Question 1: Inertia in Motion Systems (15 marks) (weeks 1-4 and prac project) L- L. Consider the robotic manipulator shown above. a) (3 marks) Write an expression for the torque exerted by the mass of the two links at the lower joint. Call this the load torque (TL). Hint, the second joint is at an angle of (0+) relative to horizontal. (1 mark for the torque exerted by the first link, 1 mark for the torque exerted by the second link, 1 mark for the combined torque) b) (3 marks) Write an expression for the mass moment of inertia exerted by the two links (JL). For convenience you may treat each link as a slender rod. (1 mark for the moment of the first link, 1 mark for the moment of the second link, 1 mark for the combined moment) c) (2 marks) What is the peak acceleration (in rad/s) required to move the lower joint from 0 to 30 degrees rad) in 2 seconds. Use a trapezoidal move profile d) What is the peak torque required to achieve an acceleration of 0.4 rad/s2 at the lower joint? Use a motor inertia of 0.6 kg.m. Assume a static friction torque Trof 0.3 Nm. L1 = L2 = 0.5 m, m = m2 = 1.0 kg. (1 mark for correctly writing the equation of motion, 1 mark for the correct peak load torque, 1 mark for the correct load inertia, 1 mark for correct answer) e) (2 marks) All mechanical systems have friction. If a motor-driven system is dominated by static and coulomb friction (Fs. Fc). define the value of friction torque for all possible values of speed and motor torque. f) (2 marks) Explain the Euler method for numerically determining the position of a machine as a function of time. Question 1: Inertia in Motion Systems (15 marks) (weeks 1-4 and prac project) L- L. Consider the robotic manipulator shown above. a) (3 marks) Write an expression for the torque exerted by the mass of the two links at the lower joint. Call this the load torque (TL). Hint, the second joint is at an angle of (0+) relative to horizontal. (1 mark for the torque exerted by the first link, 1 mark for the torque exerted by the second link, 1 mark for the combined torque) b) (3 marks) Write an expression for the mass moment of inertia exerted by the two links (JL). For convenience you may treat each link as a slender rod. (1 mark for the moment of the first link, 1 mark for the moment of the second link, 1 mark for the combined moment) c) (2 marks) What is the peak acceleration (in rad/s) required to move the lower joint from 0 to 30 degrees rad) in 2 seconds. Use a trapezoidal move profile d) What is the peak torque required to achieve an acceleration of 0.4 rad/s2 at the lower joint? Use a motor inertia of 0.6 kg.m. Assume a static friction torque Trof 0.3 Nm. L1 = L2 = 0.5 m, m = m2 = 1.0 kg. (1 mark for correctly writing the equation of motion, 1 mark for the correct peak load torque, 1 mark for the correct load inertia, 1 mark for correct answer) e) (2 marks) All mechanical systems have friction. If a motor-driven system is dominated by static and coulomb friction (Fs. Fc). define the value of friction torque for all possible values of speed and motor torque. f) (2 marks) Explain the Euler method for numerically determining the position of a machine as a function of time
