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Unformatted text preview: Massachusetts Institute of Technology Department of Mechanical Engineering 2.12 Introduction to Robotics Problem Set No.5 Out: October 19, 2005 Due: October 26, 2005 Problem 1 Consider a mass-less rod of length l constrained by two sliding joints at both ends A and B, as shown in the figure below. The rod is connected to a spring of spring constant k at A and is pulled down by mass m at B. Friction is negligible. Let θ be the angle between the horizontal line and the rod. Using the Principle of Virtual Work , show that the rod is in equilibrium at the angle θ that satisfies the following relationship: A k mg = − θ θ tan ) cos 1 ( where g is acceleration of gravity. Assume that at = θ the spring force is zero. A θ k B A mg Figure 1 Problem 2 A planar robot with three revolute joints is shown below. Let i θ and be the angle of joint i and the length of link i , respectively, and i A e e e y x φ , , be the end-effecter position and orientation viewed from the base coordinate frame, as shown in the figure. position and orientation viewed from the base coordinate frame, as shown in the figure....
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.12 taught by Professor Harryasada during the Fall '05 term at MIT.
- Fall '05