# Design of Shiitake Mushroom Robotic Picking Grasper: Considering Stipe Compressive Stress Relaxation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}) of 0.998, indicating a high fitting accuracy. Xia et al. [17] quantified the stress relaxation characteristics of the carrot by using the Maxwell model in order to analyze the impact damage of the carrot. Zou et al. [18] investigated the stress relaxation characteristics of green leafy vegetables, focusing on spinach as a representative vegetable, and derived the stress relaxation characteristics under gripping conditions using the Burgers model. Therefore, the classical linear model such as Maxwell is suitable for fitting the stress dynamic relaxation characteristics of fruits and vegetables.

## 2. Modeling of Compressive Stress Relaxation Characteristics of Mushroom Stipes

#### 2.1. Materials

#### 2.2. Compression Test

#### 2.3. Stress Relaxation Test

^{2}is 0.992, so the Maxwell model can be used to characterize the stress relaxation of the stipe. The final stress relaxation model for the stipe samples is shown in Equation (3), as follows:

#### 2.4. Finite Element Analysis of Stress Relaxation

#### 2.4.1. Finite Element Modeling

#### 2.4.2. Finite Element Modeling Results and Discussion

## 3. Structure Design of Picking Grasper

## 4. Kinematic Mechanics Analysis of the Grasper

#### 4.1. Force Analysis of Gripping Actuator

_{d}is the servo output torque; θ

_{FG}is the angle between the initial and final positions of the roller relative to the center of the grooved cam, and θ

_{FF}is the angle between the finger connector and the horizontal direction.

_{XY}is the force of member X on member Y. In order to simplify the analysis, the sliding friction of the sliding block on the grooved cam is negligible. Thus, the supporting rod is a two-force rod. Take the finger connector and finger to analyze the force and then according to the geometrical condition of the equilibrium of the plane convergent force system, a closed force triangle can be obtained. To ensure the force balance between finger connector and finger, the following can be obtained:

_{n}is the force between the finger and the mushroom stipe, i.e., the finger gripping force; γ is the angle of F

_{n}in the horizontal direction; β is the angle of F

_{FF}in the horizontal direction. According to Equations (9) and (10), the following can be obtained:

_{d}and the gripping force F

_{n}, the grooved cam is force analyzed. The moment balance equation at joint FG is given as follows:

_{FS}and F

_{SF}are in opposite directions.

#### 4.2. Contact Force Analysis between Finger and Mushroom Stipe

_{n}, the unit is N/m, and the direction is pointing to the center of the circle. F

_{s}is the static friction of the finger on the mushroom stipe, the unit is N/m, and the direction is perpendicular to the gripping force. When the finger twists the mushroom stipe, the static friction F

_{s}provides the twisting force for the twisting separation torque T. According to the torque calculation formula, the relationship between the twisting separation torque T and the static friction F

_{s}can be obtained as follows:

_{n}can be obtained as below:

_{d}and the twisting separation torque T exerted by the finger on the mushroom stipe can be obtained as follows:

#### 4.3. Grasper Picking Performance Analysis

_{n}, twisting separation torque T of the fingers on the mushroom stipe, and the servo output torque M

_{d}is established. Therefore, when the twisting separation torque required for actual picking is determined, the corresponding servo output torque M

_{d}can be obtained. At the same time, the gripping force F

_{n}acting on the surface of the stipe can be determined. Considering the stress relaxation characteristics of the stipe during twisting, it should be circumvented to avoid that the clamping force F

_{n}is greater than the maximum pressure that the stipe can withstand when twisting has just begun.

## 5. Test and Analysis

#### 5.1. Verification Test of Stress Relaxation Properties of Mushroom Stipes

#### 5.2. Test Analysis on the Picking Performance of the Picking Grasper

## 6. Conclusions

^{−t/2.7445}+ 0.03088e

^{−t/27.15}+ 0.26196. Subsequently, finite element simulation was employed to model the stress changes during stipe compression, combined with the above parameters. The pressure on the stipes obtained dynamically by the texture analyzer was verified with the finite element simulation results, while the mean square error between the simulation results and the actual results did not exceed 5%. Thus, the finite element simulation results were found to be satisfactory in comparison with the actual results.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**The stress–strain curve of stipe sample. A is the elastic limit, B is the yield point, C is the failure point.

**Figure 16.**Comparison of the FEM results with the experimental results: (

**a**) 10 mm; (

**b**) 12 mm; (

**c**) 14 mm; (

**d**) 16 mm.

Parameters | Values (mm) |
---|---|

Cap diameter | 62 ± 12.2 |

Cap height | 21.1 ± 4.2 |

Stipe diameter | 13.2 ± 2.6 |

Stipe height | 32.6 ± 5.5 |

Materials | Elastic Modulus (Mpa) | Bio-Yield Stress (Mpa) | Poisson’s Ratio (−) |
---|---|---|---|

Stipe | 0.871 | 0.418 | 0.322 |

Materials | ${\overline{\mathit{g}}}_{1}^{\mathit{p}}$ | ${\overline{\mathit{g}}}_{2}^{\mathit{p}}$ | ${\overline{\mathit{\tau}}}_{1}^{\mathit{p}}$ | ${\overline{\mathit{\tau}}}_{2}^{\mathit{p}}$ |
---|---|---|---|---|

stipe | 0.087672031 | 0.110973567 | 2.7445 | 27.15 |

Materials | 4 Days | 6 Days | 8 Days | 10 Days |
---|---|---|---|---|

Cap diameter (mm) | 55.3 | 59.6 | 64.5 | 72.1 |

Stipe diameter (mm) | 12.1 | 12.8 | 13.6 | 15.4 |

Days of Growth | Number of Successful Picks | Picking Success Rate |
---|---|---|

4 | 16 | 80% |

6 | 18 | 90% |

8 | 19 | 95% |

10 | 15 | 75% |

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**MDPI and ACS Style**

Li, J.; Feng, Q.; Ru, M.; Sun, J.; Guo, X.; Zheng, W.
Design of Shiitake Mushroom Robotic Picking Grasper: Considering Stipe Compressive Stress Relaxation. *Machines* **2024**, *12*, 241.
https://doi.org/10.3390/machines12040241

**AMA Style**

Li J, Feng Q, Ru M, Sun J, Guo X, Zheng W.
Design of Shiitake Mushroom Robotic Picking Grasper: Considering Stipe Compressive Stress Relaxation. *Machines*. 2024; 12(4):241.
https://doi.org/10.3390/machines12040241

**Chicago/Turabian Style**

Li, Jianxun, Qingchun Feng, Mengfei Ru, Jiahui Sun, Xin Guo, and Wengang Zheng.
2024. "Design of Shiitake Mushroom Robotic Picking Grasper: Considering Stipe Compressive Stress Relaxation" *Machines* 12, no. 4: 241.
https://doi.org/10.3390/machines12040241