# Design of Man-Machine Synergic Lunar Coring Device and Its Coring Dynamic Analysis
## 4 Dynamic Analysis and Verification of the Coring Device  
The schematic diagram of the impact mechanism is shown in Figure 8a. The cam roller compresses the spring under the action of the contour line of the cylindrical cam and accumulates elastic potential energy. When the cam roller moves to the position of the crest of the cylindrical convex contour line, the elastic potential energy of the spring is released, as shown in Figure 9a. It pushes the follower (cylindrical cam and impact hammer) toward the coring tube at high speed. In turn, the impact sampling of lunar soil or rock is realized. Since the cylindrical cam moves at high speed, the design should pay special attention to the impact of the cam roller when cutting into and out of the convex profile line. Therefore, the convex profile line is selected as a modified sine curve, which means that the profile equation before and after the cam is a sine acceleration motion curve, and the curve in the middle part is an isokinetic motion curve, as shown in Figure 9b. This ensures that the follower maintains a uniform motion for most of its travel and avoids shocks in the start and end phases of the cam. To analyze the dynamic and further optimize the structure, a mechanical model between the motor, the cylindrical cam, and the impact hammer was established, and the boundaries of the structural parameters were determined accordingly. Since the impact module achieves energy storage and releases through the cam mechanism, the simplified cam curve is expanded along a straight line for dynamic analysis. The cylindrical cam radius \(R\), spring preload length \(l_{0}\), cam stroke height \(h\), energy storage spring stiffness \(k_{c}\), cam loading section ratio \(\alpha\), and cam roller radius \(r\) are all impact module structural parameters in Figure 8b. These partial structural parameters need to be optimized and designed before the prototype is made, resulting in the maximum single-impact work under limited conditions. The relationship between motor torque and cam shape during energy storage of the cylindrical cam can be obtained from Figure 8b:  
\[M_{d}\geq\left[G+k_{c}(l_{0}+l)\right]\frac{h}{\pi\alpha} \tag{1}\]  
Figure 8: (**a**) Schematic diagram of the impact mechanism; (**b**) Force analysis diagram of the cylindrical cam. Figure 9: (**a**) Schematic diagram of cylindrical cam; (**b**) Cylindrical cam curve expansion diagram. where: \(M_{d}\) is the rated torque of the motor; \(l\) is the current axial displacement of the roller; \(G\) is the gravity of the impact hammer. For the impact hammer drop process, if the friction between the impact hammer and the guide wall is neglected, the equation of state of the impact hammer during release is:  
\[l=\iint-\left(g_{lunar}+\frac{k(l_{0}+l)}{m}\right) \tag{2}\]  
Since the equation of the profile line before and after the cylindrical cam is a sinusoidal acceleration motion curve, the initial velocity of the impact hammer in the initial motion condition is 0. \[\left\{ \begin{array}{l}l(0)=l_{max}\\ \dot{l}(0)=0\\ \ddot{l}(0)=-\left(g_{lunar}+\frac{k(l_{0}+l_{max})}{m}\right)\end{array} \right. \tag{3}\]  
The differential equation of the state of motion of the impact hammer is obtained from Equations (2) and (3):  
\[l=\left(l_{max}+\frac{mg_{lunar}}{k}+l_{0}\right)\cos(\sqrt{\frac{k}{m}}t)- \frac{mg_{lunar}}{k}-l_{0} \tag{4}\]  
When the cylindrical cam reaches the bottom, i.e., \(l=0\), the time from release to contact of the impact hammer is obtained as:  
\[t=\sqrt{\frac{m}{k}}\mathrm{arccos}(1-\frac{l_{max}}{\frac{mg_{lunar}}{k}+l_{ 0}+l_{max}}) \tag{5}\]  
To ensure that the impact energy of the impact hammer is effectively released to the coring tube, a certain length of the gentle section is set on the cylindrical cam for the release of the impact energy.