ME5286CourseNotes04-09 - Linear transformation which...

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Linear transformation which provides the geometric relationship between two coordinate systems: N x O x A x P x N y O y A y P y N z O z A z P z 0 0 0 1 N x - Cosine of the angle between N and X N y - Cosine of the angle between N and Y N z - Cosine of the angle between N and Z N x N y = Unit vector describing direction of N N z Similar deFnitions for and P = = Position vector relating origins of coordinate systems T = Initial coordinate system X Y Z ±inal coordinate system N O A O x O y O z A x A y A z P x P y P z
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Inverse Kinematics: The Problem
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Position and orientation of the hand typically deFned by Each of these are a function of the manipulator joint angles
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Robot Linkage and Transformation Matrices
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Confguration For all joint angles, θ i = 0
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Confguration For all joint angles, θ i = 0
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Inverse Kinematic Solutions
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To position hand, must solve for θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , θ 6 , Problem 12 transcendental equations 6 Unknowns Equations are not independent More than 1 solution for a given position and
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ME5286CourseNotes04-09 - Linear transformation which...

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