# Cutting Path Planning Technology of Shearer Based on Virtual Reality
## 3 Kinematics Analysis and Cutting Path Planning Method of Real Shearer
### Kinematics Analysis of Shearer Height-Adjusting and Walking  
While the shearer is working, it performs two main functions; traction speed regulation and drum-height regulation. The analysis of the movement of the shearer is mainly the analysis of the above two functions. The traction motion and the drum-height adjustment motion of coal mining on the horizontal and uneven ground are analyzed as follows:  
* Stationary shearer and the drum lifts  
Setting the expansion speed of the height-adjusting cylinder rod to \(v_{\rm c}\) and the running time to \(t\), the rotation angle of the rocker arm can be calculated as follows:  
\[\alpha=\arccos\left[\frac{r^{2}+a^{2}-(l+v_{\rm c}\cdot t)^{2}}{2 ra}\right]- \arccos\left[\frac{r^{2}+a^{2}-l^{2}}{2 ra}\right]. \tag{1}\]  
The rotation angle of the height-adjusting cylinder is given by:  
\[\gamma=\arccos\left[\frac{l^{2}+a^{2}-r^{2}}{2 ra}\right]-\arccos\left[\frac{(l +v_{\rm c}\cdot t)^{2}+a^{2}-r^{2}}{2(l+v_{\rm c}\cdot t)a}\right]. \tag{2}\]  
The tangential velocity of the drum at any time is:  
\[v_{\rm\tau}=v_{\rm c}\cdot\sin\!\left[arc\sin\left(\frac{r^{2}+(l+v_{\rm c} \cdot t)^{2}-a^{2}}{2\cdot r(l+v_{\rm c}\cdot t)}\right)\right], \tag{3}\]  
where \(r\) and \(p\) are the lengths of the short and the long arms (values are 543 and 1962 mm), respectively; \(a\) is the distance between the joint of the cylinder body and the fuselage and the joint of rocker arm and fuselage, its value is 1303 mm; \(l\) is the total initial length of the cylinder rod and the cylinder body,  
Figure 2: Height-adjusting system of the drum shearer. its value is 1701 mm. It can be observed that the expansion speed of the cylinder and the rotation angle of the rocker arm have a non-linear relationship. * Shearer walks on the flat floor and the drum lifts  
Under this condition, the rotation angle of the shearer rocker arm and that of the cylinder remain unchanged. The horizontal velocity of the shearer drum is expressed thus:  
\[v_{\mathrm{h1}}=-v_{\mathrm{c}}\times\sin\!\left[\cos^{-1}\!\left(\frac{r^{2}+ \left(l+v_{\mathrm{c}}\!\cdot\!t\right)^{2}-a^{2}}{2r(l+v_{\mathrm{c}}\!\cdot\!t )}\right)\right]\times\frac{p}{r}\times\sin(0.0872+\alpha)+v_{\mathrm{s}}. \tag{4}\]  
The vertical velocity of the shearer drum is:  
\[v_{\mathrm{v1}}=v_{\mathrm{c}}\times\sin\!\left[\cos^{-1}\!\left(\frac{r^{2}+ \left(l+v_{\mathrm{c}}\!\cdot\!t\right)^{2}-a^{2}}{2r(l+v_{\mathrm{c}}\!\cdot\!t )}\right)\right]\times\frac{p}{r}\times\cos(0.0872+\alpha). \tag{5}\]  
The angle between the direction of the drum movement and the horizontal direction is:  
\[\theta_{1}=\tan^{-1}\!\left(\frac{v_{\mathrm{v1}}}{v_{\mathrm{h1}}}\right), \tag{6}\]  
where the angle (in rad) between rocker arm and fuselage of shearer at initial state is 0.0872, \(v_{\mathrm{s}}\) is the traction speed (in mm/s) of the shearer. * Shearer walks on the unflat floor and the drum lifts The horizontal velocity of the shearer drum is given by: \[v_{\mathrm{h}}=v_{\mathrm{h1}}\times\cos\beta-v_{\mathrm{v1}}\times\sin\beta.\] (7) The vertical velocity of the shearer drum is: \[v_{\mathrm{v}}=v_{\mathrm{h1}}\times\sin\beta+v_{\mathrm{v1}}\times\cos\beta.\] (8)  
The angle between the direction of the drum movement and the horizontal direction is:  
\[\theta=\tan^{-1}\!\left(\frac{v_{\mathrm{v}}}{v_{\mathrm{h}}}\right), \tag{9}\]  
where \(\beta\) is the inclination angle (in rad) of shearer fuselage. * Joint analysis of shearer traction speed, cylinder expansion speed, and direction of drum movement Set the simplified expansion speed of the height-adjusting cylinder to \(v_{\mathrm{c}}=5\) mm/s and the range of traction speed of the shearer to 0-12.9 m/min (0-215 mm/s). In the process of lifting the drum from the horizontal floor, the image of the angle between the direction of the drum movement and the horizontal is as shown in Figure 3 (the upward direction is the positive direction).