NewtonRaphson_Multi-Variable Robot

NewtonRaphson_Multi-Variable Robot - Two Degree of Freedom...

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Two Degree of Freedom Robot Arm Example Dr. Dragan Djurdjanovic ME 218 Fall 2008
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Introduction The figure on the right shows a simple robotic arm. The arm can be moved in the given plane by changing the angles θ 1 and θ 2 . Also, given the link lengths, d 1 and d 2 , and the final position, P, of the arm, the angles θ 1 and θ 2 can be evaluated. θ 1 θ 2 d 1 d 2 O P
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The Problem Given this 2 degree of freedom robotic arm, with the following data: d 1 = 5 d 2 = 6 P = (3, 4) The 2 nd link is free to rotate about link 1, but is constrained such that 0<θ 2 <180 degrees We need to find out the possible orientations of the robot which allow the robot to place the end point P at the above location.
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Equating the x-coordinate position: P x = d 1 cos( θ 1 ) + d 2 cos( θ 1 + θ 2 ) 3 = 5cos( θ 1 ) + 6cos( θ 1 + θ 2 ) Equating the y-coordinate position: P y = d 1 sin( θ 1 ) + d 2 sin( θ 1 + θ 2 ) 4 = 5sin(
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This note was uploaded on 06/23/2011 for the course ME 218 taught by Professor Unknown during the Fall '08 term at University of Texas at Austin.

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NewtonRaphson_Multi-Variable Robot - Two Degree of Freedom...

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