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KINEMATICS ANALYSIS OF ROBOTS (Part 5)

KINEMATICS ANALYSIS OF ROBOTS (Part 5). Kinematics Analysis of Robots V. This lecture continues the discussion on the analysis of the forward and inverse kinematics of robots. After this lecture, the student should be able to:

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KINEMATICS ANALYSIS OF ROBOTS (Part 5)

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  1. KINEMATICS ANALYSIS OF ROBOTS (Part 5)

  2. Kinematics Analysis of Robots V • This lecture continues the discussion on the analysis of the forward and inverse kinematics of robots. • After this lecture, the student should be able to: • Solve problems of robot forward and inverse kinematics analysis using transformation matrices

  3. Z0, Z1 Y0, Y1, Z2 X0, X1, X2 Y2 Z3 X3 X4, X5, X6 Y4, Z5, Y6 Y3 Z4, Y5, Z6 A 6 DOF Robot A3 A2 d3 d4

  4. Summary of D-H parameters

  5. Transformation matrices

  6. Transformation matrices

  7. Transformation matrices

  8. Transformation matrices

  9. Transformation matrices

  10. Transformation matrices

  11. Transformation matrices

  12. Forward Kinematics Given all the joint angles (1, 2, 3, 4, 5, and 6) we can use the overall transformation matrix to solve for the position and orientation of frame {6}. The orientation of frame {6} w.r.t. frame {0} is defined by the rotational matrix: The translation of the origin of frame {6} w.r.t. frame {0} is defined by the vector

  13. Inverse Kinematics We are now given the desired orientation and position of frame {6}, i.e. We now want to solve for all the joint angles (1, 2, 3, 4, 5, and 6)

  14. Inverse Kinematics We are now given the desired orientation and position of frame {6}, i.e. We now want to solve for all the joint angles (1, 2, 3, 4, 5, and 6). First, we get the following:

  15. Inverse Kinematics

  16. Inverse Kinematics Equate elements (2,4) from both sides: Let where Therefore

  17. Inverse Kinematics Equate elements (1,4), (2,4) and (3,4) from both sides: Square all equations and add them to get:

  18. Inverse Kinematics Let where Therefore

  19. Inverse Kinematics

  20. Inverse Kinematics

  21. Inverse Kinematics

  22. Inverse Kinematics Equate elements (1,4) and (2,4) from both sides: Rearranging: We can solve for (2+ 3) from the above two equations:

  23. Inverse Kinematics Equate elements (1,3) and (3,3) from both sides: Provided s50

  24. Inverse Kinematics

  25. Inverse Kinematics Equate elements (1,3) and (3,3) from both sides:

  26. Inverse Kinematics To find 6, we use Equate elements (1,1) and (3,1) from both sides:

  27. Inverse Kinematics Given the orientation and position of frame {6}, i.e. given all the joint angles (1, 2, 3, 4, 5, and 6) can be found.

  28. Summary • This lecture continues the discussion on the analysis of the forward and inverse kinematics of robots. • The following were covered: • Robot forward and inverse kinematics analysis using transformation matrices

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