# Design and Test of an Active Pneumatic Soft Wrist for Soft Grippers

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## Abstract

**:**

## 1. Introduction

## 2. Structure Design

#### 2.1. Structure of Pneumatic Helical Actuators

#### 2.2. Structure Design of the Pneumatic Soft Wrist

## 3. Kinematic Analysis

#### 3.1. Bending Model

#### 3.2. Twisting Model

## 4. Numerical Modeling

#### 4.1. Simulation Parameters

#### 4.2. Simulation Results

## 5. Experimental Tests

#### 5.1. Sample Fabrication

#### 5.2. Experimental Results

## 6. Application for a Soft Hand

#### 6.1. Sensitivity Studies of Geometric Parameters

#### 6.2. Verfication and Validation of the Soft Wrist

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A | Force integral area (${\mathrm{m}}^{2}$) |

b | Width of inner helix surface (m) |

c | Length of the chamber internal structure (m) |

d | Pitch (m) |

${c}_{i0}$ | Material constant (Pa) |

${C}_{1}$ | Silicone rubber material parameter (Pa) |

${C}_{2}$ | Fiber material parameter (Pa) |

$D$ | Actuator diameter (m) |

${D}_{k}$ | Incompressibility parameter (Pa^{−1}) |

e | Thickness of fiber layer (m) |

$f$ | Force generated by air pressure (N) |

${G}_{0}$ | Initial shear modulus (Pa) |

$h$ | Distance from bottom edge (m) |

$I$ | Parameter in tangential stress calculation (None) |

$\overline{I}$ | The first invariant (None) |

$J$ | Volume variation ratio (None) |

$L$ | Actuator length (m) |

${M}_{P}$ | Moment generated by pressure (bending) (N$\xb7\mathrm{m}$) |

${M}_{i}$ | Moment generated by material (bending) (N$\xb7\mathrm{m}$) |

${M}_{\theta}$ | Moment generated by the material (N$\xb7\mathrm{m}$) |

${P}_{\mathrm{in}}$ | Chamber pressure (pa) |

$r$ | Actuator chamber radius (m) |

${r}_{1}$ | Internal radius (m) |

${r}_{2}$ | Outer radius (m) |

$R$ | Curvature radius |

${R}^{\prime}$ | Actuator radius (m) |

$t$ | Average equivalent thickness (m) |

${t}_{1}$ | Outer layer thickness (m) |

${t}_{2}$ | Inner layer thickness (m) |

${T}_{P}$ | Moment generated by pressure (twisting) (N$\xb7\mathrm{m}$) |

${T}_{i}$ | Moment generated by material (twisting) (N$\xb7\mathrm{m}$) |

$\beta $ | Helix angle (rad) |

$\theta $ | Bending angle (rad) |

${\lambda}_{1}$ | Stretch ratio in bending model (none) |

${\lambda}_{2}$ | Stretch ratio in twisting model (none) |

$\tau $ | Shear stress (Pa) |

$\omega $ | Angle of fiber cloth (rad) |

${\omega}_{0}$ | Helix angle of fiber cloth (rad) |

$\varphi $ | Twist angle (rad) |

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**Figure 1.**Pneumatic soft helical actuators: (

**a**) two opposite helical structures; (

**b**) longitudinal sections and the geometric parameters.

**Figure 2.**Design of a pneumatic soft wrist: (

**a**) a soft wrist module; (

**b**) cross-section of the soft wrist.

**Figure 3.**Bending model of the soft wrist: (

**a**) bending of four actuators; (

**b**) longitudinal section of a pressured actuator; (

**c**) actuator chamber transverse section.

**Figure 4.**Twisting model of the soft wrist: (

**a**) twisting of four actuators; (

**b**) longitudinal section of a pressured actuator; (

**c**) shear model of a pressured actuator.

**Figure 8.**Theoretical, simulation, and experimental results for the soft wrist: (

**a**) bending angle; (

**b**) twisting angle.

**Figure 9.**Analysis of structural parameters: (

**a**) internal radius; (

**b**) width of inner helix surface; (

**c**) length; (

**d**) pitch; (

**e**) outer layer thickness; (

**f**) inner layer thickness.

**Figure 10.**Motion of soft wrist for soft robotic hand: (

**a**) real human hand; (

**b**) simulation; (

**c**) experiments.

Motions | Pressured Chambers | Directions of Motions |
---|---|---|

Bending forward (flexion) | ||

Bending backward (extension) | ||

Bending left (abduction) | ||

Bending right (adduction) | ||

Twisting left (supination) | ||

Twisting right (pronation) |

Materials | Parameters | Values |
---|---|---|

Silicone chamber | Material constant C_{1} | 0.1 MPa [30] |

Material constant C_{2} | 0.013 MPa [30] | |

Material constant C_{3} | 0.00002 MPa [30] | |

Kevlar fiber | Young’s modulus | 28 GPa |

Poisson’s ratio | 0.37 |

Inner Hole Radius r_{1} | Inner Helix Radius r_{2} | Helix Width b | Helix Pitch d | Outward Layer Thickness t _{1} | Inward Layer Thickness t _{2} |
---|---|---|---|---|---|

4 | 6 | 1 | 5 | 2 | 1.75 |

4.5 | 7 | 1.5 | 6 | 3 | 2 |

5 | 8 | 2 | 7 | 4 | 2.25 |

5.5 | 9 | 2.5 | 8 | 5 | 2.5 |

6 | 10 | 3 | 9 | 6 | 2.75 |

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## Share and Cite

**MDPI and ACS Style**

Chen, G.; Lin, T.; Ding, S.; Chen, S.; Ji, A.; Lodewijks, G.
Design and Test of an Active Pneumatic Soft Wrist for Soft Grippers. *Actuators* **2022**, *11*, 311.
https://doi.org/10.3390/act11110311

**AMA Style**

Chen G, Lin T, Ding S, Chen S, Ji A, Lodewijks G.
Design and Test of an Active Pneumatic Soft Wrist for Soft Grippers. *Actuators*. 2022; 11(11):311.
https://doi.org/10.3390/act11110311

**Chicago/Turabian Style**

Chen, Guangming, Tao Lin, Shi Ding, Shuang Chen, Aihong Ji, and Gabriel Lodewijks.
2022. "Design and Test of an Active Pneumatic Soft Wrist for Soft Grippers" *Actuators* 11, no. 11: 311.
https://doi.org/10.3390/act11110311