# Study and Simulation of an Under-Actuated Smart Surface for Material Flow Handling
## 5 Results
### Sorting
Summarizing, thanks to the simulation described, it is possible to realize such tables depending on the specific application, considering that the results are influenced by the layout of the modules and the initial position. In particular, for Table 3 the \"S-box\" layout is the same of the sorting simulations of Figure 7b, but with more columns of sorting rotors in order to test a bigger range of velocities. Instead, for the \"B-box\" there are two more rows of rotors in the sorting line, always with the rotors oriented for sorting towards \(y<0\) (\(e_{i}=+45^{\circ}\)), making a total of four instead of two lines. The data from the simulations carried out to produce Table 3, coupled with further simulations with, as input, only the inclination of the surface, allowed for a comparison of performance with similar existing sorting systems [45]. Figure 8 presents these results. The red dots represent the values of the sorting rate when only the initial velocity is set as input, whereas the blue dots are for when only the inclination of the surface is exploited. Figure 8 shows the most common sorting capacity ranges [45] and, as can be seen, the system proposed by the authors guarantees a medium rate for most input values, with few exceptions in both directions, i.e., high capacity and low capacity. The rate is defined as objects sorted per hour (\(p_{CS}/h\)) and can be easily calculated, considering the time needed to perform the sorting and a successful sorting condition. In practice, the condition of successful sorting is when \(y_{g}\geq y_{g,limit}\) (for the rectangular shape: \(y_{g,limit}=h/2+\sqrt{(b/2)^{2}+(h/2)^{2}}\)), i.e., when the displacement in the direction \(y\) is such that, whatever the orientation of the object, the base is no longer in contact with the sorting rotors. The input velocity values presented in Figure 8 are within the common ranges of use for sorting systems. In particular, Ref. [45] for devices similar to the surface proposed by the authors, but fully actuated and called \"Torsional discs\", defines input velocities between \(0.5\) and \(1.5\ \mathrm{m}/\mathrm{s}\). \"Torsional discs\" have sorting capacities ranging between \(1600\) and \(4500\ \mathrm{pcs}/\mathrm{h}\) when the size and weight of the transported objects are comparable to those considered in the authors' simulations (\"S-box\" and \"B-box\" characteristics). The system developed in this paper, although it is under-actuated, also allows sorting rates within the same range, providing good performance and in line with the current technology. Obviously, given the under-actuation, there are minimum input speed thresholds, as shown in Table 3, however, they do not seem to limit the application ranges of the device. Tilting the surface and starting from zero initial speed requires longer sorting times and thus provides lower rates than those with velocity as input. However, according to Figure 8, the inclination also provides a predominantly medium sorting capacity, without the need for a prior conveyor. Therefore, the results obtained from the comparison of sorting performances showed that the surface introduced by the authors, with the advantage of the simplicity of the under-actuation, still guarantees sorting capabilities at the same level as current technology, both using initial speed and surface inclination as inputs. To sum up, the results of this subsection show that the surface is capable of sorting with the two different types of input (Figure 7 and Table 2). In addition, thanks to the developed simulation environment, it was possible to obtain the performance of the system proposed by the authors and compare it with the current technology. This showed that the surface provides a medium sorting capacity (Figure 8), in the same range as existing systems. Finally, for certain objects, the initial input speed was associated with the number of rotors required for sorting (Table 3).