## 3 Interference Automatic Recognition and Tamping Path Planning  
### Interference Criticality Solving and Interference Automatic-Recognition Method  
The SBHS tamping device is a two-degree-of-freedom structure [21], a rotating pair between the base and tamping device, and a moving pair between the primary and secondary tamping devices. A coordinate system was established to obtain the transformation relationship between the tamping device's head coordinates, tamping angle, and tamping path, as shown in Figure 4.  
In Figure 4, BC and DC represent the bottom and rear boundaries of the perforated bottom discharge scraper conveyor, respectively; EM is the centerline of the dumping port of the perforated bottom discharge scraper conveyor [22; 23]: \(L_{0}\) is the unextruded length of the tamping device, mm; \(L\) is the tapping path, mm; \(q_{1}\) is the tamping angle, \({}^{\circ}\): \(A(x,y)\) is the tamping head path function; \(x\) is the abscissa of the tamping head; \(y\) is the ordinate of the tamping head.  
The kinematic equation establishment of the tamping device is as follows:  
\[\left\{\begin{array}{l}x=L\cdot\cos(q_{1})\\ y=L\cdot\sin(q_{1})\\ L=L+L_{0}\end{array}\right. \tag{1}\]  
It is evident that to prevent any dumping interference in the dumping process, the tamping head coordinate must be positioned to the left of the EM straight-line portion before commencing the dumping. Therefore, the left side of the EM straight-line portion can be defined as the dumping non-interference area.  
Similarly, during the execution of the tamping process, to prevent the collision interference between the tamping device and the bottom of the perforated bottom discharge scraper conveyor when the tamping device extends, it is only necessary to ensure that the tamping head coordinate is beneath the BC straight-line portion. When retracting the tamping device, it is necessary to ensure that the tamping head ordinate is smaller than the BC straight-line ordinate to avoid collision interference between the tamping device and the rear side of the multi-space perforated bottom discharge scraper conveyor, especially when the tamping head abscissa is higher than or close to the CD straight-line abscissa. For this reason, the area where the BC straight line rotates around point C to CD can be defined as the tamping non-interference area. Based on the abovementioned principles, an SIB process interference automatic recognition and regulation algorithm was designed, as shown in Figure 5.  
Figure 4: Interference critical analysis.  
In Figure 5, \(L\) is the tamping path, mm; q is the tapping angle, \({}^{\circ}\): \(Y_{A}\) is the ordinate value of the tamping head: \(X_{A}\) is the abscissa value of the tamping head; \(Y_{IBC}\) is the ordinate value of the BC straight-line portion; \(X_{IDC}\) is the abscissa value of the straight-line DC: \(X_{IEM}\) is the abscissa value of the EM straight-line portion; \(\Delta\)q is the increment of the cyclic tamping angle adjustment, \({}^{\circ}\): \(L_{max}\) is the maximum tamping path, mm; \(n_{max}\) is the maximum number of cycles required for user-defined and designed tamping processes; and \(q_{i}\) is the tamping angle of the \(i\)-th tamping. \({}^{\circ}\).  
The left part of Figure 5 displays the automatic recognition and regulation algorithm of the dumping process, while the right part shows the automatic recognition and regulation algorithm of the tamping process. In the SIB process, the dumping and tamping processes form a loop.  
In addition, it is necessary to calculate the conversion relationship between the tamping head coordinate \(\mathbf{A}\)(x,y), tamping angle q\({}_{1}\), and tamping path \(L\) for the tamping device, which mainly involves a swing angle cylinder and tamping cylinder, and where the driving parameters are the tamping angle and tamping path, as shown below:  
\[\left\{\begin{array}{l}q_{1}=-2\cdot\arctan\left(\frac{x-\sqrt{x^{2}+y^{2} }}{y}\right)\\ L_{0}=\sqrt{x^{2}+y^{2}}-L\end{array}\right. \tag{2}\]