Exercise n2 on kinematics and dynamics

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APPLIED MECHANICS 1. KINEMATIC AND DYNAMIC ANALYSIS OF A PLANAR MECHANISM The mechanical system shown in Figures 1 and 2 is analysed in this case study . This system , that is arranged in a vertical plane, is composed of an electric induction motor, a gearbox, a gear wheel, a gear rack, a slotted-link, a coupling rod and a slider. The gear wheel is hinged at point O to a fixed frame (in a real system the wheel is rigidly mounted on a shaft supported on journal bearings: in this simplified model the hinge O substitutes the mechanical components mentioned above allowing the wheel to rotate about the axis passing through its centre). The teeth of the gear wheel engage with those of a horizontal gear rack that is mounted on two frictionless supports, H and K. A pin is rigidly connected to the gear rack at point A. This pin is forced to move inside the rectilinear guide of the slotted link BC that is connected to ground by a hinged joint at the lower end B. The pin joint located at the upper end C of this link connects the slotted-link to a coupling rod, CD. In the end, the rod CD is connected to a slider, at point D, by means of a pin joint. The slider translates on an inclined plane. The barycentre of the slotted link is G 1, while that of the slider is G 2. The ma ss and mass moment of inertia of the slotted link, evaluated about the barycentric axis, are m1 and JG1, respectively. The mass of the slider is m 2 while that of the gear rack is m 3. The mass of the coupling rod CD is assumed to be negligible. The mass moment of inertia of the rotor of the induction motor is Jd. The pin A slides on the internal surface of the guide of the slotted link: the corresponding kinetic friction coefficient is 1kf . The kinetic friction coefficient between the slider and the…