2.1. Semi-Automatic Vegetable Transplanter
The shape and main specifications of the semi-automatic vegetable transplanter of this study are shown in
Figure 1 and
Table 1, respectively. The main components of the transplanter consist of an engine that is the power source, a transmission that transmits the power of the engine to the driving wheel and transplanting device, a seedling cylinder in which seedlings are placed manually, a transplanting device to plant the seedlings supplied from the seedling cylinder into the soil, a control section that controls the operation of the transplanter, a digital plant spacing control device that adjusts the row spacing for the seedlings, a depth control device that controls the planting depth of the seedlings, and a molding wheel that covers a seedling planted in the ground with soil.
The transplanter operates as follows: A user determines the travel speed of the transplanter through the control section and supplies the seedlings to the seedling cylinders manually. The transplanter moves in the forward direction and plants the seedlings into the ground by the motion of the transplanting device. That motion makes the hopper of the transplanting device move up and down in a certain trajectory. When the hopper is at the top, it is located just below one of the seedling cylinders. At that moment, the seedling cylinder opens and drops the seedling into the hopper. When the hopper reaches the lower end, it is located at a certain depth in the ground. At that moment, the hopper is opened and the seedlings in the hopper are planted into the ground. The row spacing and planting depth suitable for the target crop can be set by the digital plant spacing control device and the depth adjustment device, respectively. The seedlings planted in the ground are covered with soil by the molding wheel installed at the rear side of the transplanter, and the transplanting work is completed.
2.3. Kinematic Analysis to Determine Theoretical Planting Trajectory
The theoretical planting trajectory of the hopper was derived by analyzing the operating positions of the main links of the transplanting device. The main links related to the planting trajectory are 6 links, including the ground (L1, L2, L3, L4, L5, and L6). When the power of the engine is transmitted to the crank (L2), which is a driving part of the transplanting device, the behavior of the transplanting device is initiated by the rotational motion of the crank. L4 is a quaternary link with four joints (C, D, G, and H) and is a coupler of the parallelogram mechanism made by two links of the same length (L5, L6) and the ground. Therefore, L4 moves in a curved translational motion, and all four joints have the same trajectory (
Figure 4).
L3 is a ternary link that consists of three joints (B, C, and J), and the position of joint J is determined by the positions of joints B and C; that is, when the positions of joints B and C are changed by the rotation of crank, the position of joint J is determined accordingly. Because the relative positions of joint J and the hopper end point Q are fixed, once the position of joint J is determined, the position of the hopper end point which is related to the planting trajectory can be finally determined (
Figure 5).
For simplification, the virtual links (L1′, L5′) and the virtual pivot point (O4′) that make joint C have the same trajectory as the existing curve are set as shown in
Figure 6. L1′ is the ground, and the positions of L5′ and O4′ can be determined by translating the link L5 to meet at point C. In this way, the two links L5 and L6 are simplified to a single link, L5′, and the two pivot points E and F are simplified to a single pivot point, O4′. The length of link L5′ is the same as that of link L5 or L6.
In this case, the position of joints B and C can be simply determined by a four-bar linkage mechanism consisting of links L1′ (ground), L2 (crank),
(coupler), and L5′ (rocker). The fixed pivot point O2 of the crank was considered as the origin of the global coordinate system (X–Y coordinate system). For convenience of analysis, the local coordinate system (x–y coordinate system) was set so that the x-axis was aligned with the ground L1′ by rotating the global coordinate system clockwise by a certain angle (α) (
Figure 7).
Regarding the four-bar linkage mechanism analysis, the input parameter is the counterclockwise angle (
θ2) between the x-axis direction and the crank. The output parameter is the counterclockwise angle (
θ3) between the x-axis direction and the coupler. When
θ3 is determined for each θ
2, the position of joints B and C in the local coordinate system can also be determined. Finally, the position of joint J and the hopper end point Q can be derived from the position of joints B and C. The value of
θ3 according to
θ2 can be obtained using the vector loop equation as shown in Equation (1) (
Figure 8) [
18].
where
= vector of link (crank);
= vector of link (coupler);
= vector of link (rocker);
= vector of link (ground).
The position of joint J is derived by Equation (2) using the position of joint B. In the equation, the position of joint B can be obtained by using the length of the crank and angle
θ2, which are known variables. The position of joint J with respect to joint B is derived from the angle (x’) between link
and the x-axis direction. When ∠CBJ is set to
δ, x’ can be obtained from the geometrical relationship between the links. As shown in
Figure 9, the figure can be rotated so that the x-axis becomes the horizontal axis, and Equation (3) can be derived based on the relationship of the angles
θ2,
θ3, and x’.
where
= position of joint J in the local coordinate system;
= position of joint B in the local coordinate system;
= position of joint J relative to joint B in the local coordinate system.
θ3 is determined by
θ2, and
δ is a constant; the position of joint J with respect to joint B can be calculated with a given
θ2. The position of joint B and the position of joint J with respect to joint B are determined by Equations (4) and (5), respectively, by which the position of joint J is determined, as shown in Equation (6).
where
= x-axis position of joint B in the local coordinate system;
= y-axis position of joint B in the local coordinate system;
a = length of (crank).
Because the rotation of the local coordinate system counterclockwise by α matches the global coordinate system, the position of joint J in the global coordinate system can be obtained using Equation (7):
where
In the global coordinate system, the Y coordinate of the hopper end point Q always maintains a constant distance (320 mm) from the Y coordinate of joint J. Furthermore, the X coordinate of Q is the same as the X coordinate of joint J. Therefore, the final position of the hopper end point can be determined using the position of joint J in the global coordinate system (Equation (8)).
where
The length and angles of the links for the existing transplanting device were obtained by measurements. The lengths of the crank (), coupler (), rocker (), and ground () were 48.22 mm, 102 mm, 80 mm, and 105 mm, respectively; the length of link and angles of α and δ were 110 mm, 22°, and 130°, respectively.
2.5. Optimization Strategy for the Main Link Lengths of the Transplanting Device
We tried to find the optimal lengths of the main links to reduce the weight while maintaining the same planting trajectory as the existing transplanting device. The main links to be optimized were the crank, coupler, and rocker, as shown in
Figure 7, because they are key links that determine the planting trajectory. A genetic algorithm was used as an optimization method. The genetic algorithm is one of the techniques used to solve optimization problems with a stochastic search method developed based on biological evolution [
20,
21].
To solve the optimal design problem of the main link lengths, based on the micro-genetic algorithm proposed by Krishnakumar [
22], we used around 10 design variables and a relatively small number of populations to make large-scale computation unnecessary. The elite genes were selected based on the total main link length and used in the next generation to preserve the desired factors. The difference of micro-genetic algorithms to general genetic algorithms is that they do not take into account mutations. This is because when the genes converge to one point, they are reconstructed into the optimal gene in the group and the additional randomly generated gene, so no separate mutation computation is required [
22].
Figure 12 presents the genetic algorithm process of this study.
The optimization process applied in this study is detailed as follows.
Step 1. Create the initial population
A set of crank, coupler, and rocker lengths was used to express a chromosome that was the solution set of genetic algorithms. The initial solution set (1st generation) was randomly generated at an interval of 0.01 mm within the range of ±5 mm based on the lengths of the crank, coupler, and rocker lengths of the existing transplanting device.
Step 2. Fitness evaluation
The fitness of the solution set was evaluated and the optimal set was selected. At this time, the fitness was determined from the objective function that was set to minimize the total link length. Because the links of the transplanting device were mainly subjected to axial load during operation, there was no significant change in the stress magnitude generated in each link if the cross-sectional area was retained. For minimizing the effect to static safety regarding stress magnitude, only the link lengths were set as an input parameter. Because the cross-sectional area was the same, the length ratio was the same as the weight ratio, and the condition in which the total length was minimized was the same as the condition in which the weight was minimized. Therefore, the optimal condition was to minimize the total main link length while maintaining the planting trajectory of the hopper within a specific range. The theoretical planting trajectory was used in the optimization process to confirm if the optimized transplanting device had the same planting trajectory as the existing one.
The constraint of the solution set was defined using the width and height of the planting trajectory. The limiting range was set to ±5 mm from the existing planting trajectory; that is, solution sets were included in the optimization process only when the maximum Y coordinate, the minimum Y coordinate, the maximum X coordinate, and the minimum X coordinate of the new trajectory fell within ±5 mm of the values of the existing trajectory.
Step 3. Selection and crossover
The solution sets were selected based on the fitness evaluation, and a crossover operation was conducted. According to the strategy of the micro-genetic algorithm, tournament selection was adopted as the selection operation and one-point crossover was adopted as the crossover operation [
23].
Step 4. Convergence
Convergence was reviewed by including the solution sets generated through the crossover operation and the elite sets. In the micro-genetic algorithm, the nominal convergence is the step of selecting and crossing solution sets repeatedly until the difference between the sets generated from the selection and crossover operations and elite sets is below a certain level. When the termination condition is set to the maximum number of generations, the nominal convergence is generally set to 5% [
24]. In this study, the degree of convergence was used as the termination criterion, so the nominal convergence was relatively relaxed and set to 10%.
Step 5. Restart
When restarting, the remaining sets except the elite sets were newly constructed using a random function. Elite sets were the result of the evolution of the last generations, and newly created sets enabled the consideration of multiple solution sets without mutation.
Step 6. Termination criteria satisfied
The above process was repeated until the termination criteria was satisfied. The termination criteria can be arbitrarily set by the user, and it was set to 10% of the nominal convergence in this study.