**4. Analysis of the Working Process and the Selection of Key Parameters**

### *4.1. Design of Pulling Device*

As shown in Figure 5a,b, the pulling device of the test platform is mainly composed of a reel and a pulling roller. When the pulling device works, the pulling roller is located below the cabbage. Through their own continuous external rotation, the cabbages are subjected to an upward pulling force. After the root of the cabbage is completely separated from the conveying system, it enters the clamping conveying mechanism through the right position of the reel above the pulling roller.

**Figure 5.** The pulling device: (**a**) reel; (**b**) pulling roller.

As shown in Formula (1), the ratio of the linear velocity at the outer edge of the reel to the forward speed of the machine is called the reeling speed ratio *λ*. When *λ* ≤ 1, the cycloid amplitude of the working trajectory of the reel is small, and the function of supporting and guiding the cabbage cannot be realized. As shown in Figure 6, when λ > 1, the working trajectory of the reel is cycloidal. At this time, the reel can work normally, and the reel effect works well.

$$\frac{V\_0}{V\_x} = \lambda \tag{1}$$

where *V*<sup>0</sup> is the speed along the outer line when the wheel is working, m/s, and *Vx* is the conveying speed of cabbage.

**Figure 6.** The movement track of the reel.

The displacement equation for the reel:

$$\mathbf{x} = V\_{\mathbf{x}} + R\_n \cos W\_n \mathbf{t} \tag{2}$$

$$y = H\_n - R\_n \sin \mathcal{W}\_n t \tag{3}$$

where *Rn* is the radius of the reel, mm, and *Wn* is the rotation speed of the reel, r/min. *Hn* is the height from the center of the reel to the ground, mm.

It is assumed that the reel has "m" reel leaves. When a reel leaf rotates one circle, the forward distance of the harvester is:

$$L = V\_{\overline{x}} \frac{60}{mV\_n} \tag{4}$$

where *L* is the forward distance of the harvester, m, and *Vn* is the angular velocity of the reel, rad/s.

When the reel works normally, the size of the reel should meet:

$$\frac{2\pi R\_n}{m\lambda} > D.\tag{5}$$

where *D* is the diameter of the cabbage.

In order to achieve continuous harvesting, the pitch of the long trochoid of the reel should meet:

$$S\_n = \frac{2\pi R\_n}{m\lambda} = \frac{S\_I}{n} \tag{6}$$

where *Sn* is the pitch of the long trochoid of the reel; *Sl* is the distance between two adjacent cabbages; and *n* is the reel leaf spacing, generally taking 1, 2, and 3.

The number of reel leaves on the test platform is 3, the radius of the reel is 240 mm, the distance of cabbage in the conveying system is 350 mm, take 1 for *n*, and the conveying speed of the conveying system is set to be 0.3 m/s. The rotation speed of the reel is set to 30, 50, or 70 r/min, and the trajectory of the reel is simulated by MATLAB-ADAMS. The simulation trajectory is shown in Figure 7.
