# Fiber Embroidery of Self-Sensing Soft Actuators

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Spiral Pattern Design for Embroidered Actuators

_{max}is the outer radius of the pattern, and 2π(m − 1)/n, where m ranges from 1 to n, is the angular offset of the mth spiral to achieve equal angular spacing.

#### 2.2. Membrane Fabrication

^{®}00-10, Smooth-On, Inc., Macungie, PA, USA) was chosen for the stretchable membrane material, because it was soft enough to achieve maximum rotation at low (<3 psi) pressures that did not cause leaking around the seal. Equal amounts of Ecoflex

^{®}00-10 (A) and (B) were thoroughly mixed, and 20 g of the mixture was poured into a plastic mold with a 90 mm diameter and 2 mm depth (Figure 1c). The silicone was degassed in a vacuum chamber. The fiber pattern was embedded Kevlar™ side down into the still-uncured Ecoflex

^{®}00-10 (Figure 1d). A similar method has been used by others to insert fine wires into elastomer castings using a sewing machine without a programmable path [20]. In our work, the machine guided the thread to each x,y coordinate as shown in Figure 1a. The silicone was then cured in a 70 °C oven for 30 min. After curing, the water-soluble plastic was washed away in smooth-running tap water (Figure 1e) with care to avoid displacing the embedded fibers.

^{®}00-10 over the mold (Figure 1f), degassing it for five minutes, and then curing it again in the oven. At the end of the process, the fiber pattern was embedded at the mid- thickness of a 3 mm thick, ≈90 mm diameter Ecoflex

^{®}circle. Optionally, after curing the top Ecoflex

^{®}layer, a stretchable optical fiber [21] was placed across the spiral pattern through its center. Ecoflex

^{®}was dispensed on top of the fiber in a thin layer and cured to attach it to the surface. Thread-embedded silicone membranes were removed from the mold and clamped for testing. Figure 1 shows one of the actuators before (Figure 1g) and after (Figure 1h) inflation. Inflation produces both rotational and vertical displacement of the membrane.

#### 2.3. Testing Methods

#### 2.3.1. Measuring Inflation of Soft Actuators

#### 2.3.2. Rotational Motion Measurements

#### 2.3.3. Shape Characterization

_{0}, and its measured center height h. A polygon-based shape metric (see Supplementary Methods, Equation (S1)) was used to compare the measured profile shape to the corresponding spherical cap.

#### 2.3.4. Torque Measurements

^{®}404 to the center of the actuator (Supplementary Figure S1). The end of the stick was pressed down on a scale to measure the torque produced at increasing angles at pressures up to 3 psi.

#### 2.3.5. Fiber Optic Lamination and Testing

^{®}00-10. Fiber ends were connected to an infrared light-emitting diode (LED) and an amplified photodiode (TSL-12, ams-Taos Inc., Plano, TX, USA).

## 3. Actuator Model

#### 3.1. Energy Balance

^{−2}, A is the surface area of the inflated thin membrane, A

_{0}is the surface area of the flat membrane, κ is a torsional spring constant for the membrane, θ is the rotation angle, P is the inflation pressure, and V is the enclosed volume.

#### 3.2. Spherical Cap Approximation

_{0}is the fixed radius of the testing plate (0.038 m) and h is the height of the membrane center above the plate, which varies with pressure.

#### 3.3. Spiral Mapping onto Spherical Cap

#### 3.4. Values for Coefficients

#### 3.4.1. Strain Energy

_{x}/L

_{x}

_{0})

^{2}and (L

_{y}/L

_{y}

_{0})

^{2}, or for equibiaxial stretching, A/A

_{0}. Setting ${\lambda}_{3}$ to 1 means the membrane thickness does not change during inflation, a simplification made to get an estimate for the value of $\gamma $ in the first-order energy balance model. Re-assembling the first term in Equation (11),

_{1}for Ecoflex

^{®}00-30 was measured by others [25] to be 1.27 × 10

^{−2}MPa; it is likely smaller for the softer Ecoflex

^{®}00-10 silicone we used. The total strain energy in the membrane is estimated by multiplying the strain energy density in Equation (11) by the volume tA of the thin membrane material, where the thickness t is ≈3 mm and the surface area A is given by the spherical cap Equation (8),

_{1}t or 76 J m

^{−2}if Ecoflex

^{®}00-30 were used. However, a smaller $\gamma $ value of 30 J m

^{−2}better matched the experimental data from the softer Ecoflex

^{®}00-10 membranes.

#### 3.4.2. Shear Energy

^{−1}in the torque measurements; experimental details are provided in Section 4.3.

## 4. Results and Discussion

#### 4.1. Rotation Angle vs. Pressure

#### 4.2. Actuator Shape Compared with Spherical Cap Model

#### 4.3. Torque Exerted by the Actuator

^{−1}neighborhood. For the model in Figure 4, a good match to the experimental data was obtained with a torsional spring constant $\kappa $ of 0.06 N m rad

^{−1}, consistent with the experimental results. At the higher end of the rotation range for the highest-twist actuator, the contact area between the actuator and the wooden stick began to decrease as the actuator took on a more cone-shaped profile (Figure 3l); debonding may explain why the k = 1.32 actuator exerted a decreasing amount of torque at higher angles.

#### 4.4. Optical Detection of Actuator State

^{1}/

_{2}k

_{f}Δs

^{2}, where Δs is the difference between the original and stretched arc length of the spiral arm, and k

_{f}is the spring constant of the fiber) could be added to the energy balance in Equation (5); the stretched arc length would be obtained from the spherical cap radius that balances the equation. A stretchable constraining material would likely yield smaller rotation and more volumetric expansion, as in [5], where 2D stretchable fabric inserts in silicone membranes led to both texture changes and volumetric expansion during inflation.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A pattern of inextensible fibers made in a water-soluble plastic sheet using (

**a**,

**b**) an embroidery machine (

**c**–

**f**) is embedded in a silicone membrane (

**g**,

**h**) causing vertical and rotational displacement. PVA: Poly(vinyl alcohol).

**Figure 2.**Spherical cap coordinate system used in energy balance model for an inflating silicone membrane (yellow region). h: Center height; R: Radius of the spherical cap; r

_{0}: Base radius of the membrane; α: Zenith angle.

**Figure 3.**Layout and implementation for three different spiral designs (

**a**–

**c**) Embroidery layout for spiral patterns with three different wrap numbers k and similar thread densities. (

**d**–

**f**) Uninflated top views. (

**g**–

**i**) Inflated top views near the maximum rotation value for each actuator. (

**j**–

**l**) Side views used for comparing inflated shapes to the spherical cap model. These three designs were fabricated and inflated. As pressures increased, the membranes approached a maximum rotation angle (Table 1) determined by the wrap number k.

**Figure 4.**Rotation vs. pressure for an individual test of each of the three spiral designs in Figure 3, along with the spherical cap energy–balance model using torsional spring constant $\kappa $ = 0.06 N m, strain energy coefficient $\gamma $ = 30 J m

^{−2}, and base radius r

_{0}= 0.038 m. Dashed lines indicate where the model extends beyond measured inflation pressures.

**Figure 5.**Sphere similarity metric vs. pressure, and measured vs. ideal spherical cap shape for three cases. A metric of 1 means the shape has 100% overlap with the spherical cap.

**Figure 6.**Torsional spring constant measured over the rotational range of three membranes with k = 0.44, k = 0.88, and k = 1.32.

**Figure 7.**Optical signal as a function of rotation angle for a membrane with an embedded spiral pattern of n = 24 and k = 0.88.

k | n | Maximum Observed Rotation Angle (Degrees) | Pressure at Maximum Rotation (psi) |
---|---|---|---|

0.44 | 32 | 80 | 2.1 |

0.88 | 24 | 115 | 1.85 |

1.32 | 18 | 176 | 2.75 |

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**MDPI and ACS Style**

Ceron, S.; Cohen, I.; Shepherd, R.F.; Pikul, J.H.; Harnett, C.
Fiber Embroidery of Self-Sensing Soft Actuators. *Biomimetics* **2018**, *3*, 24.
https://doi.org/10.3390/biomimetics3030024

**AMA Style**

Ceron S, Cohen I, Shepherd RF, Pikul JH, Harnett C.
Fiber Embroidery of Self-Sensing Soft Actuators. *Biomimetics*. 2018; 3(3):24.
https://doi.org/10.3390/biomimetics3030024

**Chicago/Turabian Style**

Ceron, Steven, Itai Cohen, Robert F. Shepherd, James H. Pikul, and Cindy Harnett.
2018. "Fiber Embroidery of Self-Sensing Soft Actuators" *Biomimetics* 3, no. 3: 24.
https://doi.org/10.3390/biomimetics3030024