Thanks to the concentrated parameters model previously described, it is possible to control the behaviour of the strip by controlling the position and the rotations of a discrete number of control sectors. As shown in Fig. 4.5, in order to be able to twist and bend the strip and obtain a geodesic trajectory, each control sector has been equipped with five degrees of freedom:
- • X, Y and Z define the absolute position of the point on the trajectory acting as reference for the control sector in the space, thus allowing the bending of the strip;
- • т defines the torsion;
- • в allows handling the tangency of the trajectory to the control point.
The degree of freedom в allows the modification of the local curvature of the strip. As regards this kind of interfaces so far developed, this degree of freedom
Fig. 4.5 Degree of freedom of control sector has never been controlled but left free to follow the elasticity of the material. This solution introduces a representation error.
As a consequence, this feature is innovative and it leads to a significant reduction of the representation error.
The sixth degree of freedom, i.e. the rotation around the Y-axis, is prevented by the physical characteristics of the strip in terms of shape of the cross section and of the physical characteristics of the material.