## 3 Application of the Design Approach to the Definition of the Innovative Test Rig
### Design of the General System ('Test Rig')
#### 3.2.1 Conceptualization of the Mechanism(s) for Operating the System (\(\rightarrow\) Step 1.c)
2.3 Preliminary Analysis and Selection of the Different Implementing Possibilities for the Inclination Mechanism (\(\rightarrow\) Step 1.d)  
Observing the line of action of the adopted generic linear actuator (hence, the dynamics of the lifting mechanism), the above-presented solutions can be grouped as follows:  
* solutions providing for the lifting of the platform support-frame by using an actuator acting vertically (Figures 15 and 16);
* solutions providing for the lifting of the platform frame by using an actuator acting horizontally and using a movable vertical-rail (Figure 17). Thanks to this classification, it is possible to formulate a several comments that are valid for more than one solution. In particular, in order to analyze the feasibility and thus the advantage or not  
Figure 17: Solution providing for the inclination of the platform support-frame with a pure-rotation movement operated by a vertical rail moved horizontally via a horizontal hydraulic actuator (_RH1_) or a threaded bar and nut (_RH2_). In the same picture some details are reported: the thrust joint \(B\), having three ball-bearings engaging the vertical rail, the complete thrust-structure. of proceeding with the implementation of one of the presented solutions/schemes, it is necessary to quantitatively analyze the components of the vector apical displacement. Indeed, it is possible to observe that the vertical component of the vector, related to the trigonometric factor 'cosine', is quantitatively predominant on the horizontal component, which is instead related to the trigonometric factor'sine', up to a 45\({}^{\circ}\)-angle. This means that, to achieve the same inclination of the platform (or the same angular speed), the vertical component of the vector displacement (or speed) will always be much greater than the horizontal component, resulting in a more favorable ratio of force multiplication. Notice also that, in a completely horizontal position for the platform, the mechanism is located in a so-called 'kinematic singularity': the alignment of point A and B on the horizontal axis, in fact, represents an equilibrium position of the system; any thrust applied at the point B and direct toward A causes a compression of the platform structure, a stress of the articulation hinge in A and might not result in a rotation of the platform around A. Also, since the trigonometric factor'sine' is zero (or near zero) in this configuration, the ratio between the horizontal thrust-force and the vertical force causing the start of the platform lifting (i.e., its inclination) tends towards infinity, hence it is extremely unfavorable for a possible horizontal component in correspondence to very small angles. Albeit potentially leading to the same result from a kinematic point of view, the presented solutions are not equivalent from the dynamic point of view. All the schemes in which the platform support-frame is lifted by using an actuator acting vertically are more favorable as regards the application of a force to the structure and, therefore, should be given preference for implementation. A second important classification can be defined by the type of motion followed by the platform during its lifting (hence, by the kinematic scheme); according to this criterion, the above-presented solutions can be divided into two groups:  
* solutions providing for the inclination of the platform frame with a pure-rotation movement (Figures 15 and 17);
* solutions providing for the inclination of the platform frame with a rotatory-translational movement (Figure 16). In case of adoption of an inclination-scheme providing a rotatory-translational movement, there are important implications to be considered. In particular, there is the need to create some guides to make the platform slide in correspondence to its pivot point A (Figure 16).