# Analysis of a Mechanism Used to Operate an Oscillating Separator
## 5 Results
Figure 7: A comparative analysis of the trajectory of point F.  
The difference between the two sets of values, which describe the linear velocity variation corresponding to point F, is illustrated in Figure 9. The values obtained from the [PERSON] simulation software and those derived from the mathematical computation (using Mathcad 15 [58]) were subtracted to create this graphical representation. This suggests there is a maximum difference of 2 mm/s between the two sets of values. The principal objective of this study is to identify a mechanism that generates the same motion as that produced by a classical mechanism, which will then be employed in the drive of an oscillating separator used for the mechanical separation process. The following analysis therefore concerns the movement executed by the literal end of the tie rod (the FG element in Figure 5) generated by the mechanism under analysis (six-bar mechanism) and by the classical mechanism (the DC element in Figure 1) found in the various types of mechanical separators operating oscillating screens (four-bar mechanism). For this reason, Figure 10 compares the trajectory produced by the six-bar mechanism (for which the values obtained using the mathematical calculation and the results obtained with the Mathcad program were used [58]) with the trajectory described by the four-bar mechanism obtained using a torque study in the Roberts simulation program (the simulation took into account the constructive characteristics presented at the beginning of this section). Figure 10: A comparison of the trajectories of the tie rod’s free end for the two mechanisms under study. Figure 9: The difference between the two methods for determining the velocity of the movement of point F.  
As illustrated in Figure 7, there is a distinction between the two trajectories in this specific case. This discrepancy can only be discerned between the two endpoints of the trajectory as follows:  
* It can be observed that the difference between the endpoints of the trajectory on the right-hand side is 0.35 mm for the OX axis and 0.18 mm for the OY axis;
* For the left side of the trajectories, the difference between the two ends is 1.317 mm for the OX axis and 1.493 mm for the OY axis. The trajectory generated by the movement of the free end of the tie rod, for the mechanism with six bars, was found to be 5 mm greater than that of the mechanism with four bars. It is important to note that the movement of the free end of the tie rod, for the four-bar mechanism, was identified using the Roberts program. A graphical comparison of the velocities obtained for the two oscillatory motion-generating systems under examination is presented in Figure 11. The data presented in Figure 10 were obtained using the programs shown above, namely, Mathcad [58] and Roberts [56]. The representation was performed in accordance with the mechanism representation mode (Figures 1 and 3). The value 0 in the graphical representation is indicative of the starting position of the mechanism analysis, namely, the crank handle. The result of the change can be observed by analyzing the representation of the change in the speed of the movement of the tie rod's free end as follows:  
* In the range of 270\({}^{\circ}\) to 90\({}^{\circ}\) (upper dial) (analysis performed in a counterclockwise direction), the two defining elements, namely, the linear velocity variation and the angular value corresponding to this velocity, are found to be close for the two mechanisms under comparison. The difference between the maximum values is 2.39 mm/s with an angular offset of 12\({}^{\circ}\);
* For the same direction of movement, but for the lower dial, i.e., that corresponding to the range of 90-270\({}^{\circ}\), the variation curves of the speed of movement of the free end of the tie rod differ for the two mechanisms analyzed. The maximum speed obtained for the four-bar mechanism is 31.69 mm/s, while the six-bar mechanism is 20.48 mm/s higher. Furthermore, the angular difference between the maximum speed values is 48 degrees.