midterm_04 - Massachusetts Institute of Technology...

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Massachusetts Institute of Technology Department of Mechanical Engineering 2.12 Introduction to Robotics Mid-Term Examination October 27, 2004 2:30 pm – 4:30 pm Close-Book. Two sheets of notes are allowed. Show how you arrived at your answer. Do not leave multiple answers. Indicate which one is your correct answer. Problem 1 Shown below is a robotic arm roaring a boat at the Charles Regatta. For the sake of simplicity, we consider only planar motion, assuming that the two-link robot arm and the oar are constrained in a horizontal plane. The oar is free to rotate about the pin, called an oarlock, and the robot pulls the oar at the distance d from the oarlock. The robot endpoint is connected to the oar at point E through a friction-less passive joint. A hydraulic force f acts on the blade at a distance D from the oarlock. Assume that the hydraulic force is perpendicular to the oar. The oarlock is at coordinates with reference to the base coordinate system attached to the first joint of the robot arm. Assume no friction and no gravity. Using the notation shown in the figure, answer the following questions. ( T o o y x , ) a). Obtain the coordinates of the robot endpoint as functions of joint angles e e y x , 2 1 , θ , and differentiate the endpoint coordinates with respect to joint angles in order to derive
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midterm_04 - Massachusetts Institute of Technology...

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