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Unformatted text preview: Robotic Arm Numerics: Robotic Arm – p. 1 Robotic Arm (Lifted from Jared Updike’s CS171 lab 7) ▽ Numerics: Robotic Arm – p. 2 Robotic Arm (Lifted from Jared Updike’s CS171 lab 7) Numerics: Robotic Arm – p. 2 Arm position Our robot’s arm is given by a position function f ( θ 1 ,θ 2 ,θ 3 ) = f x ( θ 1 ,θ 2 ,θ 3 ,θ 4 ) f y ( θ 1 ,θ 2 ,θ 3 ,θ 4 ) f z ( θ 1 ,θ 2 ,θ 3 ,θ 4 ) = cos( θ 1 )( L 3 sin( θ 2 )+ L 4 sin( θ 2 + θ 3 )+ L 5 sin( θ 2 + θ 3 + θ 4 )) sin( θ 1 )( L 3 sin( θ 2 )+ L 4 sin( θ 2 + θ 3 )+ L 5 sin( θ 2 + θ 3 + θ 4 )) L 1 + L 2 + L 3 cos( θ 2 )+ L 4 cos( θ 2 + θ 3 )+ L 5 cos( θ 2 + θ 3 + θ 4 )) ▽ Numerics: Robotic Arm – p. 3 Arm position Our robot’s arm is given by a position function f (Θ) = f x (Θ) f y (Θ) f z (Θ) = X Numerics: Robotic Arm – p. 3 Linear approximation We want a firstorder Taylor expansion. ▽ Numerics: Robotic Arm – p. 4 Linear approximation For a twodimensional function g , the firstorder Taylor expansion is g ( x + Δ x,y + Δ y ) ≈ g ( x,y ) + parenleftbigg ∂g ∂x ( x,y )Δ x + ∂g ∂y ( x,y )Δ y parenrightbigg ▽ Numerics: Robotic Arm – p. 4 Linear approximation...
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This note was uploaded on 09/25/2010 for the course CS 002 taught by Professor Barr,a during the Winter '08 term at Caltech.
 Winter '08
 Barr,A

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