2.2.4. Cam Slides

According to the working principle of the picking device, the shape of the cam chute constrains the rotation pattern and attitude of the picking spring-finger during the picking process and is a decisive factor in picking quality. According to the theory of the "reversed pendulum follower disc cam mechanism" by Sheng Kai et al., the design of the cam chute centreline should correspond to the initial position and attitude of the picking spring-finger and the law of motion during the four picking stages [17,18]. The design is based on the polynomial law of motion of the cam slide curve, and a sketch of the picking mechanism based on this design method is shown in Figure 8.

**Figure 8.** Sketch of the centreline analysis of the cam slide of the poppet pickup mechanism.

Based on the mechanism parameters, a sketch of the pop-up roller pickup mechanism was created in Auto CAD using a graphical method to obtain the phase angles *β*<sup>1</sup> = 78.36◦, *β*<sup>2</sup> = 89.15◦, *β*<sup>3</sup> = 115.93◦, and *β*<sup>4</sup> = 68.10◦ for the four stations.

As a result of the above analysis, it can be concluded that the cam slide centreline is composed of multiple circular sliding curves. The mathematical model of the cam slide centreline for each stage is established as follows.

(1) Pickup stage cam chute centreline model.

Curve segment -*AB* trajectory Equation (3):

$$\begin{cases} X = R\_1 \cos \beta \\ Y = R\_1 \sin \beta \end{cases} \tag{3}$$

where *<sup>R</sup>*<sup>1</sup> is the - *AB* radius, mm; *β* is the angle of the circle corresponding to the centreline of the cam slide, rad.

(2) Model of the centreline of the cam slipway during the lift stage.

Curve segment -*BC* trajectory Equation (4):

$$\begin{cases} X = R\_2 \cos \beta\_{BC} - X\_{O\_2} \\ \text{ } Y = R\_2 \sin \beta\_{BC} - Y\_{O\_2} \end{cases} \tag{4}$$

where *<sup>R</sup>*<sup>2</sup> is the - *BC* radius, mm; *<sup>β</sup>BC* is the angle of circularity of - *BC*, rad; *XO*<sup>2</sup> is the value of the *X*-axis coordinates of point *O*2, mm; *YO*<sup>2</sup> is the value of the *Y*-axis coordinates of point *O*2, mm.

(3) Model of the centreline of the cam slipway during the pushing stage.

Curve segment -*CD* trajectory Equation (5):

$$\begin{cases} X = R\_3 \cos \beta\_{CD} + X\_{O\_3} \\ \text{ } Y = R\_3 \sin \beta\_{CD} + Y\_{O\_3} \end{cases} \tag{5}$$

where *<sup>R</sup>*<sup>3</sup> is the - *CD* radius, mm; *<sup>β</sup>CD* is the angle of circularity of - *CD*, rad; *XO*<sup>3</sup> is the value of the *X*-axis coordinates of point *O*3, mm; *YO*<sup>3</sup> is the value of the *Y*-axis coordinates of point *O*3, mm.

(4) Model of the centreline of the cam slipway during the quick-return stage:

Curve segment - *DA* trajectory Equation (6):

$$\begin{cases} X = R\_4 \cos \beta\_{DA} - X\_{O\_4} \\ \text{ } Y = R\_4 \sin \beta\_{DA} + Y\_{O\_4} \end{cases} \tag{6}$$

where *<sup>R</sup>*<sup>4</sup> is the - *DA* radius, mm; *<sup>β</sup>DA* is the angle of circularity of - *DA*, rad; *XO*<sup>4</sup> is the value of the *X*-axis coordinates of point *O*4, mm; *YO*<sup>4</sup> is the value of the *Y*-axis coordinates of point *O*4, mm.

The final schematic diagram of the cam slide structure is shown in Figure 9.

**Figure 9.** Schematic diagram of the cam slipway structure.
