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# ps7 - 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.7 Out: November 9, 2005 Due: November 16, 2005 Problem 1 A two degree-of-freedom robot arm with one prismatic joint is shown below. The direction of the prismatic joint is perpendicular to the centerline of the first link. As shown in the figure, joint angle θ and distance z between the tip of the first link and the mass centroid of the second link are used as generalized coordinates. The first actuator fixed to the base link produces torque τ about the first joint, while the second actuator located at the tip of the first link generates linear force f acting on the second link. Using the parameters shown in the figure, answer the following questions. a). Obtain the moment of inertia reflected to Joint 1 when the second joint is fixed at 0 z z = . At which arm configuration does the moment of inertia become minimal?

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