01.12.2020  Original Article  Ausgabe 1/2020 Open Access
Automatic Scallion Seedling Feeding Mechanism with an Asymmetrical Highorder Transmission Gear Train
 Zeitschrift:
 Chinese Journal of Mechanical Engineering > Ausgabe 1/2020
1 Introduction
The scallion is an important vegetable with a high economic value. Scallion cultivation has a long history in China. The average annual planting area is about 500000 hm
^{2} at present, so an automated system is necessary. When transplanting scallions, the distance between seedlings is always less than 10 cm. A soft disctype transplanter can better meet the requirements of shortdistance planting [
1].
At present, the seedlings are delivered to the disctype transplanter by a combination of two linkage mechanisms and two band carriers. The structure is complicated and the transplanting is slow because of the disadvantages of the linkage mechanism [
2]. With the growing demand for mechanized agriculture, a new scalliondelivery mechanism is urgently needed.
Anzeige
In transplantingmachinery research, Xin et al. [
3,
4] researched a doublecrank potted riceseedling transplanting mechanism; an “8”shaped trajectory was achieved by optimizing the parameters. Jin et al. [
5] combined this mechanism with a programmable logic controller to investigate an intelligent transplanting mechanism.
Japanese and Korean scholars proposed a slidetype transplanting mechanism [
6] and a double slidetype transplanting mechanism [
7], respectively. The parameters of the slidetransplanting mechanism were optimized by Li et al. [
8] and Ji et al. [
9], thereby improving the mechanism’s transplanting performance. Because of structural limitations, these mechanisms adopt a singletype transplanting arm, so improving the efficiency is difficult.
A noncircular planetary geartrain mechanism can achieve special kinematic regularities, which are widely applied in rice and vegetabletransplanting machines because of the unequal speed transmission [
10]. Zhou et al. [
11] designed a transplanting mechanism with planetary Bézier gears. Li et al. [
12] researched a noncircular–gear computation method, based on the seedling needletip point’s static trajectory in the transplanting mechanism.
Zhao et al. [
13] proposed a reverse design of the Dshaped trajectory for clamping the rice seedlings. To create a special transplanting trajectory with a sharp tip, Zhao et al. designed a seedlingpicking mechanism with two unequalamplitude characteristics [
14]. Yu et al. [
15,
16] proposed a transplanting mechanism with intermittent noncircular gears, based on an intermittent unequalspeed transmission. Ye et al. [
17,
18] studied the kinematics and dynamics of the transmission and applied the mechanism to transplanting rice and vegetable seedlings. Sun et al. [
19] synthesized the geartrain mechanism configuration and investigated a variety of available mechanisms.
Anzeige
A planetary geartrain mechanism has the relative advantages of a simple structure, double transplanting arms that can be arranged conveniently, and high efficiency. In this paper, a new automatic scallionseedling feeding mechanism is proposed, based on an original noncircular planetary geartrain mechanism, to realize the special requirements of automatic scallionseedling feeding.
Nowadays, most noncircular planetary geartrain mechanisms have singleorder noncircular gear trains; i.e., while the planetary carrier rotates one round, the execution component rotates one round, relative to the planetary carrier. When the execution component is collinear with the planetary carrier, its terminal point will be located at the farthest or nearest location that the mechanism can reach; this happens twice in one movement cycle [
20]. Taking the rotation axis of the planetary carrier as the center, an annulus field can be defined by the farthest and nearest locations. The annulus is the mechanism’s trajectory space.
A common design goal of singleorder noncircular planetary geartrain transplanting mechanisms is to vertically push or plant a seedling. Thus, the rotation angle of the execution component should be 55°–60°. However, for automatic scallion transplanting, the seedlings should be fed horizontally into the soft disctype transplanter. This means the rotation angle of the execution component is at least 145°. Moreover, the displacement from the seedlingclamping position to the seedlingdropping position is larger. A singleorder planetary gear train cannot achieve this requirement.
Junhua Tong designed an automatic boxpicking mechanism with an ellipticcircular–gear highorder planetary gear train; except for the threeorder solar gear, all of the other gears in the mechanism are singleorder gears. The inner cycloid trajectory is formed by the movement of the terminal point of the execution component. During a motion cycle, the terminal point reaches the farthest and nearest locations three times each [
21]. The rotation angle of the execution component can change in the range of 0°–720°.
The maximum displacement of the terminal point of the execution component in space is also greatly increased, compared with a singleorder planetary gear train of the same mechanism size. The number of extreme locations in the trajectory is related to the order of the solar gear in the planetary geartrain mechanism.
The execution component of a highorder planetary gear train rotates in more than one circle, relative to the planetary carrier in one motion cycle. When the execution component rotates in one circle, relative to the planetary carrier, its terminal point passes once through both the farthest and nearest locations. A highorder noncircular planetary geartrain mechanism can reach the farthest and nearest location many times. This characteristic enables the execution component to realize a long displacement and a large rotation angle.
In existing research on highorder noncircular gear transmissions, Lin et al. [
22] designed a highorder elliptical bevelgear pair and a highorder elliptical modified bevelgear pair [
23]. Xu et al. [
24] designed a highorder Fourier noncircular gear. These transmission ratios are completely symmetrical, which means that only one section of the transmission ratio can be designed. The corresponding symmetrical section must match, and, therefore, cannot be changed independently. Moreover, the motion regularity of the execution component is also strictly symmetric, which means it is difficult to flexibly design the kinematic regularities.
This study proposed an asymmetrical highorder transmission and a design method for the asymmetrical transmission ratio of a highorder noncircular gear train. Firstly, the geartrain structure was designed. Secondly, the scallionseedling feeding mechanism of the planetary gear train with an asymmetrical highorder noncircular gear was optimized to realize the large rotation and long displacement of the execution component. Finally, the design correctness was verified through motion simulations and a prototype experiment.
2 Design of the Asymmetrical HighOrder Noncircular Gear Train
2.1 Structure and Working Principle
The structural model of the asymmetrical twoorder noncircular gear train is shown in Figure
1. Taking this model as an example, the asymmetrical highorder noncircular gear train is illustrated.
×
Figure
2 shows that both the first driving gear (1) and the second driving gear (2) are incomplete noncircular gear pieces that form a combined driving gear. The sum of the center angle of the pitch curve, corresponding to the driving gear profile of the two active wheels (i.e., the sum of
Ψ
_{1} and
Ψ
_{2} in Figure
2), is 360°. The first driven gear (3) and the second driven gear (4) are both noncircular gears that are fixed onto the same shaft. The first driving gear (1) and the first driven gear (3) are a conjugated transmission, and the second driving gear (2) and the second driven gear (4) are a conjugated transmission.
×
The working principle of the asymmetrical highorder noncircular gear train is as follows. In a movement cycle, when the driving gear rotates in a clockwise direction, the first driving gear and the first driven gear engage to work, as shown in Figure
3a. While the first driven gear rotates around, all of the teeth of the first driving gear participate in the movement transmission; the total rotational angle is
Ψ
_{1}, as shown in Figure
3b. Meanwhile, the second driving gear (2) and the second driven gear (4) engage to work, as shown in Figure
3c. While the second driven gear rotates 360°, all of the teeth of the second driving gear rotate
Ψ
_{2}, as shown in Figure
3d.
×
During one rotation cycle of the driving gears, the driven gears rotate two rounds, which means the gear train has the transmission characteristic of a highorder gear train. On the other hand, both the driving gear and the driven gear are noncircular gears with an asymmetrical pitch curve. Thus, the gear train also has the asymmetrical transmission characteristic of a noncircular gear train.
The change of the geartrain structure is also regular when the geartrain order changes. For example, in an asymmetricaltransmission
norder noncircular gear train, the driving gears are composed of
n incomplete noncircular gears, and the number of driven gears is consistent with the driving gears.
2.2 Design of the AsymmetricalTransmission Highorder Noncircular Gear Train
Figure
4 illustrates the rotationangle curves of the different gear trains. The thick line is the transmission ratio of the asymmetrical secondorder gear train. The thin line is the transmission ratio of the symmetrical secondorder gear train, which consists of a secondorder noncircular driving gear and a singleorder noncircular driven gear. Regardless of the type of gear train, when the driving gears rotate 360°, the driven gears rotate 720°, which means they all have highorder transmission characteristics.
×
The angle curve of the symmetrical transmission secondorder gear train undergoes two identical periodic changes in one motion cycle; the same characteristic appears on the transmissionratio curve in Figure
5. The thin line is the transmissionratio curve of the symmetricaltransmission secondorder gear train; it also undergoes two identical periodic changes in one transmission cycle. If the Cartesian coordinate system was transformed into a polar coordinate system, the symmetry of the transmission ratio would be more obvious.
×
The gearpitch curve of the gear train can be calculated according to Eqs. (
1)–(
3), where
a is the center distance between the two gears. The gearpitch curves are shown in Figure
6.
$$r_{1} (\alpha ) = \frac{a}{1 + i},$$
(1)
$$r_{2} = a  r_{1} (\alpha ) = \frac{ai}{1 + i},$$
(2)
$$\beta = \int_{0}^{\alpha } {\frac{1}{i}{\text{d}}\alpha } .$$
(3)
×
Neither the rotationangle curve nor the transmissionratio curve (the thick line shown in Figure
5) of the asymmetrical transmission secondorder gear train shows the symmetry characteristic. Moreover, it is not possible to directly calculate the gearpitch curves by using the equations mentioned above. To obtain the gearpitch curve, the transmissionratio curve of the asymmetricaltransmission secondorder noncircular gear train must be processed as follows:
1)
where
α
_{1} is the abscissa of point
P
_{1} and
α
_{2} is the abscissa of point
P
_{2}. The transmissionratio curve between the two points can be used to calculate one pair of gearpitch curves, and the pitch curve of the driven gear must be closed. The rest of the transmissionratio curve, outside the two division points, must satisfy Eq. (
5). Thus, the second pair of gearpitch curves can be calculated:
Two points,
P
_{1} and
P
_{2}, should be selected on the transmissionratio curve to divide the curve into three parts, as shown by the thin line in Figure
7. The ordinates of the two points are equal, which means the values of the transmission ratio
i of the two points are equal. To ensure the closure of the driven gear’s pitch curve, the abscissas of the two points should satisfy Eq. (
4):
×
$$\Delta \beta = \int_{{\alpha_{1} }}^{{\alpha_{2} }} {\frac{1}{i}\,} {\text{d}}\alpha = 360^\circ ,$$
(4)
$$\Delta \beta_{1} + \Delta \beta_{2} = \int_{0}^{{\alpha_{1} }} {\frac{1}{i}\,} {\text{d}}\alpha + \int_{{\alpha_{2} }}^{360} {\frac{1}{i}} \,{\text{d}}\alpha = 720^\circ  \int_{{\alpha_{1} }}^{{\alpha_{2} }} {\frac{1}{i}} \,{\text{d}}\alpha = 360^\circ .$$
(5)
2)
In Figure
7, points
P
_{1} and
P
_{2} divide the original transmissionratio curve into three parts; Part 1 is moved to the end to form a new transmission ratio, shown by the thick line in the same figure. Part I of the new transmissionratio curve is Part 2 of the original transmissionratio curve. Part II is formed by the combination of Part 1 and Part 2.
The gearpitch curves can be designed separately using the two parts of the new transmissionratio curve, according to Eqs. (
1)–(
3). As shown in Figure
8, the thick lines are the pitch curve of the first driving gear and the first driven gear; the thin lines are the pitch curves of the second driving gear and the second driven gear, as shown in the thick line segment of Figure
7. The second part corresponds to the second pair of main drivenwheel gearpitch curve groups, shown in the thin line segment in Figure
7.
×
The design of the highorder gear train obeys the same rule: The asymmetricaltransmission highorder gear train consists of
n pairs of driving and driven gears; thus,
n points must be found, using the same principle to divide the transmissionratio curve. After that, the transmissionratio curve should be recombined to design the gearpitch curves.
3 Kinematic Analysis of the ScallionSeedling Feeding Mechanism
The automatic scallionseedling feeding mechanism cooperates with the soft disctype transplanter. The working process follows: The seedlingclamping manipulator of the automatic scallionseedling feeding mechanism removes the scallion seedlings from the seedling tray and transports them to the flexible disc planter; then, the flexible disc planter plants them into the soil.
As shown in Figure
9, the angle between the seedling box and the horizontal plane is 60°, so at the seedlingfeeding position, the rotation angle of the execution component (seedlingclamping component) should be 150°. At the seedlingfeeding position, the scallion seedlings are horizontally fed into the soft disctype transplanter. The work trajectory was designed to look like the Arabic number “8” as shown in Figure
9.
×
The asymmetricaltransmission secondorder noncircular gear train was used to design the scallionseedling feeding mechanism. The terminal point of the seedling clamp reaches the farthest location twice; these can be designed as the seedlingclamping position and the seedlingfeeding position. Because of the characteristics of the asymmetric transmission, the design flexibility of the seedlingclamping component will be greater, to meet the long displacement and large rotationangle requirements of the scallionseedling feeding function.
4 Optimal Parameter Design for the ScallionSeedling Feeding Mechanism
The special 8shaped trajectory required by the scallionseedling feeding mechanism should meet the requirements of the displacement and the precise posture at some critical position. The asymmetric transmission ratio is critical for the mechanism parameter design. The optimal design of the scallionseedling feeding mechanism is realized using a method based on precise poses and trajectory control.
4.1 Mechanism ParameterSolving Model
The precise pose point is defined by a pair of rectangular coordinates and an angle, which shall be the critical position on the trajectory; e.g., the seedlingclamping position or the seedlingfeeding position. The parametersolving model is established in two steps:
Step 1: The planetary geartrain scallionseedling feeding mechanism is considered as a combination of the bargroup and the gear train. The rigidlink guidance theory is used to calculate the mechanism parameter, so as to obtain the transmission ratio of the planetary gear train [
25,
26]. Firstly, three precise positions
P
_{i} (
x
_{i},
y
_{i}) and postures
θ
_{i} (
i = 1, 2, 3) are given. As shown in Figure
10, the mechanism was simplified into a bargroup model and its motion was analyzed.
×
Eq. (
6) describes the three precise pose conditions
P
_{i} (
x
_{i},
y
_{i}) and
θ
_{i}. Among the equations,
\(\theta_{1i} = \theta_{i}  \theta_{1}\) is the rotation angle of the seedlingclamping manipulator when its end point moves from
P
_{1} to
P
_{i}. Eq. (
6) is used to calculate Eq. (
7) and obtain Eq. (
8):
$$\left\{ \begin{aligned} D_{11i} & = \cos \theta_{1i} , \\ D_{12i} & =  \sin \theta_{1i} , \\ D_{13i} & = x_{i}  x_{1} \cos \theta_{1i} + y_{1} \sin \theta_{1i} , \\ D_{21i} & = \sin \theta_{1i} , \\ D_{22i} & = \cos \theta_{1i} , \\ D_{23i} & = y_{i}  x_{1} \sin \theta_{1i}  y_{1} \cos \theta_{1i} , \\ D_{31i} & = 0, \\ D_{32i} & = 0, \\ D_{33i} & = 1, \\ \end{aligned} \right.$$
(6)
$$\left\{ \begin{aligned} A_{i1} & = 1  D_{11i} , \\ A_{i2} & = D_{12i} , \\ A_{i3} & =  D_{13i} , \\ A_{i4} & =  D_{23i} , \\ A_{i5} & = D_{11i} D_{13i} + D_{21i} D_{23i} , \\ A_{i6} & = D_{12i} D_{13i} + D_{22i} D_{23i} , \\ A_{i7} & = (D_{13i}^{2} + D_{23i}^{2} )/2, \\ \end{aligned} \right.$$
(7)
$$\left\{ \begin{aligned} G_{20} & = A_{21} x_{0} + A_{22} y_{0} + A_{25} , \\ K_{20} & = A_{21} y_{0}  A_{22} x_{0} + A_{26} , \\ N_{20} & = A_{23} x_{0}  A_{24} y_{0} + A_{27} , \\ G_{30} & = A_{31} x_{0} + A_{32} y_{0} + A_{35} , \\ K_{30} & = A_{31} y_{0}  A_{32} x_{0} + A_{36} , \\ N_{30} & = A_{33} x_{0} + A_{34} y_{0} + A_{37} . \\ \end{aligned} \right.$$
(8)
In Eq. (
8),
x
_{0} and
y
_{0} are the coordinate values of the fixed hinge point
A
_{0}. Eq. (
8) is used to calculate Eq. (
9), where
r is the length of the planetary carrier. Then, the solution curve of the fixed hinge point
A
_{0} can be calculated. The solution curve of the moving hinge point
A
_{c1} (
x
_{c1},
y
_{c1}) can be calculated using Eq. (
10):
$$\begin{aligned} & [N_{20} K _{30}  N_{30} K _{20}  x_{0} (G _{30} K_{20}  G_{20} K_{30} )]^{2} \\ & + [N_{20} G _{30}  N_{30} G _{20}  y_{0} (G _{20} K_{30}  G_{30} K_{20} )]^{2} \\ & = r^{2} (G_{20} K_{30}  G_{30} K_{20} )^{2} , \\ \end{aligned}$$
(9)
$$\left\{ \begin{aligned} x_{c1} = \frac{{N_{20} K_{30}  N_{30} K_{20} }}{{G_{30} K_{20}  G_{20} K_{30} }}, \hfill \\ y_{c1} = \frac{{N_{20} G_{30}  N_{30} G_{20} }}{{G_{20} K_{30}  G_{30} K_{20} }}. \hfill \\ \end{aligned} \right.$$
(10)
The parametersolution domain of the scallionseedling feeding mechanism can be obtained by Eq. (
11).
l is the length of the seedlingclamping manipulator,
φ
_{21} is the initial angle between the manipulator and the horizontal plane, and
φ
_{11} is the initial angle between the planetary carrier and the horizontal plane.
$$\left\{ \begin{aligned} & l = \sqrt {(x_{c1}  x_{1} )^{2} + (y_{c1}  y_{1} )^{2} } , \\ & \varphi_{11} = \arctan \left( {\frac{{y_{c1}  y_{0} }}{{x_{c1}  x_{0} }}} \right), \\ & \varphi_{21} = \arctan \left( {\frac{{y_{c1}  y_{1} }}{{x_{c1}  x_{1} }}} \right). \\ \end{aligned} \right.$$
(11)
Step 2: A few precise pose points cannot guarantee that the generated trajectory shape will meet the expectations. Hence, it is necessary to add some trajectoryshape control points to control the shape of the trajectory. As shown in Figure
11,
P
_{i} are the precise pose points, and
E
_{i} are the trajectoryshape control points.
×
Angles
Ф
_{1i} and
Ф
_{2i} of the planetary carrier and the seedlingclamping manipulator, relative to the initial position at each pose point and control point, can be obtained according to Eq. (
12). The relative rotation curve can be obtained by a Bspline curvefitting technique [
27]. After fitting the relationangle curve between the planetary carrier and the seedlingclamping component, the transmission ratio of the planetary gear train can be calculated from Eq. (
13). When the planetary carrier and the seedlingclamping component rotate in the same direction, the sign is negative, and vice versa. The actual generated trajectory can be calculated by Eq. (
14):
$$\left\{ \begin{aligned} & \varPhi_{ri} = \varphi_{ri}  \varphi_{r1} , \\ & \varPhi_{li} = \varphi_{li}  \varphi_{l1} , \\ \end{aligned} \right.$$
(12)
$$i\;{ = }\;\frac{{\text{d}\varPhi_{1} }}{{\text{d}\varPhi_{2} \pm \text{d}\varPhi_{1} }},$$
(13)
$$\left\{ \begin{aligned} & x = x_{0} + r\cos (\varphi_{11} + \varPhi_{1} ) + l\cos (\varphi_{21} + \varPhi_{2} ), \\ & y = y_{0} + r\sin(\varphi_{11} + \varPhi_{1} ) + l\sin(\varphi_{21} + \varPhi_{2} ). \\ \end{aligned} \right.$$
(14)
Compared with the optimal forward and reverse designs of the existing geartrain transplanting mechanism, this method has the advantages of greatly reducing the number of initially required parameters, ensuring the precise pose of the mechanism at important working positions, and obtaining more than one set of mechanism parameters that meets the requirements of the work function. If the bargroup parameter is not satisfactory, a second design can be quickly carried out by changing the trajectoryshape control points.
5 Optimized Design of the Mechanism Parameters
The working requirements of the scallionseedling feeding mechanism were analyzed, and the three precise pose points were determined as shown in Table
1, where
P
_{1} and
P
_{3} are the seedlingclamping position and seedlingfeeding position, respectively.
P
_{2} is the point at the end of the seedlingclamping manipulator, which needs to move 30 to 40 mm in a nearly straight line after clamping the seedlings, to ensure that the seedlings are pulled vertically from the tray to avoid damaging their roots. The parametersolution domain of the mechanism is calculated using the above method, and the solution curves of the two hinge points are shown in Figure
12.
Table 1
Three precise pose points
Pose position
P
_{i}

Coordinates (
x
_{i},
y
_{i}) (mm)

Pose
θ (°)


P
_{1}

(460, 220)

165

P
_{2}

(400, 240)

160

P
_{3}

(205, − 5)

15

×
The trajectory must satisfy the working requirements. The seedlingclamping position and the seedlingfeeding position are the critical working positions of the mechanism. The seedlingclamping component clamps the stem of the scallion seedling at point
P
_{1}, removes it from the seedling box, and then feeds it at point
P
_{3}. According to the above situation, two optimization objectives are set:
1)
Point
P
_{1} should be at the rightmost end of the entire trajectory, or at least within an acceptable distance from there. Considering the size of the seedling box, and to prevent the transplanting claw from entering the box too deeply, the distance from point
P
_{1} to the rightmost point is set not to exceed 5 mm;
2)
P
_{3} should be kept at the lowest position of the entire trajectory, or at least within an acceptable distance from there. Because the transplanting claw must be some distance from the soft disctype transplanter when releasing the seedling, the distance is set not to exceed 10 mm.
As shown in Figure
13, both trajectories pass through the pose points. The expected trajectory and the mechanism parameters must be designed and optimized in combination with the seedlingfeeding operation requirements. Table
2 shows the coordinates of trajectories 1 and 2, which are shown in Figure
12 at critical positions. Trajectory 1 is obviously better than trajectory 2.
Table 2
Spatial coordinates of the two extreme pose points and accurate trajectory pose points
Point

Value (mm)


P
_{1}

(465, 220)

Rightmost point of trajectory 1

(466.3, 218.1)

Rightmost point of trajectory 2

(468.1, 216.3)

P
_{3}

(205, − 5)

Lowest point of trajectory 1

(206, − 6.6)

Lowest point of trajectory 2

(216.2, − 25.9)

×
The optimal mechanism parameters obtained using the above optimization principle are shown in Table
3. To improve the design efficiency, based on the above mathematical model, the mechanism optimization design software was compiled using the GUI module of MATLAB, as shown in Figure
14.
Table 3
Values of each parameter in the optimal solution
Item

Value


Fixed hinge point
A
_{0} (mm)

(355, 217.3)

Moving hinge point
A
_{c1} (mm)

(449.7, 287.6)

Length of planetary carrier
r (mm)

118

Length of seedlingclamping manipulator
l (mm)

148.9

Initial angle of planetary carrier (°)

36.6

Initial angle of seedlingclamping manipulator (°)

19.6

×
With the optimal parameters of the scallionseedling feeding mechanism, the relative rotation curve of the planetary carrier and the seedlingclamping component can be calculated, and then the transmissionratio curve can be calculated. All values are shown in Figure
15.
×
The planetary gear train is divided into two pairs of gear trains. The first stage adopts an asymmetrical highorder noncircular gear pair and the second stage adopts a pair of circular gear pairs with the same parameters. It can be seen from Eq. (
15) that all features of the total gear ratio of the gear train are completely retained in the first stage of the asymmetrical highorder noncircular gear pair.
$$\left\{ \begin{aligned} & i = i_{1} \cdot i_{2} , \\ & i_{1} = i, \\ & i_{2} = 1. \\ \end{aligned} \right.$$
(15)
6 Kinematic Simulation and Verification of the Mechanism
The structure of the scallionseedling feeding mechanism was designed according to the optimal parameters, and the mechanism was modeled and virtually assembled using the Solidworks solidmodeling software. As shown in Figure
16a, the planetary gear train of the scallionseedling feeding mechanism consists of two pairs of gear trains. One is the asymmetricaltransmission secondorder noncircular gear train; the other is a pair of circular gears with the same parameters.
×
The threedimensional model was imported into the ADAMS dynamics simulation software to obtain the trajectory of the end point of the seedlingclamping manipulator. The simulation result is shown in Figure
16b. The trajectory obtained from the virtual simulation was compared with the one obtained from the theoretical calculation, as shown in Figure
16c. Referring to the data of critical working points
P
_{1} and
P
_{3}, as shown in Table
4, it can be seen that the error value between the two at the key working points is very small. The theoretical trajectory is basically consistent with the simulated trajectory, which verifies the correctness of the structural design.
Table 4
Comparison between theoretical and simulated trajectories at key operating points
Item

Theoretical value

Simulated value

Deviation


Position of
P
_{1} (mm)

(465, 220)

(466.5, 218.1)

(1.5, 1.9)

Posture of
P
_{1} (°)

160

161.3

1.3

Position of
P
_{3} (mm)

(205, − 5)

(206, − 6.6)

(1, − 1.6)

Posture of
P
_{3} (°)

15

16.1

1.1

7 Experiment and Result Analysis
The purposes of the experiment are as follows:
1)
Observe whether the mechanism’s posture at each precise pose point is consistent with the theoretical design value;
2)
Observe whether the working trajectory formed by the mechanism conforms to the theoretical design; and
3)
Observe whether the mechanism can realize the complete greenonion–seedling feeding operation.
Threeweekold onion seedlings were selected for the test subjects; they are shown in Figure
17. An experimental platform used for feeding scallion seedlings was set up in the Transplanting Equipment Technology Laboratory, as shown in Figure
18. The experimental platform consisted of the rack, motor, seedling box, and scallionseedling feeding mechanism.
×
×
During the experiment, the trajectory and the poses, when the mechanism passed the given three pose points, were analyzed using highspeed–photography analysis software, as shown in Figure
19.
×
The actual trajectory (Figure
19a) was equal to the theoretical movement trajectory in Figure
16c. A comparison of the trajectories showed that the mechanism could satisfy the trajectory and poses required for the scallionseedling feeding work. After 35 experiments, the feedingmechanism angles at the three precise positions were measured and their average values were obtained.
When comparing the theoretical angle values of the three precise pose points with the average of the actual measured results, as shown in Table
5, the angle errors were all less than 3°, which means the experimental results were within the allowed error range of the mechanism experiment. The causes of the errors were as follows:
Table 5
Theoretical and practical comparison of angle values at the precise pose points
Pose points

Theoretical value (°)

Measurements (°)

Deviation (°)


P
_{1}

165

167.41

2.41

P
_{2}

155

157.43

2.43

P
_{3}

15

17.26

2.26

1)
Error machining the mechanism parts;
2)
Mechanisminstallation error;
3)
Experimentalequipment error.
The results of the scallionseedling feeding experiment are shown in Figure
20. The mechanism can well complete the scallionseedling feeding work.
×
In the experiment, the set feedingsuccess criterion was for the seedlings to be taken out of the seedling box and fed smoothly. A total of 1000 seedlings were tested at a rate of 100 seedlings per minute, and the statistical success rate was 93.4%. The results of the seedlingfeeding experiment shows that the mechanism has high performance.
8 Conclusions
An automatic scallionseedling feeding mechanism with an asymmetricaltransmission highorder noncircular planetary gear train was proposed in this paper to improve the efficiency of automatic scallion transplanting. The conclusions of this study are summarized as follows.
(1)
After analyzing the working trajectory and transmission characteristics of singleorder and highorder planetary geartrain mechanisms, an asymmetrical highorder noncircular gear train structure was proposed. This mechanism was compact and flexible in the kinematic design, and could efficiently feed seedlings.
(2)
To meet the scallionseedling feeding function, a parametersolution model of the asymmetrical transmission secondorder noncircular–gear planetary geartrain mechanism was established. Using a method based on the precise pose points and trajectoryshape control points, optimal mechanism parameters and an asymmetrical transmission ratio that met the seedlingfeeding function were obtained. Kinematic simulations of the mechanism verified the validity and correctness of the design method, which represents a different strategy for an automatic scallionseedling feeding mechanism.
(3)
During the highspeed–photography and seedlingfeeding experiments, the angles of the seedlingclamping manipulator were measured when the mechanism passed each critical working position; the values were 167.41°, 157.43°, and 17.26°. The measured values differed from the theoretical values by 2.41°, 2.43°, and 2.26°, respectively. The efficiency of the proposed mechanism was verified within the allowable error range. This research provided a simple and efficient scheme for an onionseedling feeding device.
Authors’ Contributions
XZ and JC were in charge of the whole trial; JY and MC wrote the manuscript; DL, XZ, MC and JY assisted with sampling and laboratory analyses. All authors read and approved the final manuscript.
Authors’ Information
Xiong Zhao, born in 1982, is currently an associate professor at
Key Laboratory of Zhejiang Transplanting Equipment Technology, Zhejiang SciTech University, China. He received his PhD degree from
Zhejiang SciTech University, China, in 2014. His research interests include mechanism design, noncircular gear transmission and agricultural machinery.
Jun Ye, born in 1989, is currently a PhD candidate at
Zhejiang SciTech University, China. He received his master degree on mechatronics from Zhejiang SciTech University
, China, in 2015.
Mengyan Chu, born in 1993, is currently a master candidate at
Key Laboratory of Zhejiang Transplanting Equipment Technology, Zhejiang SciTech University, China.
Li Dai, born in 1978, is currently an associate professor at
Key Laboratory of Zhejiang Transplanting Equipment Technology, Zhejiang SciTech University, China.
Jianneng Chen, born in 1972, is currently a professor and a PhD candidate supervisor at
Key Laboratory of Zhejiang Transplanting Equipment Technology, Zhejiang SciTech University, China. His main research interests include machine design, noncircular gear transmission and control, agricultural machinery.
Acknowledgements
Not applicable
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
The datasets supporting the conclusions of this article are included within the article.
Funding
Supported by the National Key Research and Development Program of China (Grant No. 2017YFD0700800), National Natural Science Foundation of China (Grant Nos. 51775512, 51975536); Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ20E050003); Basic Public Welfare Technology Application Research Projects of Zhejiang Province (Grant Nos. LGN19E050002, LGN20E050006).
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