# Analysis of a Mechanism Used to Operate an Oscillating Separator
## 5 Results  
In order to perform the analytical validation of the obtained equations (Equations (16)-(21)), the following set of component values was utilized. It should be noted that whilst some of these components are shared by the two mechanisms discussed in this article, they do not match the constructive elements found in real equipment. Furthermore, the values were only utilized to confirm the precision of the mathematical relationships. * In the case of both mechanisms, the coordinates of point A are (0,0);
* The dimensional value of the crank, i.e., the AB element, is 35 mm (for both the four-bar and six-bar mechanisms);
* The coordinates of the point corresponding to the tie rod bearing, which in Figure 1 is denoted by D and in Figures 3 and 5 by G, are (133, \(-\)79);
* The size of the tie rod for both mechanisms is 114 mm (element FG in Figures 3 and 5 or element DC in Figure 1);
* The dimensional value used for the connecting rod corresponding to Figure 1, i.e., the value of the CB element, is 133 mm. In contrast, the value corresponding to the same component but in Figure 3 is 174 mm;
* Figure 5 shows the distinctive components of the six-bar mechanism:
* The following dimensional values define the ternary element BCE: element BC = 67 mm; element CE = 24 mm; and element EB = 44 mm;
* The binary element CD has a value of 55 mm. The use of the Mathcad 15 program, a valuable tool for engineers engaged in the analysis of mechanisms, enabled us to perform mathematical calculations corresponding to the equations obtained (i.e., Equations (16)-(21)) from a mathematical standpoint. The use of the Mathcad 15 program can facilitate the simplification and improvement of the kinematic analysis process. The trajectories, corresponding to torques C and E, are presented in Figure 6a,b. These values were calculated by substituting the previously mentioned terms in the calculation Equations (16)-(19). A comparison of the two trajectories reveals the following:  
* The trajectory of coupling C is represented by a circular arc, which is a consequence of the fact that one of the ends of the binary element DC is a fixed element (i.e., coupling D);
* The trajectory of coupling E is a complex trajectory, which is a consequence of the fact that the ternary element BCE is connected at the ends (i.e., in couplings C and B) to  
Figure 6: (a) The trajectory that coupling C describes. (b) The trajectory that coupling F describes. the binary elements CD and AB, which have a fixed end, and to the binary element EF which is mobile. With regard to the trajectory corresponding to point F (as illustrated in Figure 5) the results obtained were subjected to analysis by comparing the values obtained using two distinct software programs including the following:  
1. [label=1.] 2. Mathcad [58]--in this program, the trajectory of point F was calculated using mathematical methods;
3. Roberts [56]--this software is designed for the simulation of the movement of the mechanism with six bars, which allows for the determination of the trajectory of point F.  
Figure 7 displays a comparison of the trajectories, represented by point F, that were produced by the two work programs utilized. The graphical representation analysis, see Figure 7, indicates that the results obtained mathematically are comparable to those obtained using the Roberts simulation program. However, a minor discrepancy is observed on the left side of the trajectory, with a difference of 0.45 mm on the OX axis and 0.17 mm on the OY axis. Furthermore, the displacement speed of point F can be calculated using the same programs. This comparative variation is illustrated in Figure 8.  
Figure 8: The variation in the speed of point F’s movement.