HW4 - Figure 1: A two-link Robot (a) Derive the kinetic...

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Department of Mechanical Engineering Spring 2009 MEEN 408/612 Introduction to Robotics/Mechanics of Robotic Manipulators Homework 4 Due: April 1, 2009 1. Consider a two-link robot shown below. The principal moments of inertia of the first link are I x, 1 , I y, 1 and I z, 1 kgm 2 respectively. Similarly, the principal moments of inertia of the second link are I x, 2 , I y, 2 and I z, 2 kgm 2 respectively. The masses of the links are respectively m 1 and m 2 kg. The lengths shown below are in meters. A disturbance force of F N acts on the second link in the horizontal direction away from the axis of first rotation. There is a motor that exerts a torque Q 1 Nm on the first link and Q 2 Nm on the second link. You may assume any other parameters that you think are missing, but you must state them explicitly.
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Unformatted text preview: Figure 1: A two-link Robot (a) Derive the kinetic energy for the robot. (b) Derive the potential energy for the robot. (c) Derive the generalized forces acting on the robot and hence, derive the equations of motion for the robot. 1 2. The equations of motion of a robot are given by: ( 1 + 2 3 cos q 2 ) q 1 + ( 2 + 3 cos q 2 ) q 2-2 3 sin q 2 q 1 q 2- 3 sin q 2 q 2 2 + 5 cos q 1 + 6 cos( q 1 + q 2 ) = u 1 , ( 2 + 3 cos q 2 ) q 1 + 4 q 2 + 3 sin q 2 q 2 1 + 6 cos( q 1 + q 2 ) = u 2 . Derive a control scheme to ensure that x 1 tracks sin t and x 2 tracks cos t asymptoti-cally. 2...
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HW4 - Figure 1: A two-link Robot (a) Derive the kinetic...

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