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Dynamics of Serial Manipulators

ME 439. Professor N. J. Ferrier. Dynamic Modeling. For manipulator arms:Relate forces/torques at joints to the motion of manipulator loadExternal forces usually only considered at the end-effectorGravity (lift arms) is a major consideration. ME 439. Professor N. J. Ferrier. Dynamic Modeling. Ne

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Dynamics of Serial Manipulators

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    1. ME 439 Professor N. J. Ferrier Dynamics of Serial Manipulators Professor Nicola Ferrier ME Room 2246, 265-8793 ferrier@engr.wisc.edu

    2. ME 439 Professor N. J. Ferrier Dynamic Modeling For manipulator arms: Relate forces/torques at joints to the motion of manipulator + load External forces usually only considered at the end-effector Gravity (lift arms) is a major consideration

    3. ME 439 Professor N. J. Ferrier Dynamic Modeling Need to derive the equations of motion Relate forces/torque to motion Must consider distribution of mass Need to model external forces

    4. ME 439 Professor N. J. Ferrier Manipulator Link Mass Consider link as a system of particles Each particle has mass, dm Position of each particle can be expressed using forward kinematics

    5. ME 439 Professor N. J. Ferrier Manipulator Link Mass The density at a position x is r(x), usually r is assumed constant The mass of a body is given by where is the set of material points that comprise the body The center of mass is

    6. ME 439 Professor N. J. Ferrier Inertia

    7. ME 439 Professor N. J. Ferrier Equations of Motion

    8. ME 439 Professor N. J. Ferrier Equations of Motion

    9. ME 439 Professor N. J. Ferrier Equations of Motion Lagrangian Dynamics, continued

    10. ME 439 Professor N. J. Ferrier Equations of Motions Robotics texts will use either method to derive equations of motion In “ME 739: Advanced Robotics and Automation” we use a Lagrangian approach using computational tools from kinematics to derive the equations of motion For simple robots (planar two link arm), Newton-Euler approach is straight forward

    11. ME 439 Professor N. J. Ferrier Manipulator Dynamics Isolate each link Neighboring links apply external forces and torques Mass of neighboring links External force inherited from contact between tip and an object D’Alembert force (if neighboring link is accelerating) Actuator applies either pure torque or pure force (by DH convention along the z-axis)

    12. ME 439 Professor N. J. Ferrier Notation

    13. ME 439 Professor N. J. Ferrier Force on Isolated Link

    14. ME 439 Professor N. J. Ferrier Torque on Isolated Link

    15. ME 439 Professor N. J. Ferrier Force-torque balance on manipulator

    16. ME 439 Professor N. J. Ferrier Newton’s Law A net force acting on body produces a rate of change of momentum in accordance with Newton’s Law The time rate of change of the total angular momentum of a body about the origin of an inertial reference frame is equal to the torque acting on the body

    17. ME 439 Professor N. J. Ferrier Force/Torque on link n

    18. ME 439 Professor N. J. Ferrier Newton’s Law

    19. ME 439 Professor N. J. Ferrier Newton-Euler Algorithm

    20. ME 439 Professor N. J. Ferrier Newton-Euler Algorithm Compute the inertia tensors, Working from the base to the end-effector, calculate the positions, velocities, and accelerations of the centroids of the manipulator links with respect to the link coordinates (kinematics) Working from the end-effector to the base of the robot, recursively calculate the forces and torques at the actuators with respect to link coordinates

    21. ME 439 Professor N. J. Ferrier “Change of coordinates” for force/torque

    22. ME 439 Professor N. J. Ferrier Recursive Newton-Euler Algorithm

    23. ME 439 Professor N. J. Ferrier Two-link manipulator

    24. ME 439 Professor N. J. Ferrier Two link planar arm

    25. ME 439 Professor N. J. Ferrier Forward Kinematics: planar 2-link arm

    26. ME 439 Professor N. J. Ferrier Forward Kinematics: planar 2-link manipulator

    27. ME 439 Professor N. J. Ferrier Forward Kinematics: planar 2-link manipulator

    28. ME 439 Professor N. J. Ferrier Forward Kinematics: planar 2-link manipulator

    29. ME 439 Professor N. J. Ferrier Forward Kinematics: planar 2-link manipulator

    30. ME 439 Professor N. J. Ferrier Point Mass model for two link planar arm

    31. ME 439 Professor N. J. Ferrier Dynamic Model of Two Link Arm w/point mass

    32. ME 439 Professor N. J. Ferrier General Form

    33. ME 439 Professor N. J. Ferrier General Form: No motion

    34. ME 439 Professor N. J. Ferrier Independent Joint Control revisited Called “Computed Torque Feedforward” in text Use dynamic model + setpoints (desired position, velocity and acceleration from kinematics/trajectory planning) as a feedforward term

    35. ME 439 Professor N. J. Ferrier Manipulator motion from input torques

    36. ME 439 Professor N. J. Ferrier Dynamic Model of Two Link Arm w/point mass

    37. ME 439 Professor N. J. Ferrier Dynamics of 2-link – point mass

    38. ME 439 Professor N. J. Ferrier Dynamics in block diagram of 2-link (point mass)

    39. ME 439 Professor N. J. Ferrier

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