*2.3. Analysis of the Principle of Spring-Finger Movement*

The law of motion of the spring-finger roller picker is that the cam disk is not moving, the crank and the spring-finger connection point is fixed on the roller, the roller is rotating around the centre of rotation to drive the spring-finger movement. As shown in Figure 10, a coordinate system is established with the centre of the base circle of the cam mechanism as the origin *O*. The forward direction of the picker is the *X*-axis direction, and the direction perpendicular to the ground is the *Y*-axis direction, and the movement of the spring-finger is analysed.

**Figure 10.** Cam of the spring-finger pickup mechanism: *A* is the crank and spring-finger connection point; *B* is the roller centrepoint; *K* is the spring-finger end point.

The displacement of the *K* point at the end of the spring-finger is shown in Equation (7):

$$\begin{cases} X = V\_t t + R\cos\omega t - L\cos(\omega t + \varphi\_0 + \varphi) + L'\cos(\omega t + \varphi\_0 + \varphi - \gamma) \\\ Y = R\sin\omega t - L\sin(\omega t + \varphi\_0 + \varphi) + L'\sin(\omega t + \varphi\_0 + \varphi - \gamma) \end{cases} \tag{7}$$

where *X* is the horizontal displacement of the end of the spring-finger, m; *Y* is the vertical displacement of the end of the spring-finger, m; *Vt* is the forward velocity, m/s; *L* is the length of the crank, m; *L* is the length of the spring-finger, m; *γ* is the angle between the spring-finger and the crank, rad; *ϕ* is the swing angle of the cam mechanism, rad; *ϕ*<sup>0</sup> is the initial swing angle of the cam mechanism, rad; *t* is the time, s; *R* is the radius of the drum, m; *ω* picks up the speed of the disc, r/min.

Equation (8) for the radius of gyration of the end of the spring-finger *R* is:

$$
\mathbb{R}' = \mathbb{X}^2 + \mathbb{Y}^2 \tag{8}
$$

where *R* is the radius of rotation of the end of the spring-finger, mm.

Without considering the oscillating motion of the spring-finger, the trajectory of the spring-finger is a cycloid, and the shape of the cycloid depends on the size of *λ*. The equation for the shape of the cycloid (9) is:

$$
\lambda = \frac{\mathcal{R}'\omega}{V\_t} \tag{9}
$$

The picking requirements can be met with a value of *λ* ranging from 0.17 to 0.58. Combined with the forward speed of the potato harvesting machinery in the agricultural machinery design manual and references, the forward speed of the picking device is controlled at 0.4 m/s ~ 0.8 m/s. Upon launch, a disc speed of 15~25 r/min was determined to be the best, a finding that laid the foundation for later tests [19,20].
