RobotArm_2008

RobotArm_2008 - Robotic Arm Numerics: Robotic Arm p. 1...

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Unformatted text preview: Robotic Arm Numerics: Robotic Arm p. 1 Robotic Arm (Lifted from Jared Updikes CS171 lab 7) Numerics: Robotic Arm p. 2 Robotic Arm (Lifted from Jared Updikes CS171 lab 7) Numerics: Robotic Arm p. 2 Arm position Our robots arm is given by a position function f ( 1 , 2 , 3 ) = f x ( 1 , 2 , 3 , 4 ) f y ( 1 , 2 , 3 , 4 ) f z ( 1 , 2 , 3 , 4 ) = cos( 1 )( L 3 sin( 2 )+ L 4 sin( 2 + 3 )+ L 5 sin( 2 + 3 + 4 )) sin( 1 )( L 3 sin( 2 )+ L 4 sin( 2 + 3 )+ L 5 sin( 2 + 3 + 4 )) L 1 + L 2 + L 3 cos( 2 )+ L 4 cos( 2 + 3 )+ L 5 cos( 2 + 3 + 4 )) Numerics: Robotic Arm p. 3 Arm position Our robots arm is given by a position function f () = f x () f y () f z () = X Numerics: Robotic Arm p. 3 Linear approximation We want a first-order Taylor expansion. Numerics: Robotic Arm p. 4 Linear approximation For a two-dimensional function g , the first-order Taylor expansion is g ( x + x,y + y ) g ( x,y ) + parenleftbigg g x ( x,y ) x + g y ( x,y ) y parenrightbigg Numerics: Robotic Arm p. 4 Linear approximation...
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RobotArm_2008 - Robotic Arm Numerics: Robotic Arm p. 1...

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