CS545_Lecture_11

# CS545_Lecture_11 - Velocities Start at joint 1 recursion to...

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CS545—Contents XI Newton-Euler Method of Deriving Equations of Motion Newton’s Equation Euler’s Equation The Newton-Euler Recursion Automatic Generation of Equations of Motion Reading Assignment for Next Class See http://www-clmc.usc.edu/~cs545

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Newton’s & Euler’s Equations Newton’s Equation: Expresses the force acting at the CM for an accelerated body Euler’s Equations Expresses the torque acting on a rigid body given an angular velocity and angular acceleration Idea of Newton-Euler Force and torque balance at every link Recursion through all links What do we need? Angular velocities and accelerations of each link Linear velocities at each link F = m  p cm τ = I cm ω + ω× I cm
Computing Angular

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Unformatted text preview: Velocities Start at joint 1, recursion to higher joints Angular Velocity of link i+1, expressed in base coordinates What happens to prismatic joints in this equation? Nothing :-) ω i = i − 1 + θ i z i − 1 i = i − 1 Computing Angular Accelerations Start at joint 1, recursion to higher joints Angular Acceleration of link i+1, expressed in coordinate system i+1 is obtained from differentiating the angular velocities For prismatic joints ω i + 1 i + 1 = R i i + 1 i i + θ i + 1 z i + 1 i + 1 i + 1 i + 1 = R i i + 1 i i + R i i + 1 i i × i + 1 z i + 1 i + 1 + i + 1 z i + 1 i + 1 i + 1 i + 1 = R i i + 1 i i...
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CS545_Lecture_11 - Velocities Start at joint 1 recursion to...

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