# Kinematic of the System

As explained in the previous Section, two solutions for placing the system mechanisms can be taken into consideration. They can be placed on the longitudinal plane or on the transversal plane. The obvious choice would be the first one. In fact, this solution allows us to get a more compact system, as already developed in some of the devices described in Sect. 4.4.1. However, by analysing the advantage and the disadvantages of both solutions, we have decided to adopt a transversal plane solution. This choice will allow us to develop a system based on independent modules with an absolute set-up. We have opted for this configuration because our aim is to develop a new system, which overcomes the limitations of the systems developed up to day. Analysing the intrinsic features of this kind of set-up such as the possibility to manage the distance between the control sectors, the actuation the degree of freedom *в*, the possibility to achieve low curvature radii and modularity, we can consider this solution as the most suitable for obtaining an interface, which will meet and satisfy the requirements of the project.

As a consequence, it is possible to design the kinematic chain, which is able to move the degrees of freedom of the mechanism. As shown in Fig. 3, the mechanism that places a control sector in space consists of a planar articulated system, made up of two elements with two hinges at both ends. Between these elements and the control sector there are the two systems for the actuation of the rotations in charge of managing the torsion and the tangency.

**Fig. 4.9 ****Concept of the kinematic scheme**

Considering the needed degrees of freedom, it is possible to summarize:

- • The rotations of the degrees of freedom
*R*and_{z1}*R*allow us to place the control point along the X-Y plane._{z2} - • The rotation of
*R*allows rotating the sector, thus obtaining the torsion._{z3} - • The hinge
*R*enables the rotation around the X axis (orthogonal to Y-Z plane). In this way, it is possible to obtain the rotation required to control the tangency._{x} - • The degree of freedom along the Z axis, which is needed for the longitudinal translation of the control sector, is obtained with a runner sliding on a rail.

Therefore, in order to move one single module, five actuators are needed (Fig.4.9). The independent modules have a specific size, which influences the relative distance between two modules along the Z direction. Consequently, in order to allow us to further reduce the distance between the control sectors, we have decided to arrange alternately the mechanisms, so as to avoid collisions between two adjoined modules. This is another positive feature allowed by the transversal plane solution. Now the concept of the kinematic of the system is defined. Therefore, it is possible to start the design of the configuration of the single modules. We have designed a lot of different solutions. However, in order to make the discussion lighter, we will describe only the two final solutions.

# Reference

1. Bordegoni M, Cugini U, Ferrise F (2012) Requirements for an enactive tool to support skilled designers in aesthetic surfaces definition. Int J Interact Design Manuf (IJIDeM) 6(2):83-91