ps1 - Massachusetts Institute of Technology Department of...

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Massachusetts Institute of Technology Department of Mechanical Engineering 2.12 Introduction to Robotics Problem Set No.1 Out: September 14, 2005 Due: September 21, 2005 Problem 1 The torque-speed characteristics of a DC motor have been determined, as shown in the figure below. Note that u is the voltage applied to the motor armature, m τ and m ω are, respectively, the output torque and angular velocity of the motor shaft. From this plot, (a) Obtain the motor constant, torque constant, and armature resistance of the motor. (b) When the motor is rotating at 100 radians per second, what is the back emf voltage induced at the armature? (c) When the motor is producing 2x10 -3 Nm of torque, how much power is dissipated as heat at the motor windings? m m 0 4 x 10 -3 Nm 160 r/s u = 20 volts 200 r/s u = 24 volts Figure 1 Torque-speed characteristics of a DC motor Problem 2 The DC motor in Problem 1 is now used for driving a single axis robot arm with a gear reducer. See the figure below. The inertia of the motor rotor including the shaft and
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ps1 - Massachusetts Institute of Technology Department of...

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