RobotArm_2008

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

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 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 + 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...
View Full Document

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.

Page1 / 26

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

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online