## 5 Numerical Experiment and Discussion of Results  
Based on the above algorithm, a program for numerical modeling of the kinematic analysis of the mechanism has been comprised. It is assumed that link 1 (crank) performs full rotation, and link 3 (rocker) performs a hobbing motion. Four types of mechanisms of the given structure of the knee press were considered (Figure 1):  
\[ \begin{array}{l}\text{(a) link 3 performs a hobbing motion at $y_{P}\geq y_{Q}$and $x_{Q}=-e$;}\\ \text{(b) link 3 performs a hobbing motion at $y_{P}\geq y_{Q}$ and $x_{Q}=e$;}\\ \text{(c) link 3 performs a hobbing motion at $y_{P}\leq y_{Q}$ and $x_{Q}=-e$;}\\ \text{(d) link 3 performs a hobbing motion at $y_{P}\leq y_{Q}$ and $x_{Q}=e$.}\end{array}  \tag{18}\]  
At the same time, the values of the following links of the driven chain of the mechanism will remain unchanged: \(l_{1}=32.66\) mm, \(l_{BC}=89.7\) mm, \(l_{FP}=l_{CP}=94.31\) mm, \(l_{3}=77.22\) mm, \(l_{5}=l_{6}=159.38\) mm, \(l_{ED}=l_{CF}=171.46\) mm, \(e=30\) mm. Remaining parameters: \(l_{2},h\)--take different values for the corresponding types of the mechanism (Figure 2). Figure 4 shows the results of the kinematic analysis of the first type of the knee press mechanism. The varying parameters are equal: \(l_{2}=129.92\) mm, \(h=59.18\) mm. The angular velocity of the input link is equal \(\omega_{1}=0.5\)\(\frac{1}{s}\), then the time of one cycle is \(T=12.56\) s. The slider stroke is \(S_{1}=74\) mm. Output link 7 (slider) remains stationary for a long time. \(t_{b1}=4.2\) s, i.e., the slider performs almost one third of the working cycle. Figure 4a,b shows graphs of the velocity and acceleration of the interrelationship with the graph of the position function. By definition, dwell occurs when one or more consecutive derivatives of the position functions of the output link simultaneously vanishes. From Figure 4b, it can be seen that during dwell, the velocity and acceleration remain close to zero. Figure 4: Results of the kinematic analysis of the first type of the knee press mechanism: (**a**) graph of the function of the position output link (slider); (**b**) graphs of the speed and acceleration of the slider. Figure 5 shows the results of the kinematic analysis of the second type of knee press mechanism. The variable parameters are equal: \(l_{2}=79.1\) mm, \(h=59.18\) mm. In this case, the slider stroke is \(S_{2}=97\) mm \(>S_{1}\). The output link 7 (slider) remains motionless \(t_{b2}=2.5\) s. Figure 5b. At the same time, the slider 7 performs fast working stroke \(S_{2}=97\) mm in \(t_{motion}=0.34\) s and the acceleration changes rapidly within \(w_{7}\in[-600,400]\frac{mm}{s^{2}}\); that is, there is a blow. In the considered options, when \(y_{p}\geq y_{Q}\), there is a slider dwell in its upper position. At the same time, the slider dwell \(t_{b1}=4.2\) s at \(x_{Q}=-e\) significantly more than the dwell \(t_{b2}=2.5\) s at \(x_{Q}=e\). Figure 6 shows the results of the kinematic analysis of the third option of the knee press mechanism. The variable parameters are equal: \(l_{2}=131.57\) mm, \(h=150.23\) mm. In this case, the dwell of the working slider occurs in the lower position when there is direct contact with the workpiece and the slider stroke is \(S_{3}=100\) mm. The output link 7 (slider) remains stationary \(t_{b3}=4.04\) s. Figure 6a amounts to 1/3 T--total working cycle time. In some crank presses, there are requirements when it is necessary to ensure rapid compression of the forging and a long reverse of the slide stroke [4; 22]. Such a process can be provided by this structure of the crank press mechanism. In Figure 6a it can be seen that the forging compression time \(t_{co}=2.7\) s, and reverse time \(t_{co}=5.8\) s. From Figure 6b it can be seen that during the dwell, the velocity and acceleration remain close to zero. Figure 7 shows the results of the kinematic analysis of the fourth option of the knee press mechanism. The variable parameters are equal: \(l_{2}=79.1\) mm, \(h=136.23\) mm.