# Cutting Path Planning Technology of Shearer Based on Virtual Reality
## 3 Kinematics Analysis and Cutting Path Planning Method of Real Shearer
### Automatic Height-Adjusting Strategy
Q is the angle between the line connecting the next key cutting point and the instant apex of the drum and the horizontal). The specific process of automatic height-adjusting is as follows:  
* Reading data and calculating parameters  
If the right drum of the shearer runs to the horizontal position of P\({}_{i}\), the coordinates of the center of the shearer drum at this time \((X_{a1},Y_{a1},Z_{a1})\) are recorded. The coordinates of the next key cutting point \(P_{i(j+1)}\)\((X_{b1},Y_{b1},Z_{b1})\) are then read, after K (the angle of the direction of drum movement) is recorded. This is followed by the calculation of Q (the angle of the target direction):  
\[\text{Q}=\tan^{-1}\left(\frac{Y_{b1}-(Y_{a1}+9)}{Z_{b1}-Z_{a1}}\right), \tag{10}\]  
where 9 is the radius of the drum, (in decimeter). The height compensation value of the inclination angle of the shearer fuselage given M = \(L\times\sin\beta\) (where \(L\) is the length of a scraper conveyor, in dm; \(\beta\) is the inclination angle of the shearer fuselage, in rad) is calculated. When the shearer fuselage is inclined at an angle, the absolute height of the drum changes if not adjusted. * Judgment of action  
After reaching a key cutting point, the drum can experience three actions; up, down, and no adjustment. The concrete action is determined by the height difference between the apex of the drum and the next key cutting point. The thresholds of the height difference are determined by the inclination angle of the fuselage and the feasible region of the shearer traction speed. These thresholds include:  
* the maximum height difference for lifting given by \(\triangle\text{H}_{\text{max}}=L\times(\sin\beta+\sin\theta_{\text{max}})\),
* the minimum height difference for lifting \(\triangle\text{H}_{\text{up}}=L\times\sin\beta+\frac{1}{2}\varepsilon\),  
Figure 4: Automatic height-adjusting diagram. * the maximum height difference for lowering \(\Delta\mathrm{H}_{\mathrm{down}}=L\times\sin\beta-\frac{1}{2}\varepsilon\),
* the range of height difference for no adjustment \(\Delta\mathrm{H}_{\mathrm{up}}>\Delta\mathrm{H}>\Delta\mathrm{H}_{\mathrm{ down}}\),
* the minimum height difference for descending \(\Delta\mathrm{H}_{min}=L\times(\sin\beta-\sin\theta_{min})\). In the above equations, \(\Delta\mathrm{H}\) is the height difference between adjacent key cutting points, \(\beta\) is the inclination angle of the shearer fuselage, \(\theta_{max}\) and \(\theta_{min}\) are the maximum and minimum angle, respectively, between the direction of the drum movement and the horizontal direction during the lifting process, \(\varepsilon\) indicates the range of the relative height difference between the adjacent key cutting points within which the drum may not be adjusted. In this study, we set \(\varepsilon\) to 60 mm. When the adjustment direction is determined, the K is compared with the Q. The haulage speed of the shearer is then adjusted to redirect the drum toward the target point. Specific execution actions at the key points include acceleration-up, deceleration-up, acceleration-down, deceleration-down, constant speed-up, constant speed-down, and no adjustment. When matching the moving direction and the target direction of the drum, considering that there is still a slight change in the process of drum lifting, the analysis law of the shearer drum movement obtained in 3.2 is taken as the judgment knowledge and included in the strategy. The specific action judgment is shown in Table 1.