Exploring the Optimal Design for and Experimentation on a Bowl-Based Mechanism for Transplanting Potted Strawberry Seedlings


 To improve the mechanization of strawberry planting integration and the efficiency of fetching and transplanting seedlings, an integrated transplanting mechanism with protruding, fetching and planting is designed. This new device can realize rapid fetching and pushing bowl movements. The working principle of the slewing mechanism is analyzed, a kinematics model of the mechanism is established, and the optimization goal is established. Visual auxiliary analysis software is developed, optimized parameters are established, and the corresponding theoretical trajectory is provided. A three-dimensional model is established and a virtual simulation design analysis is performed to obtain a simulation trajectory. Three-dimensional printing technology is used to manufacture the test prototype, and the actual working trajectory of the test prototype is extracted using high-speed photography technology, which verifies the consistency of the actual trajectory with the theoretical and simulated trajectories. A prototype transplanting experiment is performed, showing that the success rate of seedling extraction is 91.2% and the rate of excellent planting is 82.8%, which meet the requirements for integrated strawberry harvesting, planting and transplanting and verify the correctness and feasibility of the mechanism design.


Introduction
Taxonomically, strawberry belongs to the Rosaceae family and is a perennial evergreen plant. With the rapid development of China's economy, the demand for strawberries continues to increase [1][2] , coupled with the rising labor cost, so research on strawberry transplanting machinery has practical meaning. Transplanting machinery is divided into semiautomatic and fully automatic machinery [3] . At present, there are no reports on automatic transplanting equipment for potted strawberry seedlings [4] . A semiautomatic transplanter with artificial seedlings is adopted, which is labor intensive and inefficient. The world's large-scale automatic transplanting models of potted vegetable seedlings include the Australian Williames automatic transplanter and Futura series automatic transplanter produced by Ferrari in Italy [5] . Generally, machine, electricity, gas and liquid integration is adopted, which has a high degree of automation, but the size is large, the structure is complicated, and the price is high, which is not suitable for China's national conditions [6] . Small automatic vegetable seedling transplanting machines, such as a transplanting machine produced by Yanmar Company in Japan, rely on two sets of mechanisms to complete seedling removal and planting actions [7][8] , which is reliable but low in efficiency.
High-efficiency, low-cost, lightweight and simplified automatic potted seedling transplanting machinery is still lacking worldwide [9] .
In recent years, much research has bee n done on fully automated potted seedling tr ansplanting in China. The transplanting mec hanism is the core component of potted see dling transplanters. The principle of removin g potted seedlings from pots can be divided into three stages: clamping the seedlings, ta king the pot and ejecting the seedlings. To avoid seedling damage, a bowl-type transpla nting mechanism is suitable for transplantin g potted strawberry seedlings. Such devices include the rotary transplanting mechanism composed of a noncircular gear and a crank -rocker mechanism designed by Sun Liang e t al., [10] the vegetable seedling transplanting mechanism composed of three eccentric circ les and incomplete noncircular gears designe d by Yu Gaohong et al. [11][12] , Ye Bingliang et al. [13][14] , and Zhou Meifang et al., [15][16] t he rotary hole-piercing pot seedling transpla nting mechanism designed by Zhou Maile et al., [17] and the pole-non-circular gear potte d strawberry seedling transplanting mechanis m designed by Xu Chunlin et al. [18] All of the above use the planting arm to drive an "eagle-beak" trajectory formed by a needle point into the soil, clamp the seedling, and r emove the seedling.
To improve the efficiency of seedling retrieval and planting, this paper designs an integrated transplanting mechanism with protrusion, picking and planting. It takes the seedlings by reversing the seedling needles and clamping the soil bowl, that is, the planetary carrier rotates in the direction opposite to the soil, and the seedling needles are inserted into the soil bowl under the leaves of the seedlings, such that the leaves and stems are not damaged. A "one" shape was used instead of the "eagle beak" to collect the seedling, a spring was used to make the seedling needle quickly penetrate the soil, and the time of entering the soil was reduced, thereby reducing the damage caused by the seedling needle to the root system of the seedling due to the lateral movement of the seedling box. In addition, since there is no sudden change in the theoretical trajectory of the seedling tip point of the transplanting mechanism, a higher rotational speed is allowed. To complete seedling removal more quickly to meet the needs of high-speed planting, a double cam structure is adopted on the basis of the original research results [6] . When the seedling needle is retracted, spring force is used to quickly complete the pushing action of the seedling, which reduces the time of seedling removal and improves the accuracy of planting.

Trajectory analysis
The seedling-grasping component is used to take seedling, and the seedling-pushing board pushes the seedling to ensure that it is completely removed, and at the same time, the two planting arms do not interfere with each other or with the seedling tray. To achieve rapid seedling extraction, precise seedling pushing, combined with the existing seedling taking mechanism, an integrated mechanism is proposed, and its track analysis is shown in Figure 1. The dashed line is the trajectory of a point in front of the seedling-pushing board, the thick solid line is the actual trajectory of the seedling needle point, and the thin solid line is the theoretical trajectory of the seedling needle tip under the assumption that the seedling needle does not completely protrude. The mechanical structure must complete the 4 consecutive stages of taking seedlings, holding the seedlings, pushing the seedlings, and returning the seedlings in one cycle. Seedling taking stage: in section ABC, when the seedling needle on the planting arm reaches point A, it quickly protrudes, the seedling needle is inserted into the soil bowl, and the soil bowl is clamped at point B. At the same time, the seedling needle makes the soil bowl contact the planting arm. The seedling tray is separated, reaching point C, and the soil bowl completely leaves the seedling tray. Clamping stage: in the CD section, the relative positions of the potted seedling and the seedling needle remain unchanged. The stage of pushing seedlings: in the DE section, at point D, the seedling-pushing shifting-yoke starts to move, and the seedling-pushing board quickly pushes the bowl under the action of the spring. At the same time, the seedling-taking shifting-yoke starts to move, and the seedling needles are retracted. Under this action, the potted seedlings fall into the soil hole approximately vertically. Recovery stage: in the EA section, the seedling-pushing board slowly returns to its original position, compressing the spring. At this stage, the seedling needle and the seedling-pushing board are completely reset, so the seedling-pushing board does not interfere with the seedling tray, which meets the design requirements.

Working principle
The transplanting mechanism is composed of a planetary gear train and planting arms, as shown in Figure 2. The planetary gear train is composed of left and right housings, planetary gears (1 and 5), a sun gear (3), intermediate gears (2 and 4) and so on. The planting arm part is composed of a cam (13), a seedling-taking shifting-yoke (14), a seedling-pushing shifting-yoke (16), a planting arm shell (19), a seedling needle (20), a pushing and pulling seat plate (23), a connecting rod (24), a pushing bowl (21), a pushing bowl slider (22), and a taking bowl slide (26) consisting of a spring seat, which cooperates with the spring seat on the planting arm shell. The planting arm shell is provided with a slideway, and the pushing bowl slider (22) and taking bowl slider (26) can slide on it, as shown in Figure 2(c).
The working principle of the planetary gear system is as follows: the sun shaft (8) transmits power and drives the gearbox housing (18) to rotate at a uniform speed; the sun gear (3) is fixed to the flange, and the planetary gears (1 and 5) and intermediate gears (2 and 4) follow the shell body rotation. The planting arm shell rotates at unequal speeds with the planetary axles (6 and 10).
The working principle of the planting arm is as follows: the cam (13) is fixed to the gearbox housing. The planting arm shell is fixed to the limit plates at the ends of the planetary axles (6 and 10). The seedling-taking shifting yoke (14) and seedling-pushing shifting yoke (16) rotate around the fork shafts (15 and 17, respectively). The cam (13) drives the shifting-yokes (14 and 16) to swing, which drives the sliders (26 and 22). This completes the seedling collection and seedling pushing operations.  (3), planetary axles (7,9), sun axle (8), first part of the planting arm (11), second part of the planting arm (12), cam (13), seedling-taking shifting-yoke (14), seedling-taking shifting-yoke axle (15), seedling-pushing shifting-yoke (16), seedling-pushing shifting-yoke axle (17), gearbox housing (18), planting arm (19), seedling needle (20), seedling-pushing board (21), push bowl slider (22), push-pull seat plate (23), connecting rod (24), compression springs (25,27), and seedling-taking bowl slider (26) Fig. 2 Working principle diagram of the seedling planting mechanism 2 Kinematic model of the mechanism 2.1 Noncircular gear pitch curve forming method In this paper, Lagrangian interpolation is used to obtain the noncircular gear pitch curve. To avoid the Runge phenomenon [19] , too many interpolation points are not used, so a total of 6 interpolation points are selected. In the polar coordinate system, the first and sixth interpolation points coincide to ensure the sealing of noncircular gears.
Lagrange interpolation formula in a polar coordinate system: where:  

Kinematic model establishment
The movement diagram of the noncircular planetary gear train is shown in Figure 3, and the symbols of the transplanting mechanism are described in Table 1 [20][21][22] .

Fig. 3 Schematic of the noncircular planetary gear train
Since the mechanism is symmetrical around the center of the sun gear, only one side of the mechanism is used for analysis. The sun gear is fixed on the frame, and the planet carrier (gearbox housing) rotates counterclockwise at a constant speed (counterclockwise rotation is recorded as positive, and clockwise rotation is negative).

Tab. 1 Symbol description of transplanting organization
Symbol Description r1(θ) Sun gear pitch curve radius r2(θ) Intermediate gear pitch curve radius φH0 The initial installation angle of the planet carrier θ0 Planet carrier corner δ0 The angle between the planting arm and the planet carrier before the seedling needle protrudes δ0+θ The angle between the planting arm and the planet carrier after the seedling needles are protruded a Center distance between two adjacent noncircular gears b Length of the first planting arm c The distance from the rotation center of the planetary gear to the tip of the seedling d The distance from the rotation center of the planetary gear to the tip of the seedling needle after the seedling needle protrudes In the transplanting process, the planet carrier rotates counterclockwise at a uniform speed, and the sun gear is fixed when the planet carrier rotates through φ.
The absolute rotation angle of the planet carrier relative to the frame is: The relative and absolute rotation angles of the sun gear are: The relative and absolute rotation angles of the intermediate gear are: The relative and absolute rotation angles of the planetary gear are: To compensate for the corners of the planet carrier, the rotation angle of the planetary gear is: The coordinates of the center of rotation of the sun gear are: The coordinates of the center of rotation of the intermediate gear are: The coordinates of the center of rotation of the planetary gear are: The coordinates of point E at the end of the planting arm in the first part are: The coordinates of the point at the end of the planting arm in the second part are discussed in three situations.
(1) Before the needle sticks out, the F coordinates of the end point of the planting arm in the second part are: (2) After the needle sticks out, the F' coordinates of the end point of the planting arm in the second parts are: (3) When the seedling needle protrude, a schematic diagram of establishing the tran splanting arm with integrated taking and pla nting planetary gear train was created, as sh own in Figure 4, and the symbol description of the planting arm structure is provided in Table 2. Taking point D as the origin, a re ctangular coordinate system is established. S ince the front and rear seedling needles are symmetrical, only one side is taken for anal ysis.
Tab. 2 Symbol description of the transplanting arm structure Symbol Description l1 Length of the upper section of the seedling-taking shifting-yoke l2 The y distance between the upper end of the seedling-taking shifting-yoke and the hinge point of the seedling needle lNT-l3 The x direction distance between the upper end of the seedling-taking shifting-yoke and the hinge point of the seedling needle θI Seedling needle angle l9 Seedling needle length l8 The distance in the x direction from hinge point C of the seedling-taking shifting-yoke to hinge point N of the seedling-pushing shifting-yoke l7 The distance in the y direction from hinge point C of the seedling-taking shifting-yoke to hinge point N of the seedling-pushing shifting-yoke l4 Length of the upper section of the seedling-pushing shifting-yoke l10 Length of the lower section of the seedling-pushing shifting-yoke l5 The x-direction distance between the upper end of the push bowl fork and the intersection point of the push bowl and seedling needle on the same plane l6 The y distance between the upper end of the push bowl fork and the intersection of the push bowl and the seedling needle on the same plane β The angle between the upper section of the seedling-pushing shifting-yoke and the x-axis λ The angle between the upper section of the seedling-taking shifting-yoke and the x-axis β1 The middle angle of the seedling-pushing shifting-yoke β2 The middle angle of the seedling-taking shifting-yoke The coordinates of the hinge point of the seedling-pushing shifting-yoke are: The coordinates of the hinge point of the seedling-taking shifting-yoke are: The coordinates of the upper end point of the seedling-taking shifting-yoke are: The coordinates of the hinge point of the seedling needle are: In the process of seedling needle protrusion, the coordinates of the tip point of the second part of the planting arm are: The coordinates of the upper end point G of the seedling-pushing shifting-yoke are: The coordinates of point H on the seeding-pushing plate on the same plane as the seedling needle are:

Kinematic modeling of the cam mechanism
The design of the cam has always been the greatest challenge of the transfer mechanism. The cam pressure angle is too large, which will cause a self-locking phenomenon, but the angle of the cam lift section cannot be too large, and the difficulty of matching the two cam contour lines is also a design difficulty. As shown in Figure 5, the cam has two layers of profiles, the seedling-taking profile and the seedling-pushing profile. The seedling removal stage proceeds as follows: start to take the seedlings at point g, stop the movement of the seedling-taking shifting-yoke at point h, and reach the limit position, at which point the cam angle should be less than 12° in the seedling removal phase. The clamping phase is in the 'he' phase of the cam seedling taking profile. The seedling-pushing phase proceeds as follows: start pushing the seedlings at point b, start to move the seedling-pushing shifting-yoke, and finish pushing the seedlings at point a. The cam angle should be less than 13° in the stage of pushing seedlings. When the seedling-pushing shifting-yoke reaches point b of the cam seedling-pushing profile, the seedling-taking shifting-yoke is also moving, and the seedling needles are slowly retracted. Under the combined action of the two, the pot seedlings fall approximately vertically into the soil hole. The recovery stage proceeds as follows: the seedling-pushing board slowly returns to its original position, the seedling needle is slowly retracted, and the spring is compressed, corresponding to the ad stage of the cam seedling-pushing profile and the ef stage of the cam seedling taking-profile ', such that the seedling-pushing board will not interfere with the seedling tray, the seedling needle is completely retracted, and the design requirements are met. As shown in Figure 6, the state of the seedling-taking shifting-yoke and the seedling-pushing shifting-yoke occurs in two extreme positions. When the distance between the top of the seedling-taking shifting-yoke and the seedling-pushing shifting-yoke in the extreme position is the shortest, it is in a state of holding the soil bowl. When the distance between the top of the seedling-pushing shifting-yoke and the top of the seedling-taking shifting-yoke is the longest, it is the state after the bowl is pushed. Knowing the coordinates of points Q, G, S, N, D, and C, the minor radius of the cam R1=14 mm, and the length and included angle of the upper and lower sections of the seedling-taking shifting-yoke and seedling-pushing shifting-yoke are taken. To obtain the size of the major diameter of the cam, a rectangular coordinate system is established with the center of the cam circle as the origin. Point J is the contact point of the small diameter of the seedling-taking shifting-yoke and the seedling-taking-profile cam, and point L is the contact point of the major diameter of the seedling-taking shifting-yoke and the seedling-taking-profile cam. Point K is the contact point of the small diameter of the seedling-pushing shifting-yoke and the seedling-pushing profile cam, and point P is the contact point of the large diameter of the seedling-pushing shifting-yoke and the seedling-pushing profile cam. Through geometric relationships [23] , (xp, yp) and R3 can be obtained simultaneously: According to formulas (21) ~ (23), R2 can be obtained in the same way: where: R2--The large-diameter radius of the profile cam of seedling pushing, mm R3--The large-diameter radius of the profile cam of seedling taking, mm

Design of the pressure angle of the cam mechanism
The acute angle between the direction of the rotational speed of the shift fork around the shift fork shaft and the direction of the positive pressure F received by the shift fork is the pressure angle α, and the pressure angle is less than 45° as required [24] . According to the reversal method, the cam rotation center O is the center of the circle, and OC is the radius to draw a circle. This circle is the trajectory circle of the swing center in the reversal motion. With CL as the radius, a point on the cam contour line's lift section is the center of the arc, and the intersection point with the trajectory circle Point C1 and points C2, D1, and D2 are the same. The schematic diagram is shown in Figure 7. The force analysis of taking the bowl fork as the research object is: where: Under the same other conditions, when η is greater than 90°, the greater the pressu re angle is, the smaller the denominator, and the greater the force F. If it is so large that the denominator in the formula is zero, F will increase to infinity, and the mechanism will self-lock. The pressure angles (α1, α2, α3, α4) of the cam lift section are measured, and it can be concluded that these pressure angles are all less than the maximum pressure angle of 45°. To meet this condition, the lift section of the contour line of the seedling-taking-profile cam is divided into two sections, as shown in Figure  6. The dividing point is at point k, and the slope of the second section is smaller than that of the first section; the lift section of the contour line of the seedling pushing profile cam is also divided into two sections. The dividing point is at point c, and the slope of the second section is smaller than that of the first section.
According to the agronomic requireme nts of potted strawberry seedling transplant ing, the movement interference, angle chan ge, and trajectory shape of the transplantin g mechanism involve 7 optimization goals: ① The seedling taking angle is between 310° and 320°② The angle of seedling pu shing is between 260° and 280° to ensure the erect nature of the seedlings. The angle difference between seedling taking a nd seedling pushing is 40°. The distanc e between the gearbox and the seedling fe eding point is greater than 0 to avoid inte rference between the gearbox body and the planting mechanism. ⑤The track height i s greater than 260 mm. When seedlings are taken, the swing angle of the planting arm is 0°~5° to avoid interference betwee n the gearbox body and the planting mech anism. The two planting arms do not int erfere to avoid collision between the two planting arms during seedling retrieval.

Optimization design software
The gear pitch curve parameters includ e φ1=0°, φ2=48.9°, φ3=107.1°, φ4=230.1°, φ5=268.6°, φ6=360°, r1=24.1 mm=r6, r2=29. 7 mm, r3=20.2 mm, r4=22.3 mm, and r5=2 2 mm. The structural parameters include φ H0=149°, θ0=-68°, δ0=-56°, xg=245 mm, yg= 110 mm, γ=55°, H1=144 mm, and S= 168 mm, as shown in Figure 8. The transmission ratio curve correspond ing to the transplanting mechanism under th ese parameters is shown in Figure 9. As the rotational angle of the planet carrier change s, the transmission ratio curve between the gears presents a complicated changing trend, with multiple crests and troughs appearing at the same time. Looking at the transmissio n ratio curves under this set of parameters, t he transplanting mechanism conforms to the unequal speed transmission law required fo r potted seedling transplanting [17] . According to the optimized structural parameters, the virtual design of the mechanism is completed, and motion simulation is carried out. In a working cycle (the planet carrier rotates 360° from the initial position), when the planet carrier rotates 89°, the seedling starts to be pushed, and the seedling needles begin to retract. When the planet carrier rotates through 102°, the potted seedling is pushed out under the combined action of the seedling-pushing board protruding out and the seedling needle retracting. When the planet carrier rotates 211°, the seedling-pushing board retracts to the initial position. The seedlings are taken when the planet carrier rotates to 257°. Figure 10 (a) is the Visual Basic optim ized relative trajectory, and (b) is the Visual Basic optimized absolute trajectory. Figure  11(a) shows the simulated relative motion tr ajectory, and Figure (b) shows the simulated absolute motion trajectory. The optimized a bsolute trajectory and the relative trajectory are basically similar to the simulated traject ory, and the swing angle of the planting ar m in the relative trajectory is small. When t he absolute trajectory pushes the seedlings i n the vertical direction, the uprightness of t he seedlings is guaranteed to be met upon r equest, and the next step of prototype manu facturing can be carried out. As shown in Figure 12, the solid line is the movement of the seedling-pushing board relative to the end shell, the movement stroke is 20 mm, and the left side of the wave crest is steeper in one cycle, which means that the spring is released and the seedling-pushing board moves quickly, and the right side of the wave crest is relatively smooth. This represents the slow compression of the spring, where the seedling-pushing board slowly retracts and shows the next cycle of movement. The dotted line is the movement curve of the seedling needle relative to the end shell. The movement stroke is 40 mm, the left side of the wave crest is relatively smooth, the right side of the wave crest is relatively steep, and there is a short stay in the middle of the wave crest. One cycle of movement will not cause interference. It can be seen from the figure that in the process of pushing the seedlings, the seedling-taking shifting-yoke and the seedling-pushing shifting-yoke move together to push the seedlings quickly. The rightmost point of each wave crest on the dotted line is on the right side of the point where the solid line is flat, which means that the seedling-pushing board is fully retracted before the next cycle of operations will be carried out, and the seedling-pushing board will not interfere with the removal of the potted seedlings.

High-speed photography bench test
Using 3D printed molding technology, the material is PLA [25] , which completes the physical prototype assembly. To verify the actual work trajectory of the organization, a high-speed camera was used on the platform to capture multiple key position states, as shown in Figure  The seedling needles are retracted first, and then the planet carrier is rotated through an angle. The seedling-pushing board is fully retracted, the planet carrier is rotated another angle to start taking seedlings, and the seedling needles quickly protrude without interference, which meets the design requirements. The trajectory of the seedling needle point is shown in Figure 14.

Prototype soil tank test
The mass ratio of the original soil to th e substrate is 0.4:1, the seedling tray has 72 holes, the soil depth in the soil trough is 1 20 mm, and the dimensions of the pot hole are as follows: top 40 mm×40 mm, bottom 15 mm×15 mm, and depth 40 mm. Standard s for planting seedlings are as follows: welldeveloped root system, more than 20 first-le vel roots, short petiole, approximately 15 c m long, 2~3 mm thick, 5~7 mature leaves, new stems more than 0.8 mm thick, seedlin g weight above 20 g, and no diseases or ins ect pests. The bench rotation speed is 40 r/ min, the theoretical seedling speed is 80 pla nts/branch/row, the plant spacing is 200 mm, and the soil trough is moved at a speed of 0.27 m/s. As shown in Figure 15, the exist ing benches of the research group are used for experiments [26] . According to the JB/T 1 0291-2013 Dryland Planting Machinery Indu stry Standard issued by the Ministry of Indu stry and Information Technology of the Peo ple's Republic of China.After processing th e test data, the success rate of seedling retri eval was 91.2%, and the rate of excellent pl anting was 82.8%. The results proved that t he technology can better meet the planting r equirements. Fig. 15 Planting bench test with seedlings

Acknowledgments
(1) According to the agronomic requir ements of strawberry transplanting, an inte grated seedling planting and seedling trans planting mechanism for mechanized transpl anting of potted strawberry seedlings is pr oposed, which can quickly reach out and e xtract the seedlings in a "waist"-shaped tra ck and quickly push out the seedlings to f orm a "one horizon line"-shaped trajectory. A set of mechanisms completes the three actions of seedling retrieval, transportation and planting in sequence. The working pr inciple of the mechanism is analyzed, and a mechanistic kinematics model is establish ed.
(2) The optimized design software of the strawberry seedling taking and seedling planting integrated transplanting mechanis m is compiled, and computation is used to obtain a set of mechanism parameters an d motion trajectories that meet the design requirements: the initial installation angle o f the planet carrier is 149°, and the corner of the planet carrier is -68°. The initial i nstallation angle of the planting arm is -5 6°.
(3) Through virtual prototype simulati on and high-speed photography experiment s, the simulated trajectory and actual motio n trajectory of the transplanting mechanism are obtained. A comparative analysis sho ws that the theoretical trajectory, the simul ated trajectory and the actual motion trajec tory are basically the same, thus verifying the bowl-based integrated seedling taking a nd seedling planting device. The correctnes s and feasibility of the planting mechanism design are confirmed. (4) In the prototype planting test, the success rate of seedling extraction was 91. 2%, the seedling extraction efficiency was 80 plants/min, and the excellent planting r ate was 82.8%, which satisfies the require ments of erection and transplanting and ve rifies the practicability of the mechanism. Figure 1 Trajectory of the integrated transplanting mechanism Working principle diagram of the seedling planting mechanism Schematic diagram of the end effector for seedling planting Figure 5 Schematic diagram of the double-pro le cam  Reversal method to nd the cam pressure angle Transmission ratio relationship between gears   The relationship between relative movement stroke and time of the pushing bowl and seedling needle Figure 13 Each key position  Planting bench test with seedlings