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Unformatted text preview: Massachusetts Institute of Technology Department of Mechanical Engineering 2.12 Introduction to Robotics Problem Set No.4 Out: October 12, 2005 Due: October 19, 2005 Problem 1 An astronaut is operating a shuttle manipulator with an inspection end effecter attached to the tip of the arm. For the sake of simplicity we consider only the three revolute joints, 3 2 1 , , , and the three links, as shown in the figure. A Cartesian coordinate system, O-xy, is attached to the object to be inspected. The distance of the coordinate origin O is L from the location of the first joint. Answer the following questions using the notation shown in the figure. a) Obtain the forward kinematic equations relating the end effecter position and orientation, e e e y x , , , to the three joint angles, 3 2 1 , , . Note that the end effecter position and orientation are viewed from the Cartesian coordinate system attached to the object, O-xy. b) Obtain the Jacobian matrix associated with the kinematic equations of Part a). Sketch a block diagram of Resolved Motion Rate Control where the astronaut uses a joystick for generating velocity commands, , with reference to the Cartesian coordinate system O-xy. e e y e x y v x v = = = , , c) The inspection end effecter must be moved along the object surface, i.e. the x-axis, at a constant speed, . The gap between the inspection sensor and the object ....
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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
- Mechanical Engineering