## 3 Application of the Design Approach to the Definition of the Innovative Test Rig  
### Design of the General System ('Test Rig')  
#### 3.1.1 Conceptualization of the General Idea of a System (\(\rightarrow\) Step 1.a)  
Following the specific approach for conceiving and designing a test system, it is necessary to define the typical situations leading to a sideways overturning or a lateral rollover of an agricultural machine. In particular, the overturning conditions are essentially three [37; 68; 69], possibly occurring together to outline many possible scenarios:  
1. The machine is travelling across a gradient on a flat (but not horizontal) support plane, in particular along a route not aligned with the maximum slope direction;
2. The machine is travelling along a straight path when a local modification of the ground slope is met by one wheel [70], e.g., an obstacle, a rut, or a hole in the trajectory (i.e., the support plane is horizontal but not flat and hence it is locally not horizontal and at least one wheel can lose contact with the soil);
3. A vehicle performs an abrupt turn without modifying its speed, which is excessive for the chosen turning radius (i.e., the weight-force is deviated from the perpendicular direction of the support plane by the centrifugal force). To analyze these three scenarios, it is necessary to consider that, in general, a rollover of a vehicle happens when the vector, which is the sum of the forces applied to the vehicle CoG, has a direction not intersecting the vehicle support polygon, linking the traces of all the wheels/tracks (but not necessarily lying on a horizontal plane). The forces acting on the CoG are at most two:  
* the gravity force (always present), perpendicular to the supporting plane only if the latter is horizontal;
* the inertial force, present only for vehicles moving at a not-constant speed on a straight trajectory (i.e., if a vehicle accelerates or decelerate) or following a non-straight trajectory (i.e., if a vehicle changes its trajectory/makes a turn). There are other forces acting on the vehicle, i.e., those coming from the interaction with the terrain, balancing the forces acting on the CoG in accordance with the Lagrange-d'Alembert principle. A possible classification of any overturning scenario can be done according to the presence or not of the inertial force, or, rather, based on the velocity of the vehicle CoG: if the velocity remains substantially constant (in magnitude and direction) during a maneuver, the possible overturning can be named 'quasi-static'. Vice versa, if the velocity changes (in magnitude and/or direction), the possible overturning can be classified as 'dynamic'. When the overturning happens in a lateral direction, the vehicle undergoes a side overturning and the above-enunciated rollover condition can be re-formulated in two dimensions, observing the layout of the forces in the transversal plane (Figure 4). Any possible component of the forces (gravity, inertia, interactions with the terrain) in the direction of the vehicle longitudinal axis has no influence for the incipient lateral rotation of the vehicle. If the vehicle is turning, the radial component of inertial force is commonly called 'centrifugal force' in the vehicle frame of reference, i.e., a non-inertial frame of reference. The centrifugal force is perpendicular to the tangent to the vehicle trajectory, and it points outwards from the curve [71]. Similarly to what was done before for the classification of a generic overturning, the side-overturning can be also classified on the basis of the absence/presence of the inertial force (here: the centrifugal force). Therefore, the presented scenarios can be classified as follows: the first two scenarios are '(quasi-)static' (centrifugal force negligible), while the third one can be properly defined 'dynamic' (centrifugal force determinant in the destabilization of the vehicle).