Simulation and Optimization Experiment of Seven-Link Planting Mechanism Based on Discrete Element Method and Multibody Dynamics (DEM–MBD) Coupling

Abstract

To address issues in traditional vegetable transplanter planting mechanisms such as poor hole-forming quality and low seedling uprightness, a seven-bar linkage planting mechanism with posture compensation of seedling entering soil was designed. By establishing a mathematical model of the planting mechanism and developing visual auxiliary optimization software, the optimal mechanism parameters for the best planting trajectory were determined. A DEM–MBD (Discrete Element Method and Multibody Dynamics) coupling simulation model of planting mechanism-soil-seedlings was established. The planting frequency, opening width, and opening time of the planter were used as factors, and the soil backflow and seedling uprightness were used as evaluation indicators. A quadratic regression orthogonal rotation combination simulation test was carried out. The regression model was established using Design-Expert 12.0 software to analyze the influence of various factors on the indicators. Response surface methodology was simultaneously applied for comprehensive optimization of the influencing factors. The optimal parameter combination obtained was as follows: planting frequency 57 plants/min, opening width 48.5 mm, opening time 0.76 s, corresponding to a soil backflow of 0.67 and seedling uprightness of 80.35°. Field tests were conducted to verify the following mechanism: the soil backflow was 0.64, and the seedling uprightness was 78.49°, which were 4.47% and 2.31% different from the regression model optimization results, respectively. The error variation was small, indicating that the simulation results were effective and the mechanism design was reasonable. This study provides a reference for the development of high-quality and efficient vegetable transplanters.

1. Introduction

Transplanting can effectively shorten the field growth period of crops, adjust crop rotation, and compensate for the adverse effects of delayed farming time, making it widely adopted in vegetable cultivation [1,2,3]. At present, the planting methods of transplanters globally are mainly divided into punch type and furrow type [4,5]. Among them, the punch-type method accommodates a wider range of seedling types and has become the mainstream planting approach for transplanters. The duckbill planter device is the core component for the punch-type transplanting. This device achieves reciprocating or rotary motion through multi-link mechanisms or planetary gear mechanisms [6]. After entering the soil, the seedlings are planted in the soil in an upright state. The transplanting of seedlings is completed by the joint action of the planter unit and the soil. During operation, the planter unit disturbs the soil. Factors such as planting frequency, opening width, and opening time directly affect the soil backflow, which in turn affects the uprightness of the seedlings after planting. Therefore, the kinematic characteristics of the planting mechanism determine the planting quality of the seedlings.

The duckbill planters are widely suitable for bare land or film-covered transplanting due to their shape enabling low-resistance soil entry and providing good support for seedlings during the opening moment. Yongwei Wang et al. [7] have developed an automatic eccentric disk dibble-type planting apparatuses transplanter for vegetable seedlings. The operating performance at different planting frequencies has been investigated. The results showed that the planting mechanism was complex, and the planting trajectory was highly susceptible to operational speed. It caused significant soil disturbance during operation, and the soil backflow index was unstable. Chong Liu [8] designed a reciprocating duckbill planting mechanism based on graph theory, optimized the mechanism parameters, and tested the hole size and seedling uprightness under different planting frequencies, plant spacing, and duckbill inclination angles. The hole size and seedling uprightness are greatly affected by the planting frequency and inclination angle, and the mechanism is difficult to achieve high-speed transplanting. Qizhi Yang [9] studied the hole-forming performance and film opening size of the conical planter and cone planter of the hanging cup planting mechanism under different planting frequencies based on the DEM–MBD coupling simulation method. However, the seedling model was not coupled, and the planting quality was difficult to determine. Yang Liu [10] conducted a comparative study on the influence of the cross-sectional type of the planter on the hole opening size during vegetable transplanting. Through the soil hole-forming test, it was found that the hole opening size formed by the round-mouth cross-section planter was smaller than that of the square-mouth cross-section planter, that is, the degree of damage to the film hole opening was smaller, but the influence of the planter on soil disturbance and backflow was not considered. Although many scholars have designed and studied the planting mechanism and achieved certain results, the seedling posture in the planter is fixed from seedling to soil entry, and the planting uprightness is greatly affected by the planting angle of the planter, resulting in a decrease in planting quality during high-speed operation. In addition, there are few studies on soil backflow and seedling uprightness under the coupling of the planter, soil, and seedlings [11,12,13].

This study aims to improve the hole-forming effect in soil and enhance seedling uprightness during the operation of a planting mechanism. A seven-bar linkage planting mechanism with the function of compensating the seedlings’ posture when entering the soil is designed. Through theoretical analysis, the mathematical model and motion trajectory of the planting mechanism are obtained, and the rod parameters are optimized. DEM–MBD coupling simulations were suitable for the modeling of the interactions between soil and agricultural tools, soil disturbance in cavity seeders, and other diverse areas [14]. Hence, the DEM–MBD coupling simulation method was selected to carry out the simulation and verification tests with soil backflow and seedling uprightness as evaluation indicators. The research is expected to provide a theoretical basis and technical reference for improving the planting quality of vegetable transplanters.

2. Materials and Methods

2.1. Prototype Components

The seven-bar linkage planting mechanism is mainly composed of a crank, a connecting rod, a lower rocker, an upper rocker, a cam, a swing arm, a gearbox, a frame, and a duckbill planter device, and the basic structure is shown in Figure 1. The crank, cam, and swing arm are arranged on the output shaft of the gearbox; the upper rocker and the lower rocker are arranged in parallel. Additionally, the planter device is installed at the common connecting rod of the two rockers, with the tip of the planter facing downward and the opening facing upward. The other end of the lower rocker is hinged to the frame, and the middle is hinged to the crank through a connecting rod to realize the up and down reciprocating motion of the planter. The other end of the upper rocker is hinged to one end of the swing arm, and the swing arm drives the upper rocker to realize the reciprocating swing in the opposite direction of the forward movement of the machine under the constraint of the cam, so as to adjust the movement posture of the planter in real time during the operation process to ensure the uprightness of the seedling planting.

2.2. Working Principle

The mechanism can be symmetrically arranged on both sides of the gearbox to realize the double-row planting mode of seedlings. Since the movement principle is the same, this paper only focuses on theoretical research and analysis on one set of planting mechanisms. As shown in Figure 2, Action ①: the crank drives the lower rocker to move upward through the connecting rod, and the planter is raised to the seedling throw position. Action ②: the seedlings are placed into the planter manually or by the seedling-taking mechanism. After catching the seedlings, the planter moves in the combined direction of the machine forward and the vertical downward movement direction to prepare for soil entry. Action ③: when the planter reaches the deepest point, the cam constrains the rocker to drive the upper rocker to move in the opposite direction of the machine forward. Under the pull of the upper rocker, the planter twists around the hinge point of the lower rocker in the opposite direction of the machine movement. In this process, the planter is forced to open by the pull wire, and the seedlings are planted upright in the soil. Action ④: after planting, the planter retracts vertically while gradually closing under the joint constraints of the crank profile, cables, and springs until returning to Action ①. The lower rocker mainly realizes the up-and-down reciprocating motion of the planter, and the upper rocker mainly realizes the adjustment of the planting angle of the planter. The two rockers cooperate with each other to adjust the planting posture of the seedlings. The opening and closing of the planter are controlled by the crank contour and the pull line. The angular velocity of the cam and the crank is equal.

2.3. Mathematical Modeling Establishment and Linkage Optimization

2.3.1. Establishment of Kinematic Model

In order to analyze the motion posture of the planter, it is necessary to analyze the motion trajectory of the planter entry point I and clarify the motion equation of the mechanism. The schematic diagram of the seven-bar linkage planting mechanism is shown in Figure 3. $L_{{\mathrm{O}}_2\mathrm{B}}$ is the rocker in contact with the cam. Since the cam is not within the range of the seven-bar linkage, it is not depicted here. O₁, O₂, and O₃ are the hinge points of the lower rocker arm, swing link, and crank, respectively. As the rocker arm connects the crank, swing link, and planting apparatus, a plane rectangular coordinate system is established with O₁ as the coordinate origin [15,16,17,18,19]. The horizontal rightward direction is the x-axis and the vertical upward direction is the y-axis. The angular displacement of each rod is based on the positive direction of the x-axis and y-axis, counterclockwise is positive, and the forward direction of the unit is the negative direction of the x-axis. The influence of factors such as deformation and friction of the mechanism is neglected in the kinematic modeling.

Based on the planar Cartesian coordinate system established for the schematic diagram of the seven-bar linkage planting mechanism, the mathematical models for the displacements of key points are derived as follows:

The displacement equations for points A, B, and C are, respectively:

$$\left\{\begin{array}{l}{x}_A=x_{O_3}+L_{O_{3}A}\cos {\theta }_3\\ y_A=y_{O_3}-L_{O_{3}A}\sin {\theta }_3\end{array}\right.$$

(1)

$$\left\{\begin{array}{l}{x}_B=L_{O_{2}B}\cos {\theta }_2\\ y_B=y_{O_2}-L_{O_{2}B}\sin {\theta }_2\end{array}\right.$$

(2)

$$\left\{\begin{array}{l}{x}_C=L_{O_{1}C}\cos {\theta }_1\\ y_C=-L_{O_{1}C}\sin {\theta }_1\end{array}\right.$$

(3)

In Formulas (1)–(3), (x_o3, y_o3)—the coordinates of point O₃; y_o2—the ordinate of point O₂.

Since point E, point O₁, and point C are on the same straight line, point O₁ is the origin of the coordinate system, and the displacement coordinates of point E can be obtained by the displacement coordinates of point C:

$$\left\{\begin{array}{l}{x}_E=L_{O_{1}E}\cos {\theta }_1\\ y_E=L_{O_{1}E}\sin {\theta }_1\end{array}\right.$$

(4)

According to the displacement coordinates of point B and θ₄, the displacement coordinates of point D can be obtained as follows:

$$\left\{\begin{array}{l}{x}_D=x_B+L_{BD}\cos {\theta }_4\\ y_D=y_B-L_{BD}\sin {\theta }_4\end{array}\right.$$

(5)

Point F is the midpoint of rod DE. According to the displacement coordinates of points D and E, the displacement coordinates of point F can be obtained:

$$\left\{\begin{array}{l}{x}_F={\displaystyle \frac{x_D+x_E}{2}}\\ y_F={\displaystyle \frac{y_D+y_E}{2}}\end{array}\right.$$

(6)

α is the angle between the rod FG and the horizontal direction, that is, the slope of the rod FG is k_FG = tan α, and we can obtain:

$$\alpha =\arctan {\displaystyle \frac{x_D-x_E}{y_D-y_E}}$$

(7)

According to FG⊥DE, the displacement coordinates of point G can be obtained:

$$\left\{\begin{array}{l}{x}_G=x_F+L_{FG}\cos \alpha \\ y_G=y_F+L_{FG}\sin \alpha \end{array}\right.$$

(8)

In order to find the motion trajectory of point I and the uprightness of the planter HI, it is necessary to further calculate the displacement equation of point I and the angle β between the rod HI and the horizontal direction. Since ∠FGI is known, the displacement equation of point I can be obtained based on the slope of the rod FG and the coordinates of point G:

$$\left\{\begin{array}{l}{x}_I=x_G-L_{GI}\cos \beta \\ y_I=y_G-L_{GI}\sin \beta \end{array}\right.$$

(9)

where

$$\beta =\angle FGI+\alpha$$

(10)

By taking the first-order derivative and the second-order derivative of Equation (9), the velocity and acceleration equations of point I can be obtained:

The velocity equation of point I:

$$\left\{\begin{array}{l}{v}_{Ix}={\dot{x}}_I={\dot{x}}_G+\dot{\beta }{L}_{GI}\sin \beta \\ v_{Iy}={\dot{y}}_I={\dot{y}}_G-\dot{\beta }{L}_{GI}\cos \beta \end{array}\right.$$

(11)

Acceleration equation at point I:

$$\left\{\begin{array}{l}{a}_{Ix}={\ddot{x}}_I={\ddot{x}}_G+\ddot{\beta }{L}_{GI}\sin \beta +{\dot{\beta }}^2{L}_{GI}\cos \beta \\ a_{Iy}={\ddot{y}}_I={\ddot{y}}_G-\ddot{\beta }{L}_{GI}\cos \beta -{\dot{\beta }}^2{L}_{GI}\sin \beta \end{array}\right.$$

(12)

2.3.2. Constraints

Based on the workspace requirements of the seven-bar linkage planting mechanism, it is necessary to avoid collision with other devices during operation and realize the functions of grafting and planting seedlings. Therefore, it is necessary to define the constraints before determining the specific parameters of each rod [20,21].

(1) Installation height of planting mechanism

To ensure sufficient workspace for the planting mechanism between the ridge surface and seedling throw device, the highest point of H and the lowest point of I must meet the operation requirements. According to the suitable planting depth of eggplant seedlings of 50–60 mm [22], a distance of 50 mm is reserved so that the seedling pot cannot reach the tip of the planter. Therefore, the lowest point of I is set 100~110 mm below the ridge surface, while the highest point of H during seedling collection is positioned 50~100 mm below the seedling feeding device. With the height of the planting device HI being 400 mm and referencing the chassis frame height of 700 mm from the ISEKI semi-automatic transplanter, the vertical motion range of the planting device from the lowest planting point to the highest seedling collection point can be derived as Δy = 290~350 mm.

(2) Installation height of O₁

Point O₁ is the lowest point where the planting mechanism is fixed to the frame. When the transplanter is operating, other parts, except the planter, cannot contact the ridge surface. According to the planting depth of 50–60 mm and the distance between the seedling pot and the tip of the planter of 50 mm, the lowest point O₁ should be 100~110 mm higher than the lowest point of I, leaving a margin for movement. Point O₁ is initially set to be more than 200 mm higher than the lowest point of I.

(3) Conditions for the construction of a crank-rocker mechanism

In the planting mechanism, $L_{{\mathrm{O}}_3\mathrm{A}}$, L_AC, $L_{{\mathrm{O}}_1\mathrm{C}}$, and frame $L_{{\mathrm{O}}_1{\mathrm{O}}_3}$ form a crank-rocker mechanism, which should meet the rod length condition of the crank-rocker mechanism: the shortest rod length + the longest rod length ≤ the sum of the other two rod lengths. In this planting mechanism, O₁O₃ is the frame, rod $L_{{\mathrm{O}}_3\mathrm{A}}$ is the crank, and $L_{{\mathrm{O}}_1\mathrm{C}}$ is the rocker. Among them, $L_{{\mathrm{O}}_3\mathrm{A}}$ is the shortest and frame $L_{{\mathrm{O}}_1{\mathrm{O}}_3}$ is the longest, which should meet:

$$L_{O_{3}A}+L_{O_1{O}_3}\le L_{AC}+L_{O_{1}C}$$

(13)

In a crank-rocker mechanism operating with a large height differential, the planting apparatus follows a curved trajectory, resulting in the seedlings landing in a tilted orientation. To solve this, a swing link $L_{{\mathrm{O}}_2\mathrm{B}}$ is incorporated to counteract the tilt at soil entry, with its swing angle θ₂ set in the range of 0° to 90°.

Based on the constraint conditions (1) to (3), the parameters of the seven-bar linkage planting mechanism have been preliminarily determined as follows: $L_{{\mathrm{O}}_2\mathrm{B}}$ = $L_{{\mathrm{O}}_3\mathrm{A}}$ = 50 mm, $L_{{\mathrm{O}}_1\mathrm{C}}$ = 115 mm, L_AC = 145 mm, L_DE = 70 mm, L_FG = 55 mm, L_GI = 300 mm. O₂ (0, 115), O₃ (110, 125), ∠FGI = 80°.

(4) Visual-aided constraint implementation for optimization programming

Since the swing angle of $L_{{\mathrm{O}}_2\mathrm{B}}$ is controlled by a cam, it can be regarded as stationary when in contact with the non-protruding part of the cam. When contacting the protruding portion, $L_{{\mathrm{O}}_2\mathrm{B}}$ undergoes uniform oscillatory motion. Based on the required motion trajectory of the planting point I, the maximum oscillation angle of $L_{{\mathrm{O}}_2\mathrm{B}}$ is set to 30°. To ensure hole-forming quality and transplanting efficiency, the planting time is set at 0.1 s. At a planting rate of 60 seedlings/minute, the angular velocity of $L_{{\mathrm{O}}_3\mathrm{A}}$ in uniform rotation is ω₁ = 2π rad/s, while the angular velocity of $L_{{\mathrm{O}}_2\mathrm{B}}$ is ω₂ = ${\displaystyle \frac{5}{3}}\pi$ rad/s. When L_AC lies along the extension line of $L_{{\mathrm{O}}_3\mathrm{A}}$, the planting point reaches its lowest position, according to the Pythagorean theorem and trigonometric functions, at which θ₃ = 95.33°.

According to Formula (1):

$${\theta }_3={\omega }_{1}t$$

(14)

Assume that the movement cycle of the planter is 1 s. Only the movement state of the first cycle is considered here, and θ₃ = 0° is set as the initial state. When θ₃ = 95.33°, t_I = 0.26 s. According to the seedling planting time of 0.1 s, it can be calculated that 0.16 s ≤ t < 0.26 s is the increase stage of θ₂, t = 0.26 s is the seedling planting moment, and 0.26 s < t ≤ 0.36 s is the decrease stage of θ₂. According to the mathematical model, the swing angle of θ₂ is preliminarily proposed to be 90°~120° (adjustable according to needs), that is, when 0.16 s ≤ t < 0.26 s:

$${\theta }_2=90+{\omega }_2\left(t-0.16\right)$$

(15)

when 0.26 s ≤ t ≤ 0.36 s:

$${\theta }_2=120-{\omega }_2\left(t-0.26\right)$$

(16)

At other times, θ₂ = 90°. Substituting θ₃ and θ₂ into Equations (1) and (2), respectively, can obtain a definite mathematical model, which can be used for visualization to assist in optimizing program writing.

2.3.3. Linkage Optimization

In order to verify the rationality of the seven-bar linkage planting mechanism, based on establishing the mathematical model of the planting mechanism and determining the constraints, the uprightness of the planting device is taken as the optimization target, and the motion characteristics of the lowest point I of the planting mechanism are specifically analyzed to optimize the link length [23,24,25,26]. When point I is at the lowest point, L_O3A is located below and on the same straight line as L_AC. At this time, θ₃ is 95.33° and θ₁ is 36.97°. It can be seen from Formula (9) that y_I should take the minimum value at this time, the absolute instantaneous speed of point I is 0, and Formula (11) is the relative speed of point I. According to the actual transplanting operation requirements, the forward direction of the machine is set to the negative direction of x, and the forward speed is 200 mm/s. Under this optimization condition, the optimization result of v_Ix in Formula (11) should be 200 mm/s, and the optimization result of v_Iy should be 0. To ensure upright planting, β is equal to 90°. Under this optimization condition, Equations (9)–(11) are analyzed for solutions. After analysis, it is found that a solution exists under this condition, which indicates that the design of the mechanism is reasonable.

According to the mathematical model of the planting mechanism, a Qt Creator 17.0.0-based visual optimization interface for the seven-bar linkage planting mechanism was developed, as shown in Figure 4. Trajectory optimization of the planting point was achieved by adjusting the lengths of different linkages. When the lengths and angles were set as follows: $L_{{\mathrm{O}}_2\mathrm{B}}$ = $L_{{\mathrm{O}}_3\mathrm{A}}$ = 51.9 mm, $L_{{\mathrm{O}}_1\mathrm{E}}$ = L_BD = 300 mm, $L_{{\mathrm{O}}_1\mathrm{C}}$ = 113.3 mm, L_AC = 145 mm, L_DE = 70 mm, L_FG = 48.7 mm, L_GI = 320.1 mm, ∠FGI = 79.13°, the y-direction displacement of the planting mechanism was 322.5 mm under this parameter condition, which met the spatial constraint conditions. In order to facilitate the processing and manufacturing of the linkages, the parameters were rounded to $L_{{\mathrm{O}}_2\mathrm{B}}$ = $L_{{\mathrm{O}}_3\mathrm{A}}$ = 52 mm, $L_{{\mathrm{O}}_1\mathrm{E}}$ = L_BD = 300 mm, $L_{{\mathrm{O}}_1\mathrm{C}}$ = 113 mm, L_AC = 145 mm, L_DE = 70 mm, L_FG = 49 mm, L_GI = 320 mm, ∠FGI = 79°.

2.4. Establishment of DEM–MBD Coupling Simulation Model

Based on the design of the seven-bar linkage planting mechanism and the optimization of the linkage, the three-dimensional model of the planting mechanism and the seedlings was established using Solidworks 2020 software. In the dynamic simulation software RecurDyn 2020, the corresponding motion constraints were applied to the linkages of the planting mechanism to establish a dynamic simulation model to simulate the actual operation motion of the mechanism. The discrete element simulation software Altair EDEM 2020 was used to establish a soil bin model resembling the field-test soil condition, and the contact parameters that interacted with the planting mechanism and the seedlings were applied. The operation state of the planting mechanism can be simulated in real time through the coupling window between the software [27]. The simulation model and motion constraints were adjusted according to the main factors affecting the seedling planting effect, so as to complete multiple sets of coupled simulation comparison tests. Figure 5 shows the coupled simulation model of the seven-bar linkage planting mechanism.

In Recurdyn, the Assembly Hierarchy model was selected to establish the multi-body dynamics model of the planting mechanism. Marker points were added to the components to define kinematic joints, and boundary conditions were sequentially applied to the driving links. The forward speed was set to 200 mm/s with a crank speed of 60 r/min, and all materials were defined as carbon steel. In EDEM, the Hertz-Mindlin with JKR model was adopted. The soil particles were simplified into spherical particles with a diameter of 5 mm, and a soil bin model with the dimension of 1800 mm × 200 mm × 140 mm (length × width × height) was created. The seedling particles were established (seeding tray 1 mm, lower stem 1.5 mm, upper stem 0.6 mm, leaf 0.5 mm). Referring to the literature [28,29], the material mechanical properties and mutual contact properties are shown in

Table 1. Mechanical properties of materials.

Parameters	Seeding	Soil	Planting Device
Density (kg/m3)	1000	2800	7800
Poisson’s ratio	0.25	0.25	0.25
Shear modulus (pa)	1 × 106	1 × 106	1 × 108

and

Table 2. Material contact properties.

Parameters	Seeding–Seeding	Seeding–Soil	Seeding–Plant Device	Soil–Soil	Soil–Planting Device
Static friction coefficient	0.5	0.5	0.1	0.5	0.1
Rolling friction coefficient	0.01	0.1	0.01	0.01	0.01
Impact recovery coefficient	0.5	0.5	0.5	0.5	0.5

.

2.5. Test Factors and Evaluation Indicators

Based on the theoretical analysis of planting mechanism and motion simulation research, the insignificant factors were eliminated and the planting frequency X₁, opening width X₂, and opening time X₃ were selected as the main experimental factors. The value ranges were as follows: X₁ (55–60 plants/min), X₂ (40–70 mm), X₃ (0.4–0.9 s). The soil backflow Y₁ and seedling uprightness Y₂ were used as evaluation indicators to carry out a three-factor five-level quadratic regression orthogonal rotation combination test. The experimental factor coding is shown in

Table 3. Experimental factors and levels.

Level	Factors
	Planting Frequency X1/(plant/min)	Opening Width X2/(mm)	Opening Time X3/(s)
1.682	60.00	70.00	0.90
1	59.00	68.00	0.86
0	57.50	55.00	0.65
−1	56.00	42.00	0.43
−1.682	55.00	40.00	0.40

.

The soil backflow Y₁ is defined as the ratio of the difference between the hole depth h₁ when the planter is fully opened after entering the soil and the hole depth h₂ after it is closed after exiting the soil to h₁.

The seedling uprightness Y₂ is defined as the minimum angle between the main stem of the seedling and the horizontal plane, and ≥60° is considered upright [30].

The calculation method of the Y₁ evaluation index is:

$$Y_1={\displaystyle \frac{h_1-h_2}{h_1}}$$

(17)

In Formula (14), Y₁ is the soil return flow, %; h₁ is the hole depth when the planter is fully opened after entering the soil, (mm); h₂ is the hole depth when the planter is closed after it is unearthed, (mm).

3. Results and Discussion

3.1. Test Results

The DEM–MBD coupling simulation of the seven-bar linkage planting mechanism is shown in Figure 6. The green material in the figure is the seedling, and the yellow material is the soil.

A total of 23 sets of transplanting performance tests were conducted, each test was repeated 3 times, and the average of the 3 test results was taken as the test result. Design-Expert 12.0 software was used for experimental design and result analysis, as shown in

Table 4. Experimental scheme and results.

No.	Planting Frequency X1/(Plant/min)	Opening Width X2/(mm)	Opening Time X3/(s)	Soil Backflow Y1	Seedling Uprightness Y2/(°)
1	−1	−1	−1	0.59 (0.05)	78.53 (0.59)
2	1	−1	−1	0.47 (0.08)	67.23 (1.36)
3	−1	1	−1	0.45 (0.09)	62.85 (1.54)
4	1	1	−1	0.43 (0.06)	57.47 (2.61)
5	−1	−1	1	0.72 (0.02)	75.24 (0.58)
6	1	−1	1	0.65 (0.06)	70.15 (0.93)
7	−1	1	1	0.54 (0.07)	73.54 (0.76)
8	1	1	1	0.52 (0.04)	73.43 (0.68)
9	−1.682	0	0	0.59 (0.04)	71.84 (0.92)
10	1.682	0	0	0.55 (0.05)	67.12 (1.15)
11	0	−1.682	0	0.6 (0.06)	74.66 (0.79)
12	0	1.682	0	0.45 (0.09)	67.49 (1.24)
13	0	0	−1.682	0.52 (0.07)	58.96 (2.53)
14	0	0	1.682	0.7 (0.01)	72.51 (0.66)
15	0	0	0	0.67 (0.03)	80.33 (0.25)
16	0	0	0	0.64 (0.05)	79.15 (0.38)
17	0	0	0	0.65 (0.04)	78.47 (0.49)
18	0	0	0	0.63 (0.05)	82.43 (0.17)
19	0	0	0	0.67 (0.03)	80.19 (0.41)
20	0	0	0	0.63 (0.04)	78.37 (0.65)
21	0	0	0	0.65 (0.06)	81.26 (0.57)
22	0	0	0	0.62 (0.03)	79.51 (0.48)
23	0	0	0	0.65 (0.05)	80.24 (0.32)

Note: The data in parentheses are the standard deviation.

, where X₁, X₂, and X₃ are coded factors.

3.2. Results Analysis

(1) Significance analysis

The simulation test results were analyzed by the variance analysis, as shown in

Table 5. Variance analysis of regression models.

Source		Y1					Y2
	SS	DF	MS	F	p	SS	DF	MS	F	p
Model	0.1502	9	0.0167	37.66	<0.0001 **	1102.46	9	122.50	47.74	<0.0001 **
X1	0.0065	1	0.0065	14.60	0.0021 **	65.10	1	65.10	25.37	0.0002 **
X2	0.0403	1	0.0403	91.03	<0.0001 **	94.47	1	94.47	36.81	<0.0001 **
X3	0.0460	1	0.0460	103.83	<0.0001 **	176.30	1	176.30	68.70	<0.0001 **
X1X2	0.0028	1	0.0028	6.35	0.0256 *	14.85	1	14.85	5.79	0.0317 *
X1X3	0.0003	1	0.0003	0.7051	0.4162	16.47	1	16.47	6.42	0.0249 *
X2X3	0.0021	1	0.0021	4.77	0.0479 *	91.26	1	91.26	35.56	<0.0001 **
X12	0.0146	1	0.0146	32.96	<0.0001 **	179.40	1	179.40	69.91	<0.0001 **
X22	0.0340	1	0.0340	76.63	<0.0001 **	124.24	1	124.24	48.41	<0.0001 **
X32	0.0042	1	0.0042	9.38	0.0091 **	348.64	1	348.64	135.86	<0.0001 **
Residual	0.0058	13	0.0004			33.36	13	2.57
Lack of fit	0.0033	5	0.0007	2.21	0.1530	19.70	5	3.94	2.31	0.1402
Error	0.0024	8	0.0003			13.66	8	1.71
Total	0.1560	22				1135.82	22

Note: ** indicates extremely significant effect (p < 0.01), and * indicates significant effect (0.01 ≤ p ≤ 0.05).

. The results show that the regression model of soil backflow Y₁ and seedling uprightness Y₂ has a p value of less than 0.01, indicating that the two models are extremely significant. The lack of fit item of soil backflow Y₁ with the p > 0.05 (0.1530) represents that the equation has a high degree of fit, and its determination coefficient R² is 0.9631, indicating that the model can explain more than 96% of the evaluation indicators. The lack of fit item of seedling uprightness Y₂ with the p > 0.05 (0.1402) indicating that the equation has a high degree of fit, and its determination coefficient R² value is 0.9706, indicating that the model can explain more than 97% of the evaluation indicators. Therefore, the working parameters of the seven-bar linkage planting mechanism can be optimized using those two models.

As can be seen from Table 5, the three factors (planting frequency X₁, opening width X₂, opening time X₃) correspond to soil backflow Y₁ and seedling uprightness Y₂ are p < 0.01, indicating that the three factors have extremely significant effects on the two indicators. Among them, X₁ and X₂, X₂ and X₃ have significant pairwise interactions to Y₁ (p < 0.05). X₁ and X₂, X₁ and X₃ have significant pairwise interactions to Y₂ (p < 0.05). X₂ and X₃ have extremely significant pairwise interactions to Y₂ (p < 0.01).

In order to more accurately express the impact of each factor on the corresponding indicators, the insignificant factors in the model are eliminated to obtain the regression model equation:

$$\begin{array}{l}{Y}_1 = 0.6459-0.0218X_1-0.0544X_2+0.058X_3+0.0188X_1{X}_2-0.0162X_2{X}_3\\ -0.0303X_1^2-0.0462X_2^2-0.0162X_3^2\end{array}$$

(18)

$$\begin{array}{l}{Y}_2 = 79.96-2.18X_1-2.63X_2+3.59X_3+1.36X_1{X}_2+1.44X_1{X}_3+3.38X_2{X}_3\\ -3.36X_1^2-2.8X_2^2-4.68X_3^2\end{array}$$

(19)

According to the analysis of the optimized model, the p value of the regression model Y₁ is less than 0.01, and the lack-of-fit term is p = 0.1775. The p value of the regression model Y₂ is less than 0.01, and the lack-of-fit term is p = 0.1402. It can be obtained that the optimized model is reliable.

(2) Interaction analysis

Based on the integrated analysis of Table 5 and Figure 7a–c, it can be seen that the soil backflow decreases with increasing planting frequency and opening width increase, and increases with increasing opening time. Distinct turning points appear on the response surfaces for X₁ and X₂, indicating the existence of a local maximum for soil backflow within the tested ranges of these factors. The X₃ response surface shows a monotonic upward trend, demonstrating that longer opening times correlate with greater soil backflow. The main reason is that when planting frequency and opening width are excessively large while opening time is too short, the planter’s soil-entry and opening speeds increase significantly. Under these conditions, soil particles contacting the planter experience substantial displacement due to inertial forces. At the moment of planter closure and withdrawal from soil, both the volume and velocity of soil backflow are reduced, resulting in deeper planting holes.

Based on the integrated analysis of Table 5 and Figure 7d–f, it can be seen that the uprightness of the seedlings is positively correlated with the soil backflow. Turning points appear across all three response surfaces for Y₂, revealing that uprightness initially rises rapidly to a peak before gradually declining with increasing factor levels. This demonstrates the existence of a maximum uprightness value within the experimental factor ranges. The main reason is that as the planting frequency and opening width decrease and the opening time increases, the impact inertia force of the planter on the soil particles decreases. During planter closure and withdrawal from soil, accelerated soil particle backflow toward the cavity center generates a balanced supporting force around seedlings. This dynamic equilibrium provides uniform lateral support, thereby optimizing uprightness maintenance.

3.3. Parameter Optimization

To achieve optimal planting performance, the seven-bar linkage planting mechanism’s simulation parameters were optimized with the following dual objectives: maximized soil backflow volume and maximized seedling uprightness. This optimization was executed using the Optimization-Numerical module in Design-Expert 12.0 data analysis software, with the objective functions and constraints formulated as follows:

$$\left\{\begin{array}{l}\max Y_1\left(X_1,X_2,X_3\right)\\ \max Y_2\left(X_1,X_2,X_3\right)\\ s.t.\left\{\begin{array}{l}-1<X_1<1\\ -1<X_2<1\\ -1<X_3<1\end{array}\right.\end{array}\right.$$

(20)

The optimized parameter combination yielding superior performance was determined as planting frequency 56.94 plants/min, opening width 48.52 mm, opening time 0.76 s, soil return flow 0.69, and seedling uprightness 80.57°. For practical implementation, parameters were rounded to planting frequency 57 plants/min, opening width 48.5 mm, and opening time 0.76 s. Triplicate validation simulations under these rounded parameters produced mean results of soil backflow 0.67 and seedling uprightness 80.35°. The verification value was basically consistent with the optimization result.

3.4. Field Test

Prior to transplanting, the experimental field underwent rotary tillage and ridging to ensure fine-textured and leveled soil. Employing the parameter combination of planting frequency at 57 plants/min, opening width at 48.5 mm, and opening time at 0.76 s, 120 seedlings were consecutively transplanted with triplicate trials, and measured values were averaged, as shown in Figure 8. Field test results as shown in Figure 9, soil backflow of 0.64, and seedling uprightness of 78.49°, show deviations of 4.47% and 2.31%, respectively, from the regression model’s optimized results. These minor variations within acceptable limits validate the simulation effectiveness and rational mechanism design.

3.5. Discussion

Vegetable transplanting typically employs single-seedling planting as the primary method. However, the operational quality of transplanting devices is significantly influenced by soil moisture conditions, often resulting in inconsistent planting depths and frequent seedling lodging (Figure 10a). Taking cabbage as an example, lodged seedlings develop tilted heads at maturity, severely compromising mechanical harvesting efficiency (Figure 10b). According to research findings, transplanting seedlings additional 20 mm deeper than the preset depth can effectively improve the straightness of cabbage heads to over 90% (Figure 10c), whereas shallow planting reduces this value to approximately 42%. The multi-link transplanting mechanism can achieve vegetable transplanting at varying depth requirements. Compared to planetary gear and eccentric crank transplanting mechanisms, it demonstrates advantages in structural simplicity and facilitates adjustment of planting depth. However, conventional multi-link planters typically feature fixed planting units constrained by mechanical limitations, resulting in skewed soil-entry angles that cause seedling tilting. The seven-bar linkage mechanism developed in this study achieves nonlinear trajectory motion of the planting unit, compensating for seedling posture during soil entry to enhance uprightness. This research employed EDEM-RecurDyn co-simulation for rapid mechanism design and testing of the transplanting mechanism, enabling effective simulation of the operational scenarios of the transplanter. Within the discrete element model, spherical soil particle simplification introduced deviations between simulations and physical tests; future refinements could adopt polygonal particles with uniformly distributed sizes to better approximate actual soil morphology, thereby improving simulation fidelity.

4. Conclusions

(1) A seven-bar linkage planting mechanism with seedling posture compensation function was designed. The overall structure and working principle were explained, the mathematical model of the mechanism was established, the mechanism constraints were determined, and the mechanism parameters of the optimal planting trajectory were optimized based on the visualization-assisted optimization software.

(2) A DEM–MBD coupling simulation model of planting mechanism-soil-seedlings was established. The planting frequency, opening width, and opening time of the planter were used as factors, and the soil backflow and seedling uprightness were used as evaluation indicators. A quadratic regression orthogonal rotation combination simulation test was carried out, and a regression model between each factor and indicator was established. The response surface method was used to optimize the parameter values, and the optimal parameter combination was obtained as follows: planting frequency 57 plants/min, opening width 48.5 mm, opening time 0.76 s. The test verified that the return flow was 0.67 and the seedling uprightness was 80.35.

(3) Field tests were carried out on the seven-bar linkage planting mechanism. The soil backflow was 0.64 and the seedling uprightness was 78.49°, which were 4.47% and 2.31% different from the regression model optimization results, respectively. The error change was small, indicating that the simulation results were effective and the mechanism design was reasonable.