# Study and Simulation of an Under-Actuated Smart Surface for Material Flow Handling
## 2 Concept Description  
This section provides a qualitative description of the functioning of the surface and the modules of which it is composed. The operating principle of the surface is based on an array of modules with an idle rolling element and an orientable axis of rotation. These axes are used to generate directionable friction forces on the body in contact with the surface. The origin of the friction forces lies in the very working principle of a rotor. In fact, these are constructed and used (e.g., conveyor rollers) to facilitate motion in one direction (perpendicular to their axis of rotation). This leads to a difference in the friction forces exchanged with an overlying object.  
In practice, there will be a smaller component, perpendicular to the axis, caused mainly by rotational friction, and a larger one, parallel to the axis, due to linear friction (\(F_{perp}\) and \(F_{par}\), respectively, in Figure 2c). Therefore, the main friction component will be predominantly along the axis, so by orienting the latter, the main force will also be directed. The choices of the axis directions are limited to a fixed number. For example, the simplest configuration is with two orientations (0, 90\({}^{\circ}\)), whereas more complex designs are with four (0\({}^{\circ}\), \(-\)45\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\)) (Figure 2b) or more. In Figure 2b, the four orientations are shown, with the rotors displayed like cylinders (the projection is a rectangle) and the axes like dashed lines. For applications such as slowing or stopping the material flow, two orientations may be enough, whereas for sorting, four orientations should be taken into account. Therefore, modules with four directions will be considered in the following pages. For its intended applications, the module must be used together with others to create the surface (Figure 2a), so the sum of the forces exerted by every unit will control the objects for sorting and feeding purposes. In Figure 2a, the surface setup is summarized, showing the grid of modules with the object on top, and the arrows inside each cell represent directions of motion promoted by them. As noted in the introduction section, the system is under-actuated, so the surface can only slow down the object while it completes its task of sorting or feeding. If, for example, a body is simply placed on the surface without external actuation, it will not move. To overcome this situation, the surface plane can be tilted to use the gravity effect as the missing actuation, or an initial velocity can be given to the part before crossing the surface. Depending on the application and the task of the system, one solution may be preferred over the other, or a combination of both may be chosen. For instance, if the extension of the surface is big, because the objective is to orient a body, the tilted solution could be better, whereas, if the goal is to sort parts in a conveying line, the initial velocity of the object, given by the conveyors before the sorting area, is enough.  
In addition, similar to other active surfaces that use rotors for intralogistic purposes, the application is limited to parts with at least one planar surface, in order to have simultaneous contact with three or more rotors. Another limit will be the maximum load per module, but this is related to the resistance of the device, which is not studied in this article. However, the study conducted is done considering the dimensions of the modules and their resistance comparable with the similar actuated existing systems. To provide a reference, the base of a transported object has the minimum dimensions of \(b~{}\times~{}h=[20~{}\mathrm{cm}\times 20~{}\mathrm{cm}]\), and the weight bearable by a single module is 20 kg.