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
Instructor: Jacob Rosen
Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA 6

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

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
Outward Iteration
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
Outward Iteration
Instructor: Jacob Rosen
Advanced Robotic - MAE 263D - Department of Mechanical & Aerospace Engineering - UCLA

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

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

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

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

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

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

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

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

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

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

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

31. 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