# Soft End Effector Using Spring Roll Dielectric Elastomer Actuators

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modelling and Experiment

#### 2.1. Equations of State for DEAs

#### 2.2. Charge Control and Leakage Current

_{C}is the voltage across the capacitor, $R$ is the resistance used to limit the current from the power supply, ${R}_{\mathrm{leak}}$ is the leakage current equivalent resistance, $C$ is the capacitance of the DEA and $s$ is the complex parameter from the Laplace transform. The charge on the capacitor is then converted to an equivalent field, where the leakage current is modelled using a resistor, ${R}_{\mathrm{leak}}$ [27,28]:

^{−14}[27]. The discharging process is equivalent and inverse.

## 3. Method

#### 3.1. Fabrication of Spring Rolls

#### 3.2. Experimental Setup

## 4. Results

#### 4.1. Static Response

#### 4.2. Dielectric Properties of Membrane

#### 4.3. Dynamic Response

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) A 2-DOF bending spring roll. For bending, only one span is actuated. For 1-DOF, both sides are actuated simultaneously resulting in a linear strain. (

**b**) Spring roll DEA gripper concept schematic.

**Figure 3.**(

**a**) Electric dipole moment, rotation of polymer chains in the direction of the applied voltage. (

**b**) Electric dipole moment with deformation from applied voltage.

**Figure 4.**(

**a**) Spring roll bending configuration with the right side actuated (shown in darker hue), resulting in a curvature of angle $\theta $ and radius $R$. An element of the actuated membrane is subjected to stresses when the voltage is applied, and for any forces acting on the membrane. Red surface represents the fixed end, blue surface represents the free end of the actuator and orange represents the massless spring. (

**b**) Schematic of DE membrane element from (

**a**).

**Figure 5.**Standard linear solid viscoelastic model of dielectric elastomer using two parallel springs and a viscous dashpot.

**Figure 8.**(

**a**) Gripper holding a 35 g mass in a cup. The gripper consists of three single actuators arranged radially. (

**b**) Single actuator bending test, shown in an actuated state. A lateral deflection of ~5 mm was achieved for the actuator design used.

**Figure 9.**(

**a**) Voltage-controlled bend angle for t = 10 s or t = t

_{v}/5; (

**b**) maximum lateral force generated for t = 10 s, with a resolution of ±0.005 N.

**Figure 10.**Membrane actuation for varying dielectric constant, $k$. Breakdown line for each value shown by red dashed line, with the intersection point (maximum stretch of the membrane, ${\lambda}_{\mathrm{max}}$) shown by red circles for each dielectric constant. $k$ = 3 for VHB-F9473PC.

**Figure 11.**(

**a**) Effect of spring on controllability of actuator for 3 kV; (

**b**) viscoelastic relaxation time of actuator when actuated for 50 s at 5 kV.

**Table 1.**Gent energy function model parameters for 3M VHB-F9473PC adhesive membrane [24].

Material Parameter | Value |
---|---|

${J}_{\mathrm{lim},\alpha}$ | 115 |

${J}_{\mathrm{lim},\beta}$ | 70 |

${M}_{\alpha}$ | 16,000 |

${M}_{\beta}$ | 45,000 |

$\eta $ | $2.25\times 10$^{6} |

Parameter | 2-DOF Roll (Version 1), 2004 [18] | 2-DOF Roll, 2016 [16] | This Work |
---|---|---|---|

Actuator mass | 29 g | - | 10 g |

Actuator length | 68 mm | 40 mm | 70 mm |

Dielectric elastomer (pre-stretch ratio) | VHB-4910 | VHB-4910 (3, 5) | VHB-F9473PC (1.03, 1) |

Maximum operating voltage | 5.5 kV | 5 kV | 6 kV |

Maximum stroke | - | 8.4 mm | - |

Maximum bending angle | 60° | 75.3° | 6.8° |

Maximum force | 1.68 N | 0.7 N | 0.03 N |

No. of rolls | 20 | 14 | 10 |

Dashpot fully extended | Yes | Yes | No |

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**MDPI and ACS Style**

Lewis, H.; Pan, M.
Soft End Effector Using Spring Roll Dielectric Elastomer Actuators. *Actuators* **2023**, *12*, 412.
https://doi.org/10.3390/act12110412

**AMA Style**

Lewis H, Pan M.
Soft End Effector Using Spring Roll Dielectric Elastomer Actuators. *Actuators*. 2023; 12(11):412.
https://doi.org/10.3390/act12110412

**Chicago/Turabian Style**

Lewis, Hamish, and Min Pan.
2023. "Soft End Effector Using Spring Roll Dielectric Elastomer Actuators" *Actuators* 12, no. 11: 412.
https://doi.org/10.3390/act12110412