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Manipulator Dynamics 3

Manipulator Dynamics 3. Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA. Iterative Newton-Euler Equations - Solution Procedure.

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Manipulator Dynamics 3

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  1. Manipulator Dynamics 3 Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  2. Iterative Newton-Euler Equations - Solution Procedure • Step 1 - Calculate the link velocities and accelerations iteratively from the robot’s base to the end effector • Step 2 - Write the Newton and Euler equations for each link. Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  3. Iterative Newton-Euler Equations - Solution Procedure • Step 3 - Use the forces and torques generated by interacting with the environment (that is, tools, work stations, parts etc.) in calculating the joint torques from the end effector to the robot’s base. Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  4. Iterative Newton-Euler Equations - Solution Procedure • Error Checking - Check the units of each term in the resulting equations • Gravity Effect - The effect of gravity can be included by setting . This is the equivalent to saying that the base of the robot is accelerating upward at 1 g. The result of this accelerating is the same as accelerating all the links individually as gravity does. Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  5. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  6. Iterative Newton-Euler Equations - 2R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  7. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  8. Iterative Newton-Euler Equations - 2R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  9. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  10. Iterative Newton-Euler Equations - 2R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  11. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  12. Iterative Newton-Euler Equations - 2R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  13. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  14. Iterative Newton-Euler Equations - 2R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  15. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  16. Iterative Newton-Euler Equations - 2R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  17. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  18. Iterative Newton-Euler Equations - 2R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  19. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  20. Iterative Newton-Euler Equations - 2R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  21. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  22. Iterative Newton-Euler Equations - 2R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  23. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  24. Iterative Newton-Euler Equations - 2R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  25. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  26. Iterative Newton-Euler Equations - 2R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  27. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  28. Iterative Newton-Euler Equations - 2R Robot Example • Outward Iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  29. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  30. Iterative Newton-Euler Equations - 2R Robot Example • Inward iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  31. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  32. Iterative Newton-Euler Equations - 2R Robot Example • Inward iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  33. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  34. Iterative Newton-Euler Equations - 2R Robot Example • Inward iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  35. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  36. Iterative Newton-Euler Equations - 2R Robot Example • Inward iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  37. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  38. Iterative Newton-Euler Equations - 2R Robot Example • Inward iteration Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  39. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  40. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  41. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  42. Iterative Newton-Euler Equations - 2R Robot Example Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  43. Equation of Motion – Non Rigid Body Effects • Viscous Friction • Coulomb Friction • Model of Friction Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  44. Velocity / Force Transformation - Wrist / Sensor / Tool Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  45. Velocity / Force Transformation - Wrist / Sensor / Tool Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  46. Velocity / Force Transformation - Wrist / Sensor / Tool Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  47. Velocity / Force Transformation - Wrist / Sensor / Tool Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

  48. Velocity / Force Transformation - Wrist / Sensor / Tool Instructor: Jacob Rosen Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

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