A Gas–Ribbon-Hybrid Actuated Soft Finger with Active Variable Stiffness

Abstract

A new hybrid actuated soft finger with active variable stiffness is proposed for the first time by integrating gas-driven and ribbon-driven mechanisms. By carefully coordinating the two mechanisms, the bending deformation and the stiffness modulation processes of the soft finger can be uncoupled, providing it with both high flexibility and good variable stiffness. Although the soft finger, made entirely from flexible materials, works under a low and safe gas pressure of below 35 kPa, the maximum bending angle reaches ∼210°, and a single soft finger can withstand a weight of 1.25 kg. For any bending angle, with the help of the ribbon-driven mechanism, the stiffness of the soft finger can increase by three to six times. In addition, theoretical models are established for the evaluation of the bending-deformation characteristic and the output force of the soft finger, which are verified by experiments. A dual-finger soft robotic gripper is assembled by utilizing two soft fingers, which can easily and stably grab various objects with different sizes, shapes, and weights. Both the theoretical and experimental results indicate that the proposed gas–ribbon-hybrid actuated mechanism can effectively enhance the variable stiffness property of a soft finger while retaining its good compliance with the surroundings. This work might provide future insights for the development of compact and cost-effective soft end effectors with active variable stiffness.

Introduction

Advancements in soft robotics have greatly expanded our thinking about the development of new tools and devices for serving mankind. As a research focus, soft robotic fingers, featuring high compliance and safe interactions, have received substantial attention in recent years, and can be applied to fabricate grippers as end effectors to efficiently grab complex shaped or fragile targets, or assemble robotic hands for artificial limbs or rehabilitation.^1–20 However, several key problems related to sensing, control, and stiffening still exist that impede the popularity of soft robotic applications.^3,21–23

Grasping and manipulation are basic functional requirements for soft robotic fingers.³ The flexibility of the soft end effectors enables them to grasp objects with different shapes, sizes, and materials. A high stiffness is required for stable and precise manipulations. Although both the flexibility and stiffness are the core indicators for evaluating the performance of soft robots, they produce opposite effects. Therefore, to explore the full advantages of soft robotic fingers, it is of crucial importance to coordinate the logical relationships between the high flexibility and the variable stiffness.

The concept of variable stiffness has always been an important research issue for soft robotic fingers. An ideal variable stiffness mechanism should be compatible with high flexibility. That is, with the exception of some specific applications, on the one hand, the stiffness modulation process should be uncoupled with the flexible deformation process; on the other hand, when grasping, the soft finger should be in a high-flexibility mode, and when manipulating, the soft finger should be in a high-stiffness mode. Therefore, the performance of soft robotic fingers not only depends on the structural design but is also closely related to the control logic. Generally, for a mechanical part, the stiffness mainly depends on the material properties and structural features, and several methods of stiffness modulation have been proposed in past decades.^23–49

For example, from the point of view of structural features, Brown et al. proposed a universal robotic gripper with active variable stiffness based on the jamming of granular materials²⁵; Kim et al. developed a layer jamming mechanism to realize stiffness modulation by exploiting the friction present between layers of thin material²⁶; Zuo et al. designed a sheath that can switch between flexible and rigid modes using a novel “Dragon skin” structure and a negative pneumatic shape-locking mechanism²⁷; Sadati et al. reported a variable stiffness mechanism by using a low hysteresis helical scale jamming interface inspired by teleost fish scales²⁹; and Sun et al. designed a toothed pneumatic actuator to achieve a variable stiffness inspired by pangolin scales.³²

Most of these particle/layer/scale jamming methods can achieve a high stiffness; however, there exist several shortcomings: the soft gripper contains rigid components, exerting certain negative effects on its flexibility and compliance; the appendant jamming mechanism decreases the structural compactness, while increasing the fabrication complexity; and the stiffness modulation is usually coupled with the bending deformation of the grippers.

In terms of material properties, the method of using controllable stiffness materials (e.g., shape memory alloys [SMA],^33–36 shape memory polymers [SMP],^37–41 and low melting point alloys [LMPA]^42–45) to realize a variable stiffness is widely adopted in the development of soft robotic grippers.⁴⁶ For example, Wang and Ahn reported a soft gripper with variable stiffness by using SMA³⁵; Li et al. proposed a variable stiffness finger actuated by heating the embedded SMA fibers³⁶; Yang et al. reported a three-dimensional (3D) printed variable stiffness robotic gripper by using SMP as the finger joints^39,40; and Shintake et al. designed a variable stiffness gripper by utilizing a LMPA embedded silicone substrate.⁴³ Although these grippers possess good variable stiffness, their response times are relatively long, resulting in a lower manipulation efficiency.

Actually, for inflatable soft modules (e.g., McKibben muscles), the stiffness varies with the inner gas pressure, and usually the higher the pressure is, the higher the stiffness. That is, the stiffness can be modulated by altering the pressure inside the gas cavities. For this gas pressure-based method, a variable stiffness is realized by the shared inflatable gas cavities with a bending deformation and extra mechanisms are not required, so the structure of the soft module can be more compact and cost-efficient than that of using other methods.

To date, several fiber-reinforced soft fingers with variable stiffness have been reported by using the gas pressure-based method.^47–49 Typically, Al Abeach et al. developed a variable stiffness soft dexterous gripper by utilizing McKibben muscles.⁴⁷ The stiffness of the system can be increased by raising the pressure in the two McKibben muscles without resulting in a change in the finger position. However, the compliance of this soft gripper is insufficient due to the low flexibility of McKibben muscles. According to the current state of research on soft robotic fingers, this work focuses on developing a soft finger with a compact structure and an efficient active variable stiffness based on the gas pressure-based method.

In the Structural Design and Fabrication section, the structural design and fabrication process of the gas–ribbon-hybrid actuated soft finger is introduced. The Modeling section presents the theoretical models for estimating the bending angle and output force of the soft finger varying with the gas pressure difference, as well as the required length and tension of the ribbon. In the Experiments and Discussion section, experiments are carried out to investigate the deformation characteristics, stiffness, output force, and load capacity of a single soft finger, of which the results are discussed in comparison with theoretical results. In addition, a dual-finger soft robotic gripper is assembled to test the application prospect of the soft finger. Finally, conclusions and directions for future work are presented in the last section.

Structural Design and Fabrication

Structural design

There are two basic concerns for the design of a soft finger: how to decouple the variable stiffness from the bending deformation, and how to ensure both the high flexibility required for safe and friendly interactions and the high stiffness for an end effector to execute stable and precise manipulations. Based on these concerns, the soft finger is carefully designed by utilizing a gas–ribbon-hybrid actuated mechanism, as shown in Figure 1a, which mainly consists of the main body, a tube, gas cavities, the inner strain limiting layer (ISLL), and the outer strain limiting layer (OSLL).

FIG. 1.

Illustrations of the designed gas–ribbon-hybrid actuated soft finger: (a) structure and configuration, (b) working principles.

The materials used for fabricating the soft finger are all flexible, and it does not contain any rigid parts. The walls of the five gas cavities and the main body are all made of Smooth-On 0030 silicone, a kind of flexible material with a high elasticity that is not harmful to humans. The tube, a silica gel collapsible bulb with five holes corresponding to the five gas cavities, provides a path for the gas that connects the gas cavities to a gas supply. The ISLL, embedded in the main body, is made of polyester silver, which is used to confine the elongation of the finger pulp and make it easier for the soft finger to bend. The OSLL is also made of polyester silver, with one end fixed to the end of the finger and the other end connected to a ribbon-driven mechanism. As illustrated in Figure 1b, the working principle of the soft finger is as follows: (1)

When bending deformation is required, the ribbon-driven mechanism is unlocked, that is, the OSLL is in a relaxed state. Then, by inflating the tube, the gas cavities begin to expand, driving the soft finger to bend inward due to the constraint of the ISLL. Because the input gas pressure is relatively low, the high flexibility and compliance of the finger remain.

(2)

When stiffness modulation is required, the ribbon-driven mechanism starts to work, and the OSLL is tightened. Then, by rising the input gas pressure, the stiffness of the finger can be substantially increased. Because of certain coupled deformations, the increase in the input gas pressure will unavoidably cause a slight change in the bending angle of the soft finger, which can be eliminated by adjusting the OSLL length. Thus, the active variable stiffness for a given bending angle is realized by controlling the input gas pressure and the OSLL length.

Obviously, the designed gas–ribbon-hybrid actuated soft finger possesses both a high flexibility and variable stiffness. Because the processes of the bending deformation and the stiffness modulation can be nonparallel, the two basic functions are uncoupled to some extent. It should be noted that this work focuses on finding a new stiffness modulation method, and the structural optimization is beyond the scope of this article.

Fabrication

In this work, the soft finger is prepared by a casting method, and all the molds are 3D printed. To ensure that the OSLL is tightly fixed to the soft body, the OSLL and ISLL use the same polyester sliver; thus, the fabrication process of the soft finger can be simplified accordingly. Figure 2a shows the fabrication process, which can be roughly divided into the following three steps:

FIG. 2.

The fabrication of the soft finger: (a) illustrations of the fabrication procedures and (b) the photo of the finally fabricated soft finger.

Step 1: Molds 1 and 2 are bound together by bolts with a gas tube positioned between them; here, the combination is named C-Mold 1, which is used for forming the gas cavities.

Step 2: First, C-Mold 1 and four carbon fiber bars are fixed on Mold 3, of which the combination is C-Mold 2; second, fluid silicone is poured into C-Mold 2 until the fluid level is flush with the top edge of Mold 3; third, the fluid silicone is cured at room temperature for 4–6 h, then the fully cured silicone is removed from C-Mold 2, and the dorsal portion of the soft finger is obtained.

Step 3: First, a polyester sliver, four carbon fiber bars and Mold 4 are combined into C-Mold 3; second, fluid silicone is poured into C-Mold 3 until the fluid level is flush with the top edge of Mold 4; third, the dorsal portion is placed on top of Mold 4, with the solid silicone attached to the fluid silicone; fourth, the fluid silicone cures at room temperature for 4–6 h, and then the fully cured silicone is removed from C-Mold 3; the combination of the dorsal portion and the newly cured portion forms the soft finger.

Figure 2b shows the fabricated soft finger, which is made entirely from soft materials. The weight of the soft finger is ∼30 g, and the size is 80 × 20 × 30 mm.

Modeling

Bending angles

The bending deformation of the soft finger is mainly caused by the expansion of the gas cavities, so here the bending angles are discussed with the OSLL being in a relaxed state. Considering that the elastic modulus of the soft materials constructing the soft finger is relatively low, to facilitate the modeling, the bending resistance from the soft materials is ignored in this work.

Here, we analyze two neighboring gas cavities, as shown in Figure 3a. Then, the formulas for the bending angle are derived based on the following assumptions: (1) for each gas cavity, the walls (AC, BD, AB, and CD) are all simplified as spherical surfaces; (2) the gas cavity symmetrically deforms, with the arc lengths between A and B (l_AB), C and D (l_CD), and A and E (l_AE), and the distances between A and C (d_AC), B and D (d_BD), and E and F (d_EF) are constants. In addition, for the proposed soft finger, the arc lengths l_AB and l_CD are equal. Then, according to the geometrical relationships shown in Figure 3a, the bending angle of a single gas cavity satisfies

FIG. 3.

Analysis model for (a) the bending deformation of the soft finger and (b, c) the output force of the soft finger.

\{\begin{matrix} R_{1} cos \frac{α_{0}}{2} - d_{O G} sin \frac{α_{0}}{2} - \sqrt{{R_{1}}^{2} - \frac{1}{4} {d_{E F}}^{2}} + \frac{1}{2} l_{A B} = 0 \\ α_{0} d_{O G} - l_{A B} - l_{A E} - α_{0} R_{1} sin (arcsin \frac{d_{E F}}{2 R_{1}} - \frac{α_{0}}{2}) = 0 \end{matrix},

(1)

where R₁ is the radius of curvature of spherical surface EF, and d_OG denotes the distance between the arc center of the bending finger and the intersection point (G) of spherical surfaces EF and AC. Because of the incompressibility of the soft material, the volume is constant; thus, we have $π R_{1} (2 R_{1} - \sqrt{4 {R_{1}}^{2} - {d_{E F}}^{2}}) t_{1} = d_{E F} t_{0} d,$ (2)

where t₀ is the initial wall thickness, t₁ represents the wall thickness in an inflating state, and d denotes the width of the gas cavity. According to the Young–Laplace equation, for each point on the wall, the gas pressure difference can be expressed as a function of the tension ( $γ_{1}$ ) inside the wall and the radius of curvature: $Δ p = \frac{2 γ_{1}}{R_{1}},$ (3)

where $γ_{1}$ can be calculated as the product of the elastic modulus (E) and the wall thickness (t₁): $γ_{1} = E t_{1} .$ (4)

According to Eqs. (2)–(4), the radius of curvature of the gas cavity satisfies $π Δ p {R_{1}}^{2} (2 R_{1} - \sqrt{4 {R_{1}}^{2} - {d_{E F}}^{2}}) - 2 E t_{0} d_{E F} d = 0 .$ (5)

Then, by solving Eqs. (1) and (5), the relations between the bending angle of the soft finger and the gas pressure difference can be obtained: $α = n α_{0},$ (6)

where n denotes the number of gas cavities.

Output force

When the gas pressure rises to a certain degree, the OSLL is tightened, constraining the further bending deformation of the soft finger. If a proper external force is exerted on the free end of the soft finger, the resultant deformation will let the OSLL translate to a relaxed state. Thus, the constraints of the OSLL to the soft finger are lifted. For unstretchable polyester ribbons, the required deformation for the transition between the tightened and relaxed states is relatively small. Then, given the bending angle and gas pressure, the critical external force (F_cr) can be treated as the output force of the soft finger, as shown in Figure 3b.

Considering that both the inflating and deflating processes are relatively slow, to facilitate the following discussion, the thermodynamics problems are ignored. The deformation process of the soft finger is approximately treated as a quasi-static process, and the effect of the dynamic process falls outside the scope of this study. Because of the compliance of soft materials, the resistance to the external force mainly comes from the gas pressure acting on the inner wall of the gas cavities. In terms of the bending energy, the work of the external force and gravity are approximately equal to that of the gas pressure. Assuming that the slight displacement caused by F_cr is Δs, and the resultant change in the length of the soft finger along the axial line is Δl_a, we have $F_{c r} Δ s + G Δ h = Δ p A_{a} Δ l_{a},$ (7)

where Δh is the height variation of the gravity center, A_a is the contact area between the two neighboring gas cavities, and G is the gravity of the overhanging portion of the finger. Suppose the change in the bending angle is Δα; then, according to the geometrical relationships, Δs, Δl_a, Δh, and Δα satisfy the following equations: $\{\begin{matrix} Δ h = (\frac{l_{s}}{α (α - Δ α)} (sin β - sin (b_{1} α + β)) + (\frac{b_{1} l_{s}}{α - Δ α} + b_{1} b_{2}) cos (b_{1} α + β)) Δ α \\ Δ l_{a} = \frac{1}{2} d_{E F} Δ α \\ Δ s = \frac{l_{s}}{α - Δ α} \sqrt{{(\frac{s in α}{α} - cos α)}^{2} + {(\frac{cos α - 1}{α} + sin α)}^{2}} Δ α \end{matrix},$ (8)

where l_s denotes the length of the ISLL beneath the gas cavities, b₁ is the ratio of α_G and α, b₂ is the distance from the gravity center to the inner limiting strain layer, and β is the inclined angle of the base. Under ideal conditions, b₁ and b₂ are all constant. Supposing that when the OSLL is tightened, the positions of O, E, F, A, and C remain unchanged, then we have $d_{L K} = \sqrt{{R_{1}}^{2} - {(\frac{1}{2} \sqrt{4 {R_{1}}^{2} - {d_{E F}}^{2}} cos \frac{α_{0}}{2} + \frac{1}{2} d_{E F} sin \frac{α_{0}}{2} + \frac{1}{2} l_{A E})}^{2}},$ (9)

where d_LK is the distance between the points L and K, which are both on the intersection curve. To facilitate the modeling, A_a can be approximately treated as the area encircled by the intersection curve of two spherical surfaces, as shown in Figure 3c, which can be expressed as $A_{a} = π {d_{L K}}^{2} .$ (10)

Then, the critical external force (or output force) can be expressed as a function of the gas pressure and the bending angle: $F_{c r} = \frac{c Δ p A_{a} d_{E F} - 2 c b G}{2 l_{s}},$ (11)

in which, $\{\begin{matrix} b = \frac{l_{s}}{α (α - Δ α)} (sin β - sin (b_{1} α + β)) + (\frac{b_{1} l_{s}}{α - Δ α} + b_{1} b_{2}) cos (b_{1} α + β) \\ c = \frac{α - Δ α}{\sqrt{{(\frac{s in α}{α} - cos α)}^{2} + {(\frac{cos α - 1}{α} + sin α)}^{2}}} \end{matrix}$ (12)

Because the resultant change of the bending angle Δα is relatively small and negligible compared with the bending angle α, Eq. (12) can be simplified as $\{\begin{matrix} b = \frac{l_{s}}{α^{2}} (sin β - sin (b_{1} α + β)) + (\frac{b_{1} l_{s}}{α} + b_{1} b_{2}) cos (b_{1} α + β) \\ c = \frac{α}{\sqrt{{(\frac{s in α}{α} - cos α)}^{2} + {(\frac{cos α - 1}{α} + sin α)}^{2}}} \end{matrix}$ (13)

Length and tension of the OSLL

For the bending portion of the soft finger, the OSLL and ISLL are approximately treated as arcs sharing the same arc center O. Thus, the OSLL length l_os can be expressed as a function of α: $l_{o s} = l_{s} + d_{H Q} α,$ (14)

where d_HQ is the distance between the OSLL and ISLL. It can be observed that there is a linear relationship between the OSLL length and the bending angle. When there is no external force, for a static equilibrium state, the resultant moment at the intersection of the ISLL and the base is zero. Then, according to the geometrical relationships shown in Figure 3b and c, we have: $F_{b} d_{L} - F_{o s} d_{H Q} - G b_{G Q} = 0,$ (15)

where F_os is the tension of the OSLL, F_b is the reactive force from the base caused by the gas pressure acting on the inner wall of the gas cavity, d_L is the distance from point L to the ISLL, and b_GQ is the moment arm of gravity with respect to point Q. Thus, F_os can be calculated by: $F_{o s} = π {d_{L K}}^{2} Δ p \frac{d_{L}}{d_{H Q}} - G \frac{b_{G Q}}{d_{H Q}},$ (16)

in which, $\{\begin{matrix} d_{L} = (\frac{l_{s}}{α} + \frac{1}{2} d_{E F}) cos \frac{α}{2 n} - (\frac{1}{2} \sqrt{4 {R_{1}}^{2} - {d_{E F}}^{2}} - \frac{1}{2} l_{A B}) sin \frac{α}{2 n} - \frac{l_{s}}{α} \\ b_{G Q} = \frac{l_{s} + α b_{2}}{α} (sin β cot (b_{1} α + β) - cos (b_{1} α + β) + \frac{sin (b_{1} α)}{sin (b_{1} α + β)}) - b_{2} cos β \end{matrix}$ (17)

Experiments and Discussion

Deformation characteristics

To test the deformation characteristics of the soft finger, an experimental setup was built, as shown in Figure 4a. The finger was fixed on a holder and connected to a gas supply via silicone tubes. A barometer was set to measure the input gas pressure relative to the atmospheric pressure.

FIG. 4.

Measurement of the deformation characteristics of the soft finger: (a) experimental setup and (b) experimental and theoretical results of the bending angle varying with gas pressure.

To determine the bending angles, three marks were made on one side of the finger, as circled in Figure 4a. The first and last marks correspond to the beginning and end of the five gas cavities, respectively. Then, according to the arc determined by the three marks, the bending angle can be obtained. For example, as shown in Figure 4a, during an inflating process, the bending angle is ∼49° when the gas pressure is 14.5 kPa. In this way, both the inflating and deflating processes are tested (Supplementary Video S1), and the results are recorded and compared with the theoretical results obtained by numerically solving Eqs. (1–6). Table 1 lists the values of the constant parameters used for the numerical solutions. Among them, the elastic modulus of the soft material, made of Smooth-On 0030 silicone, is measured to be ∼0.1 MPa (details can be found in the Supplementary Data, as shown in Supplementary Figure S1).

Table 1.

Constant Parameters of the Fabricated Soft Finger

Parameter	l_AB (mm)	l_AE (mm)	d_EF (mm)	d (mm)	t₀ (mm)	l_s (mm)	E (MPa)	G (N)	b₁	b₂ (mm)	n
Value	7	1	10	10	1	40	0.1	0.24	0.73	2.5	5

Figure 4b shows that the bending angle varies with the gas pressure ranging from 0 to 25.5 kPa. Because of the structure of the soft finger, the natural bending angle (when the gas pressure is zero) is ∼15°, and the maximum bending angle is ∼210° when the gas pressure reaches 25.5 kPa. The differences between the inflating and deflating processes are mainly caused by the hysteresis behavior of soft materials, which is a common problem in soft robotics. The theoretical results agree well with the experimental results, demonstrating the accuracy of the theoretical models to a certain extent.

To facilitate the trajectory planning and control of the soft finger, the deformation curve is divided into two segments: when 0 ≤ Δp ≤ 15 kPa, the curve is fitted to a quadratic one, that is, fitted curve 1 in Figure 4b; when 15 < Δp ≤ 25.5 kPa, the curve is fitted to a sigmoidal one, that is, fitted curve 2 in Figure 4b. Thus, the relationship between the bending angle and gas pressure can be expressed as: $α = \{\begin{matrix} 13.1 + 0.18 Δ p + 0.19 Δ p^{2}, & 0 \leq Δ p < 15 k P a \\ 51.9 + \frac{178.2}{1 + e^{\frac{21.2 - Δ p}{2}}}, & 15 \leq Δ p \leq 25.5 k P a \end{matrix}$ (18)

Stiffness

The stiffness is an important property for both rigid and soft robots. However, it is quite complicated to discuss or define the stiffness of soft robots. Because of the flexibility and compliance, when a soft robot interacts with targets or surrounding environments, infinite degrees of freedom exist, and every point on its surface may be a force point where passive deformation occurs. That is, for soft robots, there are no fixed force points except for the mounting surfaces, so it is almost impossible to perform a comprehensive evaluation of stiffness.

A soft finger fixed on a “palm” can be treated as a cantilever beam, and the closer to the free end the force point is located, the lower stiffness. Considering that it is the finger pulp that contacts objects, here, the endpoint of the five gas cavities is chosen as the force point to evaluate the stiffness, as shown in Figure 5a. The force point is pulled by a rope connected to a tension meter. The tension meter is fixed on a sliding table that can move horizontally. We allow the sliding table slowly move 10 mm rightward, and the changing pulling force is recorded. Then, the stiffness can be approximately calculated as the incremental ratio of the force and displacement.

FIG. 5.

Measurement of the stiffness of the soft finger: (a) experimental setup, and experimental results of the stiffness varying with gas pressure difference under an initial bending angle of (b) 45°, (c) 90°, (d) 135°, and (e) 180°, respectively.

To detect how the gas pressure affects the stiffness, four groups of experiments were carried out with bending angles of 45°, 90°, 135°, and 180°. In each group, four cases were considered with different gas pressures. Each case was repeated five times, and an average of the results was obtained. It should be noted that the maximum allowable input gas pressure of this soft finger was tested to be ∼35–40 kPa, varying among individual specimens. If the gas pressure was beyond this range, the soft finger tended to leak near the ISLL. This is because the finger was not cast in one piece but solidified in two steps, as described in the Fabrication section. The dorsal portion and the finger pulp portion did not produce a tight fit. When the gas pressure is too high, tiny cracks appeared at the interface. Therefore, the input gas pressure was kept below 35 kPa in this work.

Figure 5b–e lists the experimental results. The pulling force (F) increases nearly linearly with the displacement, in terms of which the average stiffness (k) is calculated. The stiffness increases substantially with the gas pressure, indicating that the gas pressure plays a key role in the resistance to the bending deformation. In addition, given the gas pressure, the stiffness first increases and then decreases with the bending angle ranging from 45° to 180°. This is because, on the one hand, the larger the bending angle is, the shorter the arm of the external force, and the smaller the torque exerted on the fixed end of the finger, resulting in a smaller deformation and higher stiffness; however, on the other hand, with the increase in the bending angle, the axis length (i.e., the length of the cantilever beam) of the finger increases, resulting in a larger deformation and lower stiffness.

From Figure 5b–e, although the test gas pressure is no more than 35 kPa due to the limited fabrication method, the stiffness rises nearly 6, 4, 3, and 4 times at most, respectively, indicating that the ribbon-driven mechanism can effectively improve the variable stiffness property of soft inflatable fingers.

Output force

The output force was also tested by the experimental setup shown in Figure 5a. Each experiment was repeated five times, and the average of the results was calculated. For the OSLL, the transition between the tightened and relaxed states occurs instantly; therefore, the accurate value of the critical deformation of the soft finger is difficult to determine. To provide a more reasonable discussion, given the bending angle and gas pressure, the corresponding output force was measured with the displacement ranging from 1 to 5 mm. Here, for bending angles of 45°, 90°, 135°, and 180°, the corresponding inclined angle (β) was set to −45°, 90°, −135°, and 180°, respectively.

Figure 6 lists the experimental results as well as the theoretical results obtained by solving Eq. (11). Although some errors exist, the theoretical results are basically in agreement with the experimental results: the output force increases by one order of magnitude by increasing the gas pressure; most of the theoretical results lie within the range of Δs varying between 1 and 5 mm (the gray areas shown in Fig. 6), demonstrating the accuracy of the theoretical models to a certain extent.

FIG. 6.

Experimental and theoretical results of output force varying with gas pressure difference: the bending angle is (a) 45°, (b) 90°, (c) 135°, and (d) 180°, respectively.

Length and tension of the OSLL

From the Length and Tension of the OSLL section, theoretically, the OSLL length has a linear relationship with the bending angle. However, the soft finger actually swells radially when inflating, and the higher the input air pressure is, the larger the expansion. That is, d_HQ is not constant but varies with the input gas pressure. Therefore, in the experimental section, the OSLL length is investigated by considering both the bending angle and the input air pressure. Figure 7a shows the experimental setup (the method of measurement of the bending angle is shown in Supplementary Figure S3). The tension meter fixed on the sliding table is used to measure the tension of the OSLL. The length can be output by the controller of the sliding table. In this section, the inclined angle of the base (β) is set to 0°.

FIG. 7.

Test of the length and tension of the OSLL: (a) experimental setup, (b) the OSLL length varying with the bending angle with the tension of nearly zero, (c–f) the lengths and tensions of the OSLL varying with gas pressure under an initial bending angle of 45°, 90°, 135°, and 180°, respectively, and (g) the relationships between the stiffness, bending angle, and OSLL tension. OSLL, outer strain limiting layer.

Figure 7b shows the OSLL length varying with the input gas pressure. In this case, the OSLL is not tightened but passively extends with the increase in the bending angle, that is, the tension is nearly zero at all times. Here, the negative value of α means that the soft finger bends toward the dorsal side. It can be observed that, when α is below 75°, the experimental and theoretical results coincide well with each other. When α is above 75°, a substantial difference exists between the experimental and theoretical results because of the undesired expansion of the gas cavities.

Figure 7c–f lists the tensions with bending angles of 45°, 90°, 135°, and 180°, respectively. The experimental results are always higher than the theoretical results, and the larger the bending angles, the bigger the deviations. The deviations are mainly caused by the friction between the ribbon and finger, which is difficult to determine due to the irregular radial expansion of the gas cavities and thereby is ignored in Eq. (15). It worth to note that, with the constraints of the OSLL, it requires the gas pressure to overcome both the deformation resistance and ribbon-finger friction. Therefore, the added ribbon will unavoidably bring about certain reduction in the actuation efficiency.

Figure 7c–f also presents the experimental value of l_os under different values of Δp, from which it can be observed that: for a given bending angle, the required OSLL length changes little with different input gas pressures. Figure 7g shows the relationships between the stiffness and the tension of the OSLL, indicating that the higher the stiffness, the larger the required F_OS. Then, based on these data, the stiffness of the soft finger can be modulated by adjusting the input gas pressure and the OSLL length (Supplementary Video S2). Although the volume of the finger expands with the gas pressure increasing, the bending angle changes little, verifying the good variable stiffness performance.

Load capacity

To test the load capacity of a single soft finger, an experimental setup is built as shown in Figure 8a. The soft finger was fixed on a holder with the inclined angle β and the initial bending angle of 90° and 180°, respectively. The sliding table moves rightward with a constant speed of 1 mm/s and the tension meter records the pulling force in real time. An elastic band is set between the tension meter and the soft finger to ensure that the rope can smoothly detach from the soft finger when the maximum pulling force (i.e., the load capacity) is reached (Supplementary Video S3). Then, the load capacity of a single soft finger was tested by altering the input gas pressure.

FIG. 8.

Test of the load capacity of a single soft finger: (a) experimental setup and (b) the load capacity varying with gas pressure.

Figure 8b lists the results. Given a bending angle of ∼180°, without the OSLL, the input gas pressure is ∼23 kPa, and the load capacity of the soft finger is ∼414 g. With the constraints of the OSLL, when the input gas pressure rises to 35 kPa, the load capacity is as high as 1.25 kg, an enhancement of nearly three times.

Dual-finger soft robotic gripper

To further investigate the application prospect, a soft robotic gripper is assembled by integrating two soft fingers. Figure 9a shows the experimental setup, which mainly consists of a dual-finger soft robotic gripper, a holder, an electric slide table, and a ribbon-driven mechanism. The gripper is connected to a gas supply via a set of tubes. A programmable controller is used for the control of the motion of the slide table, the ribbon-driven mechanism, and the input gas pressure. The ribbon-driven mechanism is actuated by a step motor. The free ends of the OSLLs are wrapped around a wheel that is fixed to the motor shaft. The OSLL lengths can be adjusted by controlling the step motor.

FIG. 9.

Photos of the dual-finger soft robotic gripper grabbing different targets: (a) a 63 g egg, (b) a 350 g toolkit, (c) a 370 g mini vise, (d) a plastic bottle containing about 400 g water, (e) a sheet, and (f) a soft bag.

To ensure that the soft finger possesses both a high flexibility and variable stiffness, the control procedures for the dual-finger soft robotic gripper are as follows: Step 1, the ribbon-driven mechanism draws the OSLLs to expand the opening angle of the gripper to fit for larger size objects; Step 2, the gripper moves toward the target; Step 3, the ribbon-driven mechanism elongates the OSLLs to a certain degree; Step 4, the gas supply is turned on and operates until the preset input gas pressure is achieved, meanwhile the target is grasped; and Step 5, the gripper takes the target away. Then, experiments were carried out to test the grasping abilities of the dual-finger gripper (Supplementary Video S4).

Figure 9a–d shows the experimental photos. The dual-finger soft robotic gripper can easily and stably grab various objects with different sizes, shapes, and weights, indicating that this new gas–ribbon-hybrid actuated soft finger possesses good application prospects in the development of soft end effectors with active variable stiffness. It is worth noting that, even without the variable stiffness mechanism, the gripper can also pick up the targets with the same input gas pressures, as shown in the last figures of Figure 9a–d. The main difference is that without the constraints of the OSLLs, the finger deforms exaggeratedly due to its inherent softness.

Then, what are the benefits of the variable stiffness mechanism? Actually, for the soft finger proposed in this work, both the bending deformation and the stiffness modulation are realized by adjusting the input gas pressure. That is, for the experiments shown in Figure 9, some of the input gas pressure is responsible for the bending deformation, whereas the left is used for modulating the stiffness. Then, experiments of only considering the input gas pressure for the bending deformation were performed, as shown in Supplementary Video S4. It can be observed that, without the modulated stiffness, although the deformation of the finger is big enough for enclosing the targets, the gripper failed to pick up the targets. From this perspective, in the cases when the OSLL works, it is the variable stiffness mechanism that contributes to the success of target grasping.

Generally, for soft finger-based grasping, an active variable stiffness is not necessary for all target objects. However, in some cases, controlling the finger stiffness can greatly enhance the quality of grasping, especially for grasping easy deformation or vulnerable objects. Usually, a stable grasp requires a higher input gas pressure because the stiffness of the soft finger under a lower pressure may not be high enough to afford the weight of the target. However, as the input gas pressure increases, the clamping force from the fingers to the target also increases, which may easily cause undesired damage and deformation to the target.

For the soft finger proposed in this work, when a high stiffness is required, the clamping force can be offset by the ribbon. To better understand this point, two simple experiments of grasping easy-deformation objects were performed (Supplementary Video S5), as shown in Figure 9e and f. It can be observed that, without the active variable stiffness function, the bag and the sheet deform obviously. When the ribbon-driven mechanism works, a limited and safe bending angle can be obtained without much clamping force generated. Then, by modulating the stiffness, the objects are successfully grasped accompanied by little deformation that is mainly caused by the weight of the objects. Therefore, the capability of the active variable stiffness can help better preserve the original states of the target objects during the grasping and operating processes.

The weight that the dual-finger gripper can hold not only depends on the physical properties of the target object (such as the size, shape, surface roughness, and stiffness) but also greatly relates to the gap between the two fingers. In this case, the gap is 40 mm. A cylinder of 30 mm in diameter is applied to test the load capacity, as shown in Figure 10a. The experimental principle is similar to that of Figure 8a. The measured friction coefficient between the cylinder and the finger is ∼1.7, and the friction can be evaluated.

FIG. 10.

Test of the load capacity of the fabricated dual-finger gripper: (a) experimental setup and (b) the load capacity varying with gas pressure.

Figure 10b shows the load capacity, the corresponding normal force (F_n), and friction (F_f) varying with the input gas pressure. The maximum weight that the fabricated dual-finger gripper can withstand is ∼400 g with the input gas pressure of 35 kPa (Supplementary Video S6), which is much lower than that of a single finger. This is because, in this case, the maximum bending angle is limited to be ∼50° by the gripper configuration. Nevertheless, a further optimal design can substantially improve the load capacity, which is beyond the scope of this work.

What is more, to better understand the contribution of the OSLLs to the load capacity, experiments without the OSLLs were performed. From Supplementary Fig. S2b, when the input gas pressure is 17.5 kPa, the bending angle approaches 50°. Thus, to facilitate the comparative analysis, the load capacities with the input gas pressure of 15 and 17.5 kPa were tested (Supplementary Video S6), of which the results are also listed in Figure 10b.

It can be observed that whether or not the OSLLs work, the load capacity differs little when the pressure is below 17.5 kPa. However, in practice, the bending deformation of the gripper is usually limited (e.g., as shown in Supplementary Fig. S2b, when the gas pressure is above 20 kPa, the deformation of the gripper is too big to tightly grasp the cylinder). Given the same limited bending angle, with the constraints of the OSLLs, the input gas pressure can be much higher, resulting in a higher load capacity. From this perspective, in some cases, the added ribbon can improve the load capacity.

Comparison with other soft grippers

Table 2 lists the properties of some typical soft grippers reported in recent years. Tendon-driven grippers³ can have a good load capacity mainly due to the unstretchable driving tendons, which provide high resistance to passive deformations. Because of that, their compliance is usually not high compared with pneumatic grippers.

Table 2.

Parameters of Some Typical Soft Grippers/Fingers

Type	Load capacity (g)	Working conditions	Variable stiffness			Response time	Compliance	Constituent materials
Type	Load capacity (g)	Working conditions	Active/passive	Implement method	Stiffness range (N/mm)	Response time	Compliance	Constituent materials
Tendon-driven³	3500	—	—	—	—	Short	Fair	Soft
Dielectric elastomer actuator⁸	82.1	3.5 kV	—	—	—	Short	High	Soft
Fluidic elastomer actuator⁹	4000	0–120 kPa	—	—	—	Short	High	Soft
Fluidic elastomer actuator¹⁰	500	—	—	—	—	Short	High	Soft
Fluidic elastomer actuator¹¹	1100	0–350 kPa	—	—	—	Short	High	Soft
Fluidic elastomer actuator¹⁶	220	0–500 kPa	—	—	—	Short	High	Soft
Compliant mechanism¹⁷	2100	—	—	—	—	Short	Low	Soft
Fluidic elastomer actuator²⁸	1673	20–80 kPa	Passive	Particle jamming	—	Short	Fair	Soft
Fluidic elastomer actuator³¹	—	0–40 kPa	Active	Particle jamming	0.2–0.7	Short	Low	Soft
Fluidic elastomer actuator³²	750	0–90 kPa	Passive	Scale structure	0.049–0.075	Long	Fair	Soft
Shape memory polymer³⁵	590	27–60°C	Active	Temperature	0.045–2.509	Long	Fair	Soft-rigid hybrid
Fluidic elastomer actuator/shape memory polymer³⁹	—	0–125 kPa 25–65°C	Active	Temperature	0.004–0.1	Long	Fair	Soft-rigid hybrid
Fluidic elastomer actuator⁴⁷	—	0–400 kPa	Active	Gas pressure	0.043–0.098	Short	Fair	Soft
Fluidic elastomer actuator⁴⁹	2400	0–200 kPa	Active	Gas pressure	0.029–0.137	Short	Fair	Soft
Shape memory alloy⁵⁰	910	—	—	—	—	Long	High	Soft-rigid hybrid
Proposed by us
Single finger	1360	0–35 kPa	Active	Gas pressure	0.07–1.4	Short	High	Soft
Dual-finger gripper	400	0–35 kPa	Active	Gas pressure	0.07–1.4	Short	High	Soft

For fluidic elastomer actuator-based grippers without variable stiffness mechanisms,^9–11,16 the stiffness and load capacity are usually inversely correlated with the compliance. The gripper reported in the study of Zhou et al.⁹ possesses a high load capacity of 10 times the self-weight by utilizing passive compliant surfaces covered with milli-scale nail arrays that endow reliable contact with targets. Although the enhanced load capacity mainly results from the increased adhesion or friction forces, it also requires the gripper to have certain stiffness, which in turn affects the compliance.

Jamming methods have been widely used to achieve high stiffness and good load capacity. However, particle jamming mechanisms^28,31 contain rigid components, bringing down the compliance and the structural compactness, whereas scale jamming-based stiffness modulation³² is usually passive and coupled with the bending deformation of the grippers. The fiber-reinforced gripper reported in the study of Fei et al.⁴⁹ has variable stiffness and high load capacity; however, it works under a high gas pressure and has a relatively low compliance.

Compliant grippers,¹⁷ operating with the passive deformations of the compliant mechanism, have greatly enhanced the compliance to targets while maintaining the good load capacity in comparison with rigid grippers. However, the stiffness and load capacity are also inversely correlated with the compliance. For dielectric elastomer grippers,⁸ a very high voltage is required for routine grasping, which may introduce problems related to safety. Because of the heat dissipation problems, the response time of SMA/SMP-based grippers^35,39,50 is relatively long, decreasing the grasping efficiency.

For the gas–ribbon-hybrid actuated soft finger proposed in this work, although an individual parameter may not be the best solution, it possesses good comprehensive performance in comparison with the existing solutions: the finger is entirely made of highly flexible materials, enabling good compliance; the active variable stiffness is realized by adding a ribbon, so the finger is compact, lightweight, and cost-effective; and the finger works under a low and safe gas pressure below 35 kPa, while it possesses a wide range of stiffnesses and a relative high load capacity. It is worthy to note that if further improving the preparation technology, the soft finger can withstand a much higher operating gas pressure; thus, both the active variable stiffness and load capacities can be strengthened accordingly.

Conclusions

A new hybrid actuated soft finger is proposed for the first time by integrating gas-driven and ribbon-driven mechanisms. The two mechanisms coordinate with each other, and an active variable stiffness is realized at any bending angle. The bending deformation of the soft finger, mainly arising from the expansion of the inflatable gas cavities, is uncoupled with the stiffness modulation process. Theoretical models are established to describe the deformation characteristics and the output force of the soft finger, as well as the required length and tension of the OSLL, which are verified by experiments.

The soft finger, made entirely of soft materials, works under a range of low and safe gas pressures of 0–35 kPa, whereas the maximum bending angle reaches ∼210°. With the help of the ribbon-driven mechanism, the stiffness of the soft finger can be increased by three to six times. A single soft finger can withstand a weight of 1.25 kg. Then, a soft robotic gripper is assembled by integrating two soft fingers, and grasping experiments are carried out based on a preplanned control flow. The dual-finger soft gripper can easily and stably grasp various objects with different sizes, shapes, and weights, and better preserve the original states of the targets during the manipulation process.

It was found that the proposed gas–ribbon-hybrid actuated mechanism can effectively enhance the variable stiffness property of a soft finger while retaining good compliance to target objects, indicating that this new mechanism has good application prospects in the development of soft end effectors for several application areas such as medical treatment, rehabilitation training, and manipulation. Further work will focus on developing a soft robotic hand with active variable stiffness by utilizing this new gas–ribbon-hybrid actuated mechanism and detecting relevant high-efficiency control methods.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work is mainly supported by the Natural National Science Foundation of China (NSFC) (51705110) and the Fundamental Research Funds for the Central Universities (HIT.NSRIF.2019011).

Supplementary Material

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Supplementary Material

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