# Modeling and System Integration for a Thin Pneumatic Rubber 3-DOF Actuator

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Structure of the 3-DOF Micro-Hand

#### 2.2. Modeling

#### 2.2.1. Model of McKibben Pneumatic Artificial Muscle

#### 2.2.2. Model of 3-DOF Micro-Hand

#### 2.2.3. Relation between Input Pressure and Output Angle

**n**is obtained from calculating an outer product of $\overrightarrow{{H}_{2}{H}_{1}}$ and $\overrightarrow{{H}_{2}{H}_{3}}$. Moreover, each component of

_{1}**n**in Equation (13) is designated as a, b, and c, respectively.

_{1}#### 2.2.4. Geometric Transformation into the $xyz$ Coordinate System

## 3. Results

#### 3.1. Experiment

- The air compressor provides an air pressure for the safety regulator.
- The safety regulator converts the pressure to at most $300\mathrm{k}\mathrm{Pa}$ for not breaking the micro-hand.
- The computer sends electrical signal to the controller for the electro-pneumatic regulator.
- The controller provides 4 mA–20 mA for the electro-pneumatic regulator and decides the opening of the electro-pneumatic regulator.
- Desired pressures are sent into the muscles of the micro-hand respectively and the micro-hand bends or contracts.

- Obtain a color image captured by two cameras and convert into a gray scale.
- Dissolve the image into 3 pixel numbers; R, B, G.
- Extract only R pixels from the image in comparison with a gray scale.
- Obtain the center coordinate from extracted R pixel area.

#### 3.2. Experimental Result

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

DOF | Degrees of freedom |

## References

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**Figure 2.**(

**a**) Contracting motion toward z direction. (

**b**) Bending motions in the y directions. (

**c**) Bending motions in the x directions. (

**d**) Bending motion when ${P}_{1}=0\mathrm{k}\mathrm{Pa},{P}_{2}=125\mathrm{k}\mathrm{Pa}$ and ${P}_{3}=250\mathrm{k}\mathrm{Pa}$.

**Figure 12.**The coordinate values y and z of the tip of the micro-hand (${P}_{1}={P}_{3}=0\mathrm{k}\mathrm{Pa}$, ${P}_{2}=$ 0 kPa–250 kPa).

**Figure 14.**The coordinate values x and z of the tip of the micro-hand (${P}_{1}={P}_{2}=0\mathrm{k}\mathrm{Pa}$, ${P}_{3}=$ 0 kPa–250 kPa).

**Figure 15.**The coordinate values y and z of the tip of the micro-hand (${P}_{1}={P}_{2}=0\mathrm{k}\mathrm{Pa}$, ${P}_{3}=$ 0 kPa–250 kPa).

Parameter | Definition | Value |
---|---|---|

${L}_{0}$ | Initial length of the micro-hand | $50\times {10}^{-3}\mathrm{m}$ |

${D}_{0}$ | Initial radius of the muscle | $2.1\times {10}^{-3}\mathrm{m}$ |

${\theta}_{{f}_{0}}$ | Initial braid angle | $0.54105\mathrm{rad}$ |

d | Gap between muscle 2 and 1(3) | $0.5\times {10}^{-3}\mathrm{m}$ |

n | Number of divided micro-hand | 100 |

${C}_{11}$ | Correction factor 1 of muscle 1 | 500 |

${C}_{21}$ | Correction factor 2 of muscle 1 | $-1.59\times {10}^{-5}{\mathrm{Pa}}^{-1}$ |

${C}_{12}$ | Correction factor 1 of muscle 2 | 530 |

${C}_{22}$ | Correction factor 2 of muscle 2 | $-1.45\times {10}^{-5}{\mathrm{Pa}}^{-1}$ |

${C}_{13}$ | Correction factor 1 of muscle 3 | 500 |

${C}_{23}$ | Correction factor 2 of muscle 3 | $-1.59\times {10}^{-5}{\mathrm{Pa}}^{-1}$ |

${C}_{x}$ | Correction factor of x-coordinate | $0.9$ |

${C}_{\gamma}$ | Correction factor of bending direction angle | $0.21$ |

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**MDPI and ACS Style**

Kawamura, S.; Sudani, M.; Deng, M.; Noge, Y.; Wakimoto, S.
Modeling and System Integration for a Thin Pneumatic Rubber 3-DOF Actuator. *Actuators* **2019**, *8*, 32.
https://doi.org/10.3390/act8020032

**AMA Style**

Kawamura S, Sudani M, Deng M, Noge Y, Wakimoto S.
Modeling and System Integration for a Thin Pneumatic Rubber 3-DOF Actuator. *Actuators*. 2019; 8(2):32.
https://doi.org/10.3390/act8020032

**Chicago/Turabian Style**

Kawamura, Shuhei, Mizuki Sudani, Mingcong Deng, Yuichi Noge, and Shuichi Wakimoto.
2019. "Modeling and System Integration for a Thin Pneumatic Rubber 3-DOF Actuator" *Actuators* 8, no. 2: 32.
https://doi.org/10.3390/act8020032