Consider the mechanical system represented in Figure 1 and placed in the vertical plane. The system is in its static equilibrium position. A body, having mass m, is connected to the piston rod (having mass mp) of a hydraulic actuator. There is no sliding between the bodies m and M. The body with mass M and moment of inertia J is pinned to the ground at point A and connected to the ground by means of a spring k. G is the centre of mass of the body M. All the moments of inertia are computed with respect to the centres of mass. Consider the elongations of the spring to be null in the configuration depicted in figure. The hydraulic system is controlled by a four-way spool valve and a double-acting, double-rod actuator. Discuss when this configuration is preferred highlighting the advantages and the drawbacks. 1. Compute the full non-linear equation of motion of the mechanical system 2. Draw a detailed schematic of the hydraulic actuator and the control valve. Derive a model neglecting the fluid dynamics and highlighting on the schematic the meaning of each introduced coefficient; 3. Size the actuator and the valve considering that a maximum force of 5 kN is required act mechanical system and the no-load velocity must be 20 mm s-; QB mp QA 2L R W k A Figure 1 L M, J m the