3.1. Extension layer design

There are various cross-sectional shapes of the extension layer of the FEA. In the past, rectangles, circles, and semicircles have been used for the design of the extension layer. Polygerinos et al. [Reference Polygerinos, Wang, Overvelde, Galloway, Wood, Bertoldi and Walsh25] confirmed that extension layers with circular cross-sections have better bending properties compared to rectangular cross-sections. Sun et al. [Reference Zs, Zh and Tang20] analyzed the bending performance of several circular cross-section extension layers using finite element analysis and confirmed that the semicircular cross-section has better bending performance. In this paper, we explore the relationship between the curvature of the FEA and various parameters on the basis of the semicircular hydraulic network structure, and based on this, we design the soft hand structure.

The relationship between actuator curvature and bending moment is shown in Eq. (1).

(1) \begin{equation} k = \frac{M}{E_l} \end{equation}

Where $k$ is the curvature of the actuator, $M$ is the bending moment of the actuator, and $E_l$ is the rotational stiffness.

The bending moment can be obtained from Eq. (2).

(2) \begin{equation} M = \frac{{E_l}\times{\theta }}{L} \end{equation}

Where $\theta$ is the bending angle of the actuator, $L$ is the length of the actuator.We set the actuator length to $130\, {\rm mm}$ [Reference Deimel and Brock26], and the actuator length is related to the fluid chamber transverse axis length and the fluid chamber spacing as shown in Eqs. (3) and (4).

(3) \begin{equation} L_1 = n \times (l + a) \end{equation}

(4) \begin{equation} L = L_1 + L_2 + L_3 \end{equation}

Among them, $L_1$ is the total length of the hydraulic network, $L_2$ is the length of the proximal cap,take $L_2=15mm$ , $L_3$ is the distal cap length, take $L_3=5mm$ , n is the number of fluid chambers, $l$ is the fluid chamber transverse axis length, and $a$ is the fluid chamber spacing.

Assuming that the pressure applied to each fluid is $P_{in}$ , the stress applied to the fluid chamber can be obtained from Eq. (5).

(5) \begin{equation}{\sigma }_{x}={P_{in}}\times{\frac{r}{h-r}} \end{equation}

Where ${\sigma }_{x}$ is the axial stress in the fluid chamber under pressure $P_{in}$ , $r$ is the radius of the semicircular fluid chamber, and $h$ is the height of the actuator. From Eq. (5), it can be seen that the larger the value of $\frac{r}{h}$ , the greater the axial stress of the fluid chamber.

The resulting axial strain ${\varepsilon }_{x}$ should be a nonlinear function of ${\sigma }_{x}$ , and the total axial deformation ${\delta }_{x}$ is an accumulation of deformations in each fluid chamber.

(6) \begin{equation}{\delta }_{x}=nl{{\varepsilon }_{x}}({\sigma }_{x}) \end{equation}

Since the restriction layer does not deform axially during the deformation of the extension layer, the actuator undergoes bending deformation. The bending angle is shown in Eq. (7).

(7) \begin{equation}{\theta }=2narctan{\frac{l{{\varepsilon }_{x}}({\sigma }_{x})}{2r}} \end{equation}

Integrating Eqs. (1) to (7) yields Eq. (8).

(8) \begin{equation} k ={\frac{2narctan{\frac{l{{\varepsilon }_{x}}({\sigma }_{x})}{2r}}}{(l+a)+ L_2 + L_3}} \end{equation}

Since the value of $arctan{\dfrac{l{{\varepsilon }_{x}}({\sigma }_{x})}{2r}}$ fluctuates in $[0-{\frac{\pi }{2}}]$ , the distance between the centers of the two fluid chambers has a greater influence on the curvature. In order to increase the curvature, the center-to-center distance should be smaller, that is, the fluid chambers are more closely distributed. We set the center-to-center distance to $10\,{\rm mm}$ , where $l=8\,{\rm mm}$ and $a=2\,{\rm mm}$ . To make $\dfrac{r}{h}$ take a larger value, the radius of the fluid chamber is $13mm$ , and the height of the actuator is $18\,{\rm mm}$ . Wu et al. [Reference Wu, Jiangbei and Yanqiong24] deduced the relationship between the wall thickness of the fluid chamber and the input pressure. In the same bending angle, the smaller the wall thickness, the smaller the input pressure, in order to achieve the same bending used less pressure, the wall thickness $b$ is set to $2\,{\rm mm}$ in this paper. The main parameters of the extension layer are summarized in Table 1.

Table I. Extension layer parameters.

3.2. Spring steel plate design

The restriction layer of the FEA is usually made by embedding a layer of non-extendable flexible fiber material in silicone [Reference Onal and Rus13]. To improve the soft gripper gripping force, we use a spring steel plate as the insert of the restriction layer. The cross-section of the spring steel plate is rectangular, and its length and width are compatible with the FEA and slightly smaller than the FEA. The spring steel plate needs to improve the rigidity of the soft gripper, so we need to choose the right thickness of the steel plate.

From Hooke’s law, the stress is proportional to the strain in the stress limit range.

(9) \begin{equation} \sigma ={E}\times{\varepsilon } \end{equation}

Where $\sigma$ is the stress on the spring steel plate, $\varepsilon$ is the strain generated by the spring steel plate, and $E$ is the modulus of elasticity of the material.

The spring steel plate should work with less stress than its required stress.

(10) \begin{equation}{\sigma } \leq [\sigma ] \end{equation}

The strain of the specimen can be expressed by Eq. (11).

(11) \begin{equation}{\varepsilon } = \frac{{\Delta }s}{s} = \frac{d{\alpha }}{2l} \end{equation}

Where $d$ is the thickness of the spring steel plate, $\alpha$ is the bending angle of the spring steel plate, and $s$ is the length of the spring steel plate.

Substituting (9) and (10) into (11) to obtain Eq. (12).

(12) \begin{equation}{d} \leq{\frac{2[\sigma ]s}{E{\alpha }}} \end{equation}

In this experiment, the material used is $65\,{\rm Mn}$ ,whose modulus of elasticity is ${2.11}\times{10^{11}} \,{\rm Pa}$ . Since the allowable stress of spring steel plate is $570\,{\rm MPa}$ and the allowable stress of silica gel is $420\,{\rm MPa}$ ,thus $[{\sigma }]=420\,{\rm MPa}$ , $l=110\,{\rm mm}$ , ${\theta }={\dfrac{\pi }{2}}$ .

Calculated to get formula (13).

(13) \begin{equation}{d} \leq{0.32\,{\rm mm}} \end{equation}

Due to the coupling of the restriction layer and the extension layer, the two is connected by silicone adhesive, and there is stress concentration in the fluid chamber structure, so the actual allowable stress should be less than $420\,{\rm MPa}$ . Here, a spring steel plate thickness of $0.1 \,{\rm mm}$ is chosen and the spring steel plate is embedded in a $2 \,{\rm mm}$ thick restriction layer. Integrating the parameters of the extension layer and the restriction layer, the structure of the FEA obtained is shown in Fig. 2.

Figure 2. Extension layer and restriction layer views (a) The top view of the extension layer; (b) The main view of the extension layer; (c) The section view of the extension layer; (d)The top view of the restriction layer; (e)The main view of the restriction layer; and (f) Restriction layer.

As shown in Fig. 2, the extension layer consists of a distal cap, a proximal cap, and a hydraulic network. The restriction layer contains a empty space for embedding spring steel plates and has a channel for sensor wiring at its top.The assembly diagram of the FEA is shown in Fig. 3.

Figure 3. Fluidic elastomer actuators assembly view (a) Assembly view and (b) Exploded view.

4.1. Circuit principle

4.1.1. Full bridge circuit

Resistance strain gauges work based on the resistance-strain effect. The resistance-strain effect is a phenomenon that directs the mechanical deformation of a conductor or semiconductor material under the action of an external force, with a corresponding change in its resistance value. Based on this effect, the change in mechanical quantity can be converted into a change in electrical quantity. The resistance-strain effect can be expressed by Eq. (14).

(14) \begin{equation}{\Delta }{R} = \frac{{\partial }R}{{\partial }l}{\Delta }l + \frac{{\partial }R}{{\partial }l}{\Delta }A + \frac{{\partial }R}{{\partial }l}{\Delta }{\rho } \end{equation}

where $R$ is the resistance of the resistance strain gauge, $l$ is its length, $A$ is its cross-sectional area, and $\rho$ is the resistivity of the resistance strain gauge.

The resistance strain gauge sensor is a circuit that uses the resistive strain effect to convert the detected signal into an electrical signal [Reference Hoffmann27]. The strain gauges are applied to the elastomer, and when the elastomer is deformed, the strain gauges are deformed at the same time, causing a change in the resistance of the strain gauges, which is then converted into a voltage change by the measurement circuit. The measurement circuit of the strain gauge sensor usually adopts a bridge circuit. Because of the high sensitivity and low non-linear error of the full bridge circuit, we adopt the full bridge circuit as the measurement circuit of the strain gauge. The operating schematic of the full-bridge circuit is shown in Fig. 5.

Figure 5. Full bridge circuit.

When the FEA is deformed under water pressure, the output signal of the full bridge circuit can be obtained by Eq. (15).

(15) \begin{equation}{E}_{out}={\frac{{R_2}\times{R_4}}{R_2+R_4}}+\left({\frac{{\Delta }R_1}{R_1}}+{\frac{{\Delta }R_2}{R_2}}+{\frac{{\Delta }R_3}{R_3}}+{\frac{{\Delta }R_4}{R_4}}\right)\times{{E}_{in}} \end{equation}

4.1.2. Signal processing circuit

Since the voltage signal output from the measurement circuit is very weak and easily covered by noise, signal amplification, filtering, and conversion are required before signal acquisition, and the signal processing flow is shown in Fig. 6.

Figure 6. Signal processing process.

As the core of the analog circuit, the op-amp can be powered by dual or single power supply. Since the total dynamic range, output voltage/current, accuracy, and load immunity of the dual-supply op-amp are better than those of the single-supply op-amp, we use a dual-supply op-amp in the amplifier circuit. The entire signal processing circuit consists of a preamplifier stage, a filter amplifier stage, and a buffer stage. The manufacturing process of the sensing circuit is shown in Fig. 7.

Figure 7. Sensing circuit patching process (a) Spring steel plate patching position processing; (b) Patching: two resistance strain gauges in the middle of each of the upper and lower surfaces of the spring steel plate; (c) Moisture-proofing and insulation: a sticky layer of plastic sheet under the lead wire and a moisture-proofing layer on top of the strain gauges; and (d) Embedding the processed spring steel plates into the restriction layer, the extension layer is glued to the restriction layer and the amplification circuit is connected to the strain gauges.

4.2. Sensor calibration

The signal processed by the amplification circuit is still a voltage signal. In order to achieve the role of measuring the system water pressure, a pressure sensor is installed in the hydraulic circuit in this paper, so as to obtain the standard water pressure value, and the output signal of the resistive strain sensor is compared with the standard water pressure value for fitting, thus calibrating the resistive strain sensor. The no-load water pressure of the pump used in this calibration experiment was 12.8 kPa. Twenty-four sets of data were collected in the experiment, and matlab was used to fit a polynomial to the collected data, and the curve obtained is shown in Fig. 8.

Figure 8. Sensor calibration (a) Fitting the collected data by the least squares method, where ^* represents the collected data and the green curve is the fitted curve; (b) Comparing the theoretical curve with the fitted curve, where ^* represents the collected data, the green realization represents the fitted curve, and the black dashed line represents the theoretical curve.

The curve equation obtained by fitting is shown in Eq. (16).

(16) \begin{equation} P=0.7606{V^3}-3.7409{V^2}+21.7588V-2.7595 \end{equation}

Where $P$ is the system water pressure and $V$ is the voltage signal output from the resistance strain gauge sensor.

By comparing the theoretical curve and the fitted curve, it can be seen that the two basically overlap. To further evaluate the accuracy of the curve, we calculated the R-square of the curve using matlab. The R-square value of the calculated curve is 0.9933, so the sensor has high accuracy.

4.3. System control process

Two sensors are involved in the system, where sensor 1 is a standard water pressure sensor and sensor 2 is a resistance strain gauge water pressure sensor. Sensor 1 only provides the basis for calibration and testing of Sensor 2 and is not involved in the control of the system. Power supply provides energy for the main controller, pumps, valves, and sensors. The system controls the action of the hydraulic pump and valve through the main controller, thus controlling the action of the soft gripper. When the soft gripper moves, sensor 1 and sensor 2 will sense the system’s real-time water pressure, sensor 2 will pass the water pressure value back to the main controller, and the main controller will use the returned water pressure value to further control the valve and pump action. The system control flow is shown in Fig. 9.

Figure 9. System control process.

5.1. FEA manufacturing

In this paper, a silicone rubber with a hardness of 30 degrees Shore is used to manufacture the FEA body, and a spring steel plate is used as an insert in the restriction layer of the FEA. A strain gauge is attached to the spring steel plate as described in Chapter 4, and the strain gauge is connected to the amplifier circuit through a lead wire. The mold for the FEA was molded by fused deposition modeling [Reference Şahin28].

The manufacturing process of the FEA is shown in Fig. 10.

Figure 10. Fluidic elastomer actuator manufacturing process (a) Restriction layer molding: liquid silicone with curing agent added is poured into the restriction layer mold and waited for molding; (b) Extension layer molding: liquid silicone with curing agent is poured into the extension layer mold and waited for molding; (c) Restriction layer and extension layer; and (d) Finished product: the spring steel plate is embedded in the restriction layer and the restriction layer is glued to the extension layer using silicone adhesive.

5.2. Pressure-bearing capacity and bending capacity experiments

In this group of experiments, we tested the ultimate pressure-bearing and bending capacity of the FEA, and also studied the effect of the spring steel plate on the ultimate pressure-bearing and bending capacity of the FEA.

Due to the process, there is a slight difference between the FEAs manufactured each time, this experiment uses different batches of manufactured FEAs to test the pressure-bearing capacity and bending capacity. The experimental results are shown in Fig. 11.

Figure 11. Fluidic elastomer actuator bending capacity and pressure-bearing capacity test (a) $-$ (c) Fluidic elastomer actuator with spring steel plate; (d)–(f) Fluidic elastomer actuator without spring steel plate.

By extracting the coordinates of the discrete points of the bending curve of the FEAs in Fig. 11, we plotted the scatter plots of the bending curve of the FEAs, and fitted the discrete points with a circle, the fitting results are shown in Fig. 12.

Figure 12. Fluidic elastomer actuators bending curve.

In this group of experiments, we explored the pressure-bearing and bending capacities of the FEA and the effect of spring steel plates on them. The ultimate pressure and curvature of the FEAs are shown in Table II.

Table II. Curvature and ultimate pressure values.

The average pressure of the first three experiments was calculated to be 71.09 kPa with an average curvature of 0.0024, and the average value of the last three experiments was 58.45 kPa with an average curvature of 0.0086. Thus the pressure-bearing capacity of the fluid-elastic actuator was increased by 21.63% after filling with the spring steel plate. The bending capacity was reduced by 72.09% after filling with the spring steel plate.

5.3. Gripper experiment

To verify the grasping performance of the soft gripper and the effect of the spring steel plate on the grasping performance of the soft gripper, we built a four-finger soft gripper system and conducted grasping experiments for different shapes and masses of objects.

5.3.1. Experiment on the effect of the spring steel plate on gripping performance

In this experiment, we conducted three sets of grasping experiments on objects of different shapes and masses using soft grippers with and without spring steel plates, to investigate the grasping performance of soft grippers and the effect of spring steel plates on the grasping performance. The experimental results are shown in Fig. 13, where the soft grippers used in experiment (A) to experiment (C) contain spring steel plates, and the soft grippers used in experiment (D) to experiment (F) do not contain spring steel plates.

Figure 13. Gripping experiment (a) A porcelain spoon; (b) A cup with 20 g weights inside; (c) A 200-g porcelain bowl; (d) A porcelain spoon; (e) A cup with 20 g weights inside; and (f) A 184 g porcelain bowl.

The experimental data are shown in Table III.

Table III. Comparison experiment data.

When using the soft gripper with spring steel plates for grasping, all three groups of experiments conducted can achieve stable grasping. However, the use of soft gripper without spring steel plates to grasp the spoon and cup are not stable, there is a gradual decline, and the water pressure of the system at the time of gripping is greater than that of the former. Although it adapted well to the surface profile of the bowl when grasping the porcelain bowl, the soft gripper without spring steel plates was broken due to excessive pressure when trying to pick up the bowl. The experimental result is shown in Fig. 14.

Figure 14. Gripping experiment: The soft gripper without spring steel plates was broken.

5.3.2. Soft gripper sensor accuracy verification

Since the sensor needs to be mounted on a spring steel plate, a soft gripper with a spring steel plate is used in this experiment. In the above experiments, we have used the soft gripper with a spring steel plate for three sets of experiments, and in this experiment we added three sets of experiments on this basis, and the experimental data were collected and recorded. The experimental results are shown in Fig. 15.

Figure 15. Gripper experiment (a) Porcelain spoon; (b) Metal box; (c) Porcelain bowl; (d) A cup with 20 g weight inside; (e) A cup with 30 g weight inside; and (f) A cup with 50 g weight inside.

The experimental data are shown in Table IV.

Table IV. Gripper experiment data.

The standard value is measured by a standard water pressure sensor, and the experimental value is measured by the resistance strain gauge sensor we built. The average accuracy of the six experiments is 99.64% .