# Kinematic Analysis of a Clamp-Type Picking Device for an Automatic Pepper Transplanter

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## Abstract

**:**

^{2}, along the x- and y-axes, respectively, for 30 to 90 rpm operating conditions. A suitable picking device dimension was identified and validated based on the suitability of the picking device working trajectory, velocity, and acceleration of the grippers, and no significant difference (p ≤ 0.05) occurred between the simulation and validation tests. This study indicated that the picking device under development would increase the pepper seedling picking accuracy and motion safety by reducing the operational time, gripper velocity, acceleration, and mechanical damage.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Structure of Transplanter and Working Principle of the Picking Device

#### 2.2. Kinematic Analysis of the Picking Device Grippers

_{1}is the picking stand and acts as a fixed bar, and L

_{2}, L

_{3}, L

_{4}, and L

_{5}are moving bars. A vector-loop model was used to define the kinematic parameters (position, velocity, and acceleration) of the gripper by solving the angles of the moving bars in the case of the known position of the fixed bar. Table 1 indicates the variable notations, definitions, and measurement units are used in this analysis.

#### 2.2.1. Variables of Picking Device for Optimization of the Design

#### 2.2.2. Position and Trajectory Evaluation of the Gripper with Vector-Loop Modeling

_{2}, L

_{3}, and L

_{4}) [36,37]. The vector loop of the picking device can be expressed as Equation (2).

_{4}) moves upward and downward. Because it is fully translated; θ

_{4}= 0.

_{3}and L

_{4}. The angle ∆θ determines the position of L

_{5}. The position of the required path of the x-axis can be determined by Equations (7) and (8).

#### 2.2.3. Velocity of the Gripper with Vector-Loop Modeling

_{2}and L

_{3}bars are fixed on one side; therefore, $\dot{{L}_{2}}=\dot{{L}_{3}}=0$.

_{5}bar.

#### 2.2.4. Acceleration of the Gripper with Vector-Loop Modeling

_{2}and L

_{3}bars are fixed on one side; therefore, $\dot{{L}_{2}}=\dot{{L}_{3}}=\stackrel{\dot{}\dot{}}{{L}_{2}}=\stackrel{\dot{}\dot{}}{{L}_{3}}=0$. From Equations (15) and (16), the real and imaginary part yields,

#### 2.2.5. Simulation with Virtual Model

#### 2.2.6. Experiment with a Prototype

## 3. Results and Discussion

#### 3.1. Position and Trajectory of the Gripper

_{3}bar), and the x-axis movement depended on the length of the picking stand (L

_{1}bar). To enable the volume of the picking device for stable operation, the ratio (reflecting factor, δ) between the picking working space and dimensions should be considered within a reasonable range. Therefore, it is recommended that δ = 1.1 to 1.2 [29]. The position analysis result shows that the 380-mm manipulator and the 250- to 350-mm range for the picking stand were acceptable combinations to maintain the recommended reflecting factor. The position analysis is based on the various dimensions (combination) used in Table 2, as presented in Table 5.

#### 3.2. Motion Evaluation of the Gripper Using Velocity Analysis

#### 3.3. Motion Evaluation of the Gripper Using Acceleration Analysis

^{2}and from 2.42 to 6.14 m/s

^{2}, respectively. In the manipulator range: 380 mm and picking stand range: 250 to 350 mm had comparatively less difference in acceleration between the x and y-axis for 60 rpm condition. In this study, pepper seedlings of age 45 days and an average height of 122 mm were considered for designing the seedling transplantation. Han et al. [42] evaluated a tomato seedling picking device with a plant height ranging from 110 to 130 mm for 42-day seedlings, and found the maximum acceleration of the gripper in the x- and y-axis as 103.80 and 86.90 m/s

^{2}, respectively, and the success ratio in picking up the seedlings as 90% by analyzing the number of damaged seedlings. Based on the acceleration analysis, the gripper acceleration was lower than the previous research results.

^{2}, respectively. During the measurement, the highest accelerations for the y- and x-axes were 8.77 and 5.34 m/s

^{2}, respectively. There was no acceleration in the z-axis in the simulation, but the same region of velocity analysis (rotational speed of the motor and the friction of metal) induced some acceleration in the z-axis. The highest acceleration for the z-axis was 1.12 m/s

^{2}. During the simulation and experiment, the acceleration levels were statistically the same (p ≤ 0.05) for the two axes. The maximum average acceleration was recorded as 1.82 m/s

^{2}for the x-axis in the experimental condition, whereas the minimum average velocity (1.03 m/s

^{2}) was shown for the y-axis in the simulation condition (Table 7).

^{2}.

## 4. Conclusions

_{3}bar), reflecting factor (δ), and gripper movement (∆θ) were taken into consideration when designing the dimensions. The simulation and experimental results indicated that the developed picking device can transfer five seedlings at a time under a 60 rpm (150 plants/min) operating condition with minimum velocity and acceleration. This low velocity and acceleration could contribute to a more successful picking operation by decreasing pepper seedling damage. In the field test, 18.59 W power was required for operating the picking mechanism of a low-powered automatic pepper transplanter. The outcomes of this study provide the guidelines for developing a small-scale automatic transplanting mechanism to achieve more accurate pepper seedling transplantation.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Schematic diagram of the picking device: (

**a**) azimuth angle of the trajectory; (

**b**) kinematic model for the picking device: (L

_{1}) picking stand, (L

_{2}) crank, (L

_{3}) connecting rod, (L

_{4}) gripper, (L

_{5}) manipulator, (A-B-C-D-A) trajectory path.

**Figure 3.**Timing profile of the device from seedlings pick to drop: (θ

_{2}) crank rotational angle, (∆θ) cam rotational angel, (

**A**) pick the seedlings, (

**B**) change y-axis to x-axis, and (

**C**) drop the seedlings.

**Figure 4.**Validation test bench of the prototype picking device: (

**a**) velocity, acceleration, and power measurement and (

**b**) trajectory evaluation.

**Figure 5.**Simulated and measured trajectory curves of the gripper in the x- and y-axis directions for one complete picking cycle.

**Figure 6.**Maximum velocity values of the gripper for different length combinations and operating speeds.

**Figure 7.**Simulated and measured velocity curves for the gripper in the x-, y-, and z-axis directions for one complete picking cycle.

**Figure 9.**Simulated and measured acceleration curves of the gripper in the x-, y-, and z-axis directions for one complete picking cycle.

Notation | Definitions and Measurement Units |
---|---|

$\eta $ | Maximum distance between the cam follower and slider, mm |

b | Distance between the picking stand and seedling tray, mm |

${L}_{5}$ | Picking stand length, mm |

${L}_{2}$ | Crank length, mm |

${L}_{3}$ | Connecting rod length, mm |

${L}_{4}$ | Gripper length, mm |

$e$ | Euler’s formula base of the natural logarithm |

$i$ | Imaginary unit |

${\theta}_{2}$ | Crank angle, radians |

${\theta}_{3}$ | Connecting rod angle, radians |

${\theta}_{4}$ | Gripper angle, radians |

$\Delta \theta $ | Cam rotational angle, radians |

${X}_{{A}_{1}}$ | Gripper x-axis coordinates |

${Y}_{{A}_{1}}$ | Gripper y-axis coordinates |

$\dot{{L}_{2}}$ | Crank velocity, mm/s (convert to m/s) |

$\dot{{L}_{3}}$ | Connecting rod velocity, mm/s (convert to m/s) |

$\dot{{L}_{4}}$ | Gripper y-axis velocity, mm/s (convert to m/s) |

${\omega}_{2}$ | Crank angular velocity, rad/s |

${\omega}_{3}$ | Connecting rod angular velocity, rad/s |

${V}_{OA}$ | Gripper x-axis velocity, mm/s (convert to m/s) |

$\stackrel{\dot{}\dot{}}{{L}_{2}}$ | Crank acceleration, mm/s^{2} (convert to m/s^{2}) |

$\stackrel{\dot{}\dot{}}{{L}_{3}}$ | Connecting rod acceleration, mm/s^{2} (convert to m/s^{2}) |

$\stackrel{\dot{}\dot{}}{{L}_{4}}$ | Gripper y-axis acceleration, mm/s^{2} (convert to m/s^{2}) |

${\alpha}_{2}$ | Crank angular acceleration, rad/s^{2} |

${\alpha}_{3}$ | Connecting rod angular acceleration, rad/s^{2} |

$\alpha $ | Gripper x-axis acceleration, mm/s^{2} (convert to m/s^{2}) |

Combination | Manipulator, mm | Picking Stand Length, mm | Manipulator Movement Angle (Δθ), ° |
---|---|---|---|

1 | 350 | 250 | 33.64 |

2 | 350 | 300 | 36.29 |

3 | 380 | 250 | 27.21 |

4 | 380 | 300 | 28.46 |

5 | 380 | 350 | 30.01 |

6 | 410 | 250 | 26.92 |

7 | 410 | 300 | 24.67 |

8 | 410 | 350 | 24.89 |

9 | 410 | 350 | 22.92 |

10 | 440 | 300 | 23.56 |

11 | 440 | 250 | 26.42 |

12 | 440 | 400 | 25.62 |

13 | 480 | 450 | 22.38 |

Component | Range | Activity |
---|---|---|

Picking stand, L_{1} | 250 to 500 mm | Determines the working space |

Manipulator, L_{5} | 250 to 500 mm | Moves the grippers |

Crank, L_{2} | Depend on L_{5} | Moves the seedling in the y-axis |

Connecting rod, L_{3} | Depend on L_{5} | Moves the seedling in the y-axis |

Gripper, L_{4} | Depend on L_{5} | Pick or drop the seedling |

Cam and follower, e | 25.5 mm | Moves the seedling in the x-axis |

Gear and gear shaft | 30 to 90 rpm | Run the cam and crank |

Component | Parameter | |
---|---|---|

Simulated | Measured | |

Picking stand, L_{1} | 250 mm | 250 mm |

Manipulator, L_{5} | 380 mm | 380 mm |

Gear and gear shaft | 60 rpm | 60 rpm |

Combination | Gripper y-Axis Movement, mm | Reflecting Factor, δ |
---|---|---|

1 | 94.73 | 1.26 |

2 | 80.44 | 1.26 |

3 | 117.09 | 1.17 |

4 | 117.68 | 1.17 |

5 | 118.41 | 1.17 |

6 | 140.79 | 1.08 |

7 | 139.59 | 1.08 |

8 | 139.71 | 1.08 |

9 | 154.08 | 1.08 |

10 | 154.45 | 1.01 |

11 | 79.45 | 1.01 |

12 | 155.64 | 1.01 |

13 | 193.13 | 0.93 |

Axis | Simulated Velocity, m/s | Measured Velocity, m/s |
---|---|---|

x-axis | 0.28 ± 0.29 ^{a} | 0.32 ± 0.34 ^{a} |

y-axis | 0.18 ± 0.28 ^{a} | 0.29 ± 0.32 ^{a} |

^{a}Identified the statistical differences among gripper simulated and measured velocity, according to Tukey’s one-way comparisons (p ≤ 0.05).

Axis | Simulated Acceleration, m/s^{2} | Measured Acceleration, m/s^{2} |
---|---|---|

x-axis | 1.60 ± 1.68 ^{a} | 1.82 ± 1.96 ^{a} |

y-axis | 1.03 ± 1.60 ^{a} | 1.68 ± 1.86 ^{a} |

^{a}Identified statistical differences among gripper simulated and measured acceleration, according to Tukey’s one-way comparisons (p ≤ 0.05).

Parameter | Power Requirement, W | ||||||
---|---|---|---|---|---|---|---|

30 rpm | 40 rpm | 50 rpm | 60 rpm | 70 rpm | 80 rpm | 90 rpm | |

Min. | 0.01 | 0.01 | 0.19 | 0.20 | 0.21 | 0.25 | 0.29 |

Avg. | 0.30 ± 0.63 ^{a} | 0.80 ± 0.92 ^{a} | 1.08 ± 1.33 ^{b} | 1.80 ± 2.06 ^{b} | 1.27 ± 2.43 ^{b} | 2.73 ± 3.32 ^{c} | 2.48 ± 4.31 ^{c} |

Max. | 7.59 | 10.41 | 13.06 | 19.38 | 22.91 | 28.70 | 34.42 |

^{a,b,c}Identified the statistical differences among different speed conditions according to Tukey’s one-way comparisons (p ≤ 0.05).

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## Share and Cite

**MDPI and ACS Style**

Islam, M.N.; Iqbal, M.Z.; Ali, M.; Chowdhury, M.; Kabir, M.S.N.; Park, T.; Kim, Y.-J.; Chung, S.-O.
Kinematic Analysis of a Clamp-Type Picking Device for an Automatic Pepper Transplanter. *Agriculture* **2020**, *10*, 627.
https://doi.org/10.3390/agriculture10120627

**AMA Style**

Islam MN, Iqbal MZ, Ali M, Chowdhury M, Kabir MSN, Park T, Kim Y-J, Chung S-O.
Kinematic Analysis of a Clamp-Type Picking Device for an Automatic Pepper Transplanter. *Agriculture*. 2020; 10(12):627.
https://doi.org/10.3390/agriculture10120627

**Chicago/Turabian Style**

Islam, Md Nafiul, Md Zafar Iqbal, Mohammod Ali, Milon Chowdhury, Md Shaha Nur Kabir, Tusan Park, Yong-Joo Kim, and Sun-Ok Chung.
2020. "Kinematic Analysis of a Clamp-Type Picking Device for an Automatic Pepper Transplanter" *Agriculture* 10, no. 12: 627.
https://doi.org/10.3390/agriculture10120627