MAE 593 Final Project Presentation

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Mathematical Methods in Robotics - Final Project

PRRR Serial Manipulator
RRR-RPR-RRR Parallel Manipulator

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MAE 593 Final Project Presentation

  1. 1. MAE 593 Project Presentation PRRR- SERIAL MANIPULATOR RRR-RPR-RRR -PARALELL MANIPULATOR By Nikhil Sapre Tejas Puntambekar
  2. 2. PRRR Serial Manipulator <ul><li>RRR Manipulator mounted on Sliding Base </li></ul><ul><li>2 d.o.f at EE (Redundant) </li></ul><ul><li>Forward Kinematics </li></ul><ul><li>Inverse Kinematics </li></ul><ul><li>Workspace Plotting </li></ul><ul><li>Trajectory </li></ul><ul><ul><ul><li>Trace Ellipse </li></ul></ul></ul><ul><ul><ul><li>Trace Circle </li></ul></ul></ul><ul><ul><ul><li>Trace Curve </li></ul></ul></ul>P P R R R EE L1 d1 L3 L2 Theta1 Theta2 Theta3
  3. 3. Basic Features <ul><li>Base Position fixed to (0,0) </li></ul><ul><li>Can Slide along X-Axis from -50 to 50 </li></ul><ul><li>User defined Link Lengths (5-50) </li></ul><ul><li>Task Space Configuration </li></ul><ul><li>Join Space Configuration </li></ul><ul><li>Plot WorkSpace </li></ul><ul><li>Trace Ellipse/Circle </li></ul><ul><li>Trace Curve </li></ul><ul><li>Return to Home Position </li></ul>
  4. 4. GUI – Home Position
  5. 5. Forward Kinematics Xee=d1+L1*cos(theta1)+L2*cos(theta2)+L3*cos(theta3) Yee=L1*sin(theta1)+L2*sin(theta2)+L3*sin(theta3)
  6. 6. Manipulator Forward Kinematics
  7. 7. Inverse Kinematics <ul><li>Redundant System </li></ul><ul><li>4-Unknowns, 2 equations </li></ul><ul><li>Newton-Raphson Numerical method </li></ul><ul><li>Pseudo Inverse of Jacobian </li></ul>
  8. 8. Manipulator Inverse Kinematics
  9. 9. Plot WorkSpace <ul><li>Divide the space into grid </li></ul><ul><li>Check for each point whether inverse exists </li></ul><ul><li>Mark green diamond if within workspace and red cross if out of reach </li></ul><ul><li>No internal singularities </li></ul>
  10. 10. Manipulator – Work Space
  11. 11. Trace Ellipse/Circle <ul><li>User input co-ordinates of center and Major and Minor Axis dimensions </li></ul><ul><li>Trace the ellipse/circle using inverse kinematics </li></ul>
  12. 12. Trajectory-Trace Ellipse
  13. 13. Trajectory-Trace Circle
  14. 14. Trace Curve <ul><li>Input 5 points using mouse </li></ul><ul><li>Interpolation between points using interp1 function </li></ul><ul><li>Trace the curve using inverse kinematics </li></ul><ul><li>Curve in X and Y direction </li></ul>
  15. 15. Trajectory-Trace Curve Curve in X direction
  16. 16. Trajectory-Trace Curve Curve in Y direction
  17. 17. Trajectory-Trace Curve Random Curve
  18. 18. Trajectory-Trace Curve Error Messages
  19. 19. Demo
  20. 20. RRR-RPR-RRR Parallel Manipulator <ul><li>Chain1-RRR </li></ul><ul><li>Chain2-RPR </li></ul><ul><li>Chain3-RRR </li></ul><ul><li>3 d.o.f at EE </li></ul><ul><li>Forward Kinematics </li></ul><ul><li>Inverse Kinematics </li></ul>d1
  21. 21. Parallel Manipulator GUI
  22. 22. Forward Kinematics <ul><li>First aim is to find unknown joint space variables </li></ul><ul><li>Then we can find the Task Space Variables </li></ul>Forward Kinematics <ul><li>First aim is to find unknown joint space variables </li></ul><ul><li>Then we can find the Task Space Variables </li></ul>

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