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# Longitudinal Plane Solution and Transversal Plane Solution

As previously described, it is possible to control the deformations of the strip by controlling the degree of freedom of a finite number of control sectors. In order to manage the behaviour of the strip, we need to control, and therefore to actuate, at least three sectors, which can be placed at the same distance from each other.

To actuate the control sectors according to the degree of freedom described in the Sect.4.4, we can choose between two solutions, as depicted in Fig.4.6. The two options are listed in the following:

• • longitudinal plane solution;
• • transversal plane solution.

Fig. 4.6 Longitudinal plane solution and Transversal plane solution

## Longitudinal Plane Solution

The longitudinal plane solution requires that the actuation systems in charge of moving the control sectors are designed so as to work up along the plane that lies on the centre line of the strip. This disposition is appropriate for relative actuation mechanisms, where the system in responsible for moving the control point is usually a sequential open kinematic chain. With this kind of configuration the location in space of a generic point depends on the position of the previous point, as shown in Fig.4.7.

The solution of relative actuation systems organized on longitudinal plane entails the following advantages and disadvantages.

Compactness of actuation mechanisms: relative actuation system allow us to design mechanism with small size because these are closer than the solutions available with transversal plane solution to the control points.

Fig. 4.7 Relative actuation systems

• Transversal dimension limited: thanks to the small dimension of the mechanisms it is possible to place them directly under the strip. This feature allows us to decrease the transversal size of the interface.
• Simple to control: the relative actuation option does not require mechanisms with high level of complexity. Therefore, the position of control points can be easily controlled.
• Low size servomotors: each sector is actuated by a mechanism that is place close to the control sector. Therefore, it is not required to have complex transmissions. Furthermore, thanks to the relative configuration, the displacements needed to move the control sectors in the space are little. All these features allow us to use servomotor with low size.
• High stiffness: as previously described, the relative configuration allows obtaining an actuation system that is compact and without complex transmission. These features allow us to obtain mechanisms with high stiffness values. This characteristic is very important. Indeed, low values of stiffness spread positional error.

• Distance among the control sectors: the development of the actuation system along the longitudinal plane implies that the amount of space needed to host the mechanisms determinates the distance among the control sectors. This feature influences the resolution of the whole tactile system. The difficulty, and in some case the impossibility of, in decreasing or just modifying the distance between the control sectors can create problems, if we want to increase the rendering resolution.
• Difficulty to actuate the degree of freedom в: this rotation allows handling the tangency of the trajectory to the control point, and therefore, the modification of the local curvature of the strip. In the relative configuration, where the mechanisms are placed near the strip, it can be very difficult to host the mechanisms in charge of providing the rotation needed to actuate this degree of freedom.
• Difficulty to achieve low curvature radii: this feature is a consequence of the difficulty in managing the distance between the control sectors and the impossibility of managing the degree of freedom в. Indeed, in order to correctly manage trajectories with low values of curvature radii it is needed to manage the distance between control sectors and the rotation in charge of controlling the local curvature. Moreover, when the strip is bended the distance among the control points changes, and therefore, also the distance among the control sectors has to change (Fig. 4.7a). In the relative configuration, this displacement is possible only if we leave the strip free to slide on the connections with the mechanisms or if we provide a uncontrolled joint. In any case, these features are leaded by the elastic behaviour of the strip.
• Limited length of the strip: the disposition along the longitudinal plane of the actuation mechanisms and the consequent relative configuration involves that the whole interface is grounded by means of two links at the extremity of the strip or by one at the centre. In any case, each mechanism sustains the next one. As a consequence, increasing the distance from the grounded supports will require increasing the power needed by the motors to move the system. Therefore, the maximum number of control sectors, and consequently the length of the strip, is proportional to the maximum power of the servomotor. If we want to overcome this limit, we need to increase the power and consequently the dimension of the servomotors by changing the whole system.
• Low modularity: In order to customize the length of the strip (without changing the servomotors) according to the kind of surface to render, it is necessary to add or remove some modules of the strip itself. This is first of all an activity that requires efforts and time.
• Incremental error: the relative disposition of the mechanisms causes the effect of the error propagation. Indeed, the positional error related to each control sector affects also the following modules. Therefore, moving from the framed mechanism to the extremities the positional error increases.

In the KAEMaRT research group, researchers have developed some concepts of the device based on relative actuation systems with mechanisms on longitudinal plane, as shown in Fig.4.8.

Fig. 4.8 Concepts of tactile device based on relative actuation systems

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