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Industrial Automation, Communication and Data Management Prof. Cesana, Rocco, Tanca January xx, 2020 name: university ID number: signature: Warnings • This file consists of 8 pages (including cover). • During the exam you are not allowed to exit the room for any other reason than handing your work or withdrawing from the exam. • You are not allowed to withdraw from the exam during the first 30 minutes. • During the exam you are not allowed to consult books or any kind of notes. • You are not allowed to use calculators with graphic display. • Solutions and answers can be given either in English or in Italian . • Solutions and answers must be given exclusively in the reserved space . Only in the case of corrections, or if the space is not sufficient, use the back of the front cover. • The clarity and the order of the answers will be considered in the evaluation. • At the end of the test you have to hand this file only . Every other sheet you may hand will not be taken into consideration. Consider the robot carrying a glass with liquid sketched in the picture: The robot should be moved in such a way to avoid spilling of the liquid from the container. In a first approximation, the sloshing dynamics of the liquid can be modelled with a pendulum, see the following picture: For simplicity, assume that the pendulum moves on a vertical plane. 1. Explain what are the direct and the inverse kinematics problems for a robotic manipulator. How many solutions does the inverse kinematics for an anthropomorphic manipulator have? 2. Write the equations of a dynamic system that describes the motion of the pendulum (when the robot is still). 3. Write the general equation that allows to find the equilibrium states in a dynamic system. Apply such formula to find the equilibrium states for the…