipulator with suitable positions and areas of stiffening regions can be realized.

For hardware implementation, the reconfiguration module, shown in Figure 2, consists of three components: a movable jamming layer stock, a heating system, and a pneumatic sealer. The movable jamming layer stock is realized by a motorized lead screw and pneumatic linear actuators, which move in two perpendicular directions. They drive the jamming layer stock in two directions to select and engage the sliding tendon with a suitable jamming layer. Regarding the heating system, a hot air gun with silicone rubber tubing is used. They can create a high-temperature airflow and direct it to target jamming layers to melt the heat-sensitive adhesion layer as specified in procedure 2.2 in Figure 4. The sealer addresses procedure 4, and a double-acting pneumatic cylinder with a stopper mounted on its rod is adopted to provide tolerance in position while maintaining a constant pressing force.

Analytic model

The model of the variable stiffness manipulator based on piecewise constant-curvature approximation^41,42 is addressed. The manipulator is composed of segments, as shown in Figure 5, with different stiffness experiencing the same bending moment. The mechanics modeling, which takes the stiffness and the moment into considerations, is adopted. As derived in the previous works,^43,44 the angle of the flexible segment $θ_{f i}$ can be expressed by

FIG. 5.

Convention on the model based on the piecewise constant curvature approximation. s_i represents the segment i length, Θ_i represents the angle, and r_i represents the radius. The black segments represent the flexible regions, whereas the gray segments represent the rigid regions. Both their deformations are modeled while the radii of the gray segments are significantly larger.

θ_{f i} = \frac{M}{K_{θ f i}},

(1)

where $K_{θ f i}$ denotes the effective bending stiffness of the segment, and M denotes the bending moment, which is a constant under the assumption of negligible friction.

The rigid regions can also be modeled by a similar approach but with a higher bending stiffness. As the bending angles of the rigid regions are small compared with the flexible regions, we can assume the stiffness changing ratio among the operation range is constant with respect to deflections, and the effective bending stiffness of the rigid regions can be expressed by $K_{θ r i} = R K_{θ f i},$

where R denotes the stiffness changing ratio. And thus, $θ_{r i} = \frac{R M}{K_{θ r i}} .$

However, as the joint space variable is the tension of the tendon or the bending moment, the controlling of the robot necessitates the force control on the tension of the actuating tendon. Force control requires high control frequency, high precision of actuators and force sensors, and suitable noise rejection measures, which greatly increase the cost while reducing the reliability. Therefore, a method is proposed to circumvent the needs of force control while satisfying the requirement of relating the region with different stiffnesses. The tendon length difference between two tendons $Δ l$ , which represents the difference in the lengths of two actuating tendons, becomes the joint space variables.

From the geometry, the length difference of segment i can be presented by $Δ l_{i} = 2 d (θ_{i}),$ (2)

where $θ_{i}$ denotes the angle of segment i, d is the distance between the attachment point and the center of the manipulator, which is the radius of the manipulator.

We then assume there exists a single segment equivalent system with the same bending moment M, distance $d$ , and its tendon length difference $Δ l_{t o t a l}$ is defined as $Δ l_{t o t a l} = \sum_{i}^{n} Δ l_{i} .$

It can be derived that $K_{e q} = {(\sum_{i}^{n} \frac{1}{K_{i}})}^{- 1} .$

Also, we can obtain the bending moment of the equivalent system by substituting Eq. (2) into Eq. (1) $M = \frac{Δ l_{t o t a l} K_{e q}}{2 d} .$

By equating the bending moment of the equivalent system and that of the segment i of the manipulator, we can get the angle $θ_{i}$ of the flexible or rigid region as $θ_{i} = \frac{Δ l_{t o t a l} K_{e q}}{2 d K_{i}} .$

Arranging the equation in matrix form, we can obtain the curvatures of individual segments: $[\begin{matrix} θ_{i} \\ ⋮ \\ θ_{i} \end{matrix}] = \frac{Δ l_{t o t a l} K_{e q}}{2 d} [\begin{matrix} K_{1}^{- 1} \\ ⋮ \\ K_{n}^{- 1} \end{matrix}] s^{*},$

where $s^{*} = [\begin{matrix} s_{1}^{- 1} & 0 & 0 \\ 0 & ⋱ & 0 \\ 0 & 0 & s_{n}^{- 1} \end{matrix}]$ .

Results

The study is aimed to gain insight into the influence of individual design parameters on the performance of the honeycomb jamming mechanism as well as comparing it with the state-of-the-art variable stiffness mechanism. To evaluate the performance of the variable stiffness mechanisms, an experimental platform was set up to examine the force–deflection relationship, as shown in Figure 6. The load cell was mounted on a motorized lead screw, which can exert a lateral force to induce certain deflection on the test pieces with three trials for each test piece. The force–deflection curve of the test pieces in the flexible and rigid state can be obtained from the average reading of the load cell and the distance traveled by the lead screw. The stiffness changing ratio can also be obtained by comparing the restoring force in the flexible and rigid state to achieve certain deflection.

FIG. 6.

Experimental setup of the lateral test. The blue arrow indicates the moving direction of the load cell driven by the motorized lead screw to exert a lateral force on the test piece. The test pieces firmly clamped by a mounting.

Comparison with existing methods

In this experiment, the honeycomb jamming mechanism was compared with granular jamming and layer jamming technologies to evaluate the performance of the proposed mechanism. As the stiffening capacity is highly dependent on the size of the device, test pieces with different variable stiffness approaches enclosed by the same envelope were built to make a fair comparison. The granular jamming test piece was fabricated by filling the envelope with ground coffee,²⁶ whereas the layer jamming test piece was fabricated by laminating 43 layers of copy paper sheets⁴⁰ to reproduce the height of the honeycomb core. The honeycomb test pieces possessed a size of the honeycomb core l, wall thickness w, and height h of 6, 1, and 2 mm, respectively. Only jamming technologies are studied as they share common characteristics of rapid transition between flexible and rigid states, fail-safe design, and biocompatibility.

Figure 7b presents the load–deflection curve and the stiffness changing ratio of granular jamming, layer jamming, and honeycomb jamming test pieces in the flexible and rigid state, respectively. It can be observed that the test pieces of granular jamming and honeycomb jamming in the flexible state share a similar stiffness. For the deflection range from 3 to 24 mm, honeycomb jamming exhibits a higher stiffness in the rigid state with a higher stiffness changing ratio. The average stiffness changing ratio of the granular jamming test pieces is 1.36, while that of honeycomb jamming is 7.39, which is 4.45 times of that of granular jamming. For the layer jamming test piece, it shows the highest stiffness in both flexible and rigid states, and its average stiffness change ratio is 6.94, which is 6.51% lower than that of honeycomb jamming. The result shows that the reconfiguration can be realized without compromising the stiffening ability.

FIG. 7.

(a) Convention on the parameters of (left) the hexagon pattern and (right) the square pattern. The size of the honeycomb core l is represented by (left) the diameter of the circle in which the hexagon is inscribed or (right) the width of the square. The wall thickness w and the height h are also shown in the diagram. (b) Force–deflection curve (left) and stiffness changing ratio–deflection curve (right) of the honeycomb jamming, granular jamming, and layer jamming test pieces. (c) Force–deflection curve (left) and stiffness changing ratio–deflection curve (right) of the honeycomb jamming test pieces with a hexagon and square pattern. Color images are available online.

Pattern design evaluation

The pattern of the honeycomb core could largely contribute to the performance and is investigated below. Two patterns of the honeycomb core with the same dimensions including hexagon and square with the same size of the honeycomb core l, wall thickness w, and height h were fabricated, as illustrated in Figure 7a. Figure 8c presents the result of the experiment, where l, w, and h equals 6, 0.3, and 2 mm, respectively. The hexagonal structure shows the higher stiffness in the rigid state and higher stiffness changing ratio.

FIG. 8.

Force–deflection curve (left) and stiffness changing ratio–deflection curve (right) of the honeycomb jamming test pieces. The evaluation addresses change in performance with respect to (a) sizes of the honeycomb core l, (b) wall thicknesses w, and (c) heights h. The unit of length is expressed in millimeter. Simulation result of the force–deflection curve (left) and visualization of the model (right) of the test piece with the dimension of (d) l = 6 mm, w = 1 mm, h = 2 mm and (e) l = 7 mm, w = 0.3 mm, h = 2 mm. Color images are available online.

Design parameter evaluation

Test pieces with different design parameters were fabricated with different parameters. As demonstrated in Figure 8a, design parameters including the size of the pattern l, the wall thickness of the pattern w, and the height h of the honeycomb core are studied in this analysis.

Figure 8 illustrates the performance of the mechanism of different parameters. Figure 8a addresses the size of the honeycomb core l, ranging from 5 to 7 mm, Figure 8b addresses the wall thicknesses w, ranging from 0.3 to 1 mm, and Figure 8c addresses the height h, ranging from 2 to 4 mm. For all test pieces, general trends of load–deflection relationship are exhibited. The stiffnesses of the test pieces in flexible states are less dependent on the honeycomb core parameters, whereas those in rigid states show a greater dependency. It is because the stiffness of the silicone rubber envelop dominates the overall stiffness of the composite in the flexible state. In addition, the stiffness changing ratios of the test pieces decrease gradually with the deflection converging to a certain level. For the larger size of the pattern l of 7–6 mm, the design shows a higher stiffness in the rigid state and a higher stiffness changing ratio, as illustrated in Figure 8a. For the wall thickness of the pattern w, the result is shown in Figure 8b, in which the stiffness changing ratio and the stiffness of the test piece with w = 1 mm are the highest. The height of the honeycomb core h has a larger influence on the stiffness of the flexible state, as illustrated in Figure 8c. It also indicates that a larger height can offer a better stiffness changing ratio for deflection large than 3 mm and a higher stiffness in the rigid state.

Finite element model

To further investigate the behavior of the honeycomb jamming mechanism, we have built a finite element model based on Abaqus software (Dassault Systèmes Simulia Corp.) to simulate the deformation. Due to the symmetrical shape of the mechanism, only half of the device was modeled with symmetrical boundary conditions. In addition, the envelope is omitted, due to its negligible stiffness. Another reason is that the deformation of the envelope will result in instability in the simulation. The friction coefficient was obtained empirically. Similar to the lateral test carried out, pressure forces were applied to the jamming layers, and displacement constraint was applied to the loading end. Forces required to made the displacement constraint were then calculated.

The force–deflection curves generated from the simulation were shown with the comparison with the empirical result in Figure 10d and e. The test piece of the dimension (l = 6 mm, h = 2 mm, $w$ = 1 mm) in Figure 10d and (l = 7 mm, h = 2 mm, $w$ = 0.3 mm) in Figure 10e is selected to demonstrate the simulation model. The simulation results are in reasonable agreement with the empirical results when the deflection is small (<8 mm). For a large deflection, the discrepancies become larger. It may result from the manufacturing error and nonlinearity of the friction due to the multimaterial abrasive paper, which is not a concern in the works⁴⁰ using sheets of copy paper. Furthermore, some of the abrasive particles on the jamming layers are loose and are released during operation, which largely enhances the difficulties of modeling. However, unlike actuators, the working range of the variable stiffness mechanisms is usually within the small deflection portion, where the simulation's results closely agree with the empirical ones. Therefore, the finite element model reasonably predicts the behavior of the variable stiffness mechanisms within the normal working range.

Configuration matching

One of the applications of variable stiffness mechanisms is to incorporate with actuators to reduce the actuator requirements.^35,36,45 Generally speaking, soft actuators, which can offer an omnidirectional actuation or are hyper-redundant, are surrounded by multiple independent variable stiffness mechanisms that act as strain constraining layers. In the flexible regions of deactivated variable stiffness mechanisms, they are vulnerable to bending moments or tensile forces and exhibit most of the deformation creating a unidirectional actuation. While for the regions of activated mechanisms, their stiffened bodies can withstand the actuation forces of the soft actuator and remain unchanged. Therefore, only a few actuators are required to provide omnidirectional actuation because the regions with different stiffnesses can direct the deformation and the actuation direction. As the power and precision requirement of actuators are generally higher than those of variable stiffness mechanisms, the requirement of the whole device can be lowered while the same level of motion complexity can be realized.

In this section, we focus on determining and achieving the optimal positions and areas of stiffening regions that can replicate targeted configurations. In other words, the stiffening regions of the manipulator are reconfigured, so that even with only one set of actuating tendons, it can achieve some complex robot postures. Our approach is to first break down the manipulator into multiple segments: flexible and rigid segments with specific stiffnesses. The rigid segments represent stiffening regions with jamming layers, and the flexible segments represent flexible regions without jamming layers. The optimal segment number and segment lengths of flexible and rigid segments are then determined by an optimization algorithm.

Through minimizing the cost function, $f = \sum_{i}^{N} w_{i} (P_{d i}^{2} - P_{a i}^{2}),$

where N is the number of sample points, w_i is the weighting term for sample point i, $P_{d i}$ is the position of sample point i of the desired configuration, and $P_{a i}$ is the position of sample point i of the robot computed by forward kinematics, we can get the optimal segment lengths to replicate the desired configuration. The optimal segment lengths can then be implemented by the reconfiguration module as explained in the Reconfiguration Module section by incorporating extra jamming layers into the manipulator. The tendon for active bending can be then pulled for a length computed by the algorithm.

Different desired configurations are implemented in this study: two circular curves with different radii, a parabolic curve, a broken line, and two straight lines with different inclined angles. In Figure 9, the dashed lines represent the desired configurations, the colored thick lines are generated from the theoretical prediction and the optimization algorithm, and the dashed lines with asterisks represent the actual the robot posture measured. It can be observed that the theoretical prediction resembles the desired configurations, while discrepancies are caused due to the constraints of the optimization algorithms. The constraints are imposed to model the physical limitations including the length of the jamming layers, the maximum number of segments, and the maximum bending angle of the flexible regions. We can see reasonable agreement between the theoretical and actual robot posture with some errors. It can be explained by the nonlinearity of the deformation, which leads to inaccuracies toward the stiffness of the flexible regions and cannot be compensated by the linear compensator included. In addition, the manufacturing errors of the manipulator can lead to unmodeled twisting of the manipulator, which leads to errors in tendon lengths.

FIG. 9.

Result of the configuration matching of (a) circular curves with 120 mm radius, (b) circular curves with 300 mm radius, (c) parabolic curves, (d) broken lines, (e) inclined straight lines with a slope of −1.96, and (f) inclined straight lines with a slope of −3. The desired configurations are represented by the dashed line, the theoretical predictions are represented by the colored thick line, and the robot postures exhibited by the actual manipulator are represented by the dashed line with asterisks. Color images are available online.

Reconfigurable gripper

During the grasping process, the grasping posture places great importance in making an effective and stable grasp.^46–48 Depending on the sizes and weights of the targeted objects, different postures should be adopted. Recent research has applied variable stiffness mechanisms in altering grasping posture,^49–51 as well as increasing the load of the grippers.^52–54 Generally, variable stiffness mechanisms are incorporated into the joints of the fingers or the structure of the whole fingers. By activating or deactivating individual mechanisms, the gripper can achieve fingertip pinch or power grasping.^46,49,50 This section proposes a new method to achieve a variable stiffness gripper for different grasping posture by reconfiguration of stiffening regions, rather than embedding multiple variable stiffness mechanisms. The proposed approach is characterized by altering the grasping posture through reconfiguring properties of the gripper, without relying on onsite control of variable stiffness mechanisms. In other words, once the operation mode is set, certain grasping posture can be realized easily, without additional effort of tendon force control, temperature control, or pneumatic pressure control.

We present a tendon-driven gripper design using the honeycomb jamming mechanism and sliding layer module to achieve reconfiguration. From the equation $κ_{i} = \frac{Δ l_{i}}{2 d s_{i}}$ , the inherent curvature $κ_{i}$ of the finger is inversely proportional to the bending length $s_{i}$ 4². Curvature control can be realized by altering the active bending length. As shown in Figure 10a, stiffening the bases of the fingers can concentrate the deformation on the tip, and a power grasp can be achieved. When a fingertip pinch is required, the gripper can reconfigure itself such that the whole finger remains flexible. Then, the whole finger would exhibit similar bending and the fingertip pinch can be realized.

FIG. 10.

(a) Conceptual illustration of the proposed gripper. Rigid components represent the structural component of the gripper or the stiffened regions of the fingers, whereas flexible components refer to non-stiffened regions of the gripper. (b) Simplified illustration of the internal structure of the finger. Different from the variable stiffness manipulator discussed in the previous section, the finger is composed of inactive regions serving as a reservoir of jamming layers. Grasping of (c) 20 mm diameter 3D printed cylinder, (d) 27 mm diameter bottle, (e) 4 mm side to side length hex key, (f) 15 mm aluminum profile. (g) Illustration of the experimental setup of the grasping force evaluation is also shown. Note that the objects refer to the 40 mm diameter or 20 mm diameter 3D printed cylinder. Result of maximum grasping force evaluation of (h) power grasp and (i) fingertip pinch.

A simple three-fingered gripper was designed and constructed. As shown in Figure 10b, each of the fingers has a single pair of jamming layers sandwiching a core. The core was composed of a honeycomb region and an inactive region. Stiffening happens in the honeycomb regions covered by jamming layers, whereas the inactive region serves as a reservoir to accommodate the remaining length of the jamming layer. Enabled by the sliding layer module, the jamming layers can slide into the honeycomb regions, resulting in partial coverage or full coverage. Therefore, the active bending region can be defined as the regions without the coverage of the jamming layer. When grasping, the active bending length bends with a desired curvature to grasp the targeted objects. Thus, by positioning the jamming layers, we can alter the grasping posture.

We demonstrate the grasping of objects with different sizes, in Figure 10c, to evaluate the allowable targeted object size. In the experiments, we have selected two modes of operation for evaluation: non-stiffened mode and half stiffened mode. The non-stiffened mode refers to the status that all jamming layers have slided into the inactive zone, allowing bending of the whole finger. The half stiffened mode, in contrast, indicates jamming layers cover half of the honeycomb region, allowing bending of the other half. Noted that negative pressure is applied in both two modes, but the only determining factor of stiffening is the coverage of the jamming layers. In Table 1, the result of the experiments is shown, and generally, the gripper in the non-stiffened mode can grip objects with a smaller size than that of the half stiffened mode. It is because the fingers in the non-stiffened mode have a larger workspace, due to larger active bending length. It leads to a larger grasping range so that the finger can reach the edges of the small objects.

Table 1.

The Result of Object Grasping

Targeted objects	Size (mm)	Weight (g)	Succeed number
Targeted objects	Size (mm)	Weight (g)	Half stiffened mode	Non-stiffened mode
Cylinder	∅40, l90	58.7	10	10
Cylinder	∅20, l90	23.6	10	10
Al profiles	15X15X140	18.4	10	10
Bottle	∅27, l85	38.2	8	8
Aluminum rod	∅10, l100	29.7	4	6
Hex key	Hex side to side:4, l147	18.2	0	5
Hex key	Hex side to side:2, l97	2.7	0	3

Figure 10d shows the evaluation of the maximum grasping force of the gripper in two modes with different grasping postures. Cylinders with a diameter of 40 or 20 mm are gripped by fingertip pinch and power grasp in non-stiffened mode and half stiffened mode, respectively. The objects are then driven by uninterrupted actuation until separation happens, and the maximum forces required are recorded by a load cell with five trials for each object. The figure shows that the power grasp achieved by the half stiffened generally has a larger maximum gripping force than that of the non-stiffened mode.

It can be seen that, from the above experiments, the gripper in non-stiffened mode has a larger allowable targeted object range, whereas the gripper in half stiffened mode can achieve a power grasp, which has a larger payload. Therefore, we can reconfigure the gripper to suit various objects. For targeted objects of smaller sizes, the non-stiffened mode can be selected to maximize the grasping success rate, whereas the stiffened mode can be selected to achieve the power grasp for heavier objects. Through introducing reconfiguration of the stiffening regions, this study enables soft gripper to be more adaptable to grasp various objects with a large range of weights and sizes.

Conclusions

The article introduces the honeycomb jamming mechanism to realize a variable stiffness with a high transition speed, biocompatibility, and a reasonably high stiffening capacity. The sliding layer module and the reconfiguration module were further proposed to reconfigure the positions and areas of the stiffening regions. A manipulator capable of replicating desired configurations was proposed to illustrate the concept of variable stiffness reconfiguration, and a reconfigurable gripper was presented with the evaluation of operation modes. A comparison with granular jamming and layer jamming was made, which showed improvement in the stiffness changing ratios. Then, an experimental search was performed to determine the optimal design parameters of the honeycomb jamming mechanism with the aid of a finite element model, and an analytic model of robot posture was derived from the piecewise constant–curvature approximation.

Future work includes a stiffness analysis to study the influence of the stiffening regions on the stiffness of the end effector. Improving the mechanism such that the reconfiguration of the stiffening regions can be made during the operation is another aspect of further research.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work is supported in part by the HK RGC under T42-409/18-R and 14202918, in part by project 4750352 of the CUHK-SJTU Joint Research Fund, in part by the VC Fund 4930745 of the CUHK T Stone Robotics Institute, CUHK, and in part by Shenzhen Science and Technology Commission via the Shenzhen-HK Collaborative Zone Project.

Supplementary Material

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Supplementary Material

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