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Robot Modeling and the Forward Kinematic Solution

Robot Modeling and the Forward Kinematic Solution. ME 4135 Lecture Series 4 – PART 2 6 DOF Articulating Arm. Another? 6dof Articulating Arm – ( The Figure Contains Frame Skelton). l 2. l 3. l 4. LP Table.

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Robot Modeling and the Forward Kinematic Solution

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  1. Robot Modeling and the Forward Kinematic Solution ME 4135 Lecture Series 4 – PART 2 6 DOF Articulating Arm

  2. Another? 6dof Articulating Arm – (The Figure Contains Frame Skelton) l2 l3 l4

  3. LP Table * With End Frame in Better Kinematic Home, otherwise is (6 - 90), which is a problem!

  4. Using MathCad:

  5. A Matrices, in Robot shorthand

  6. A Matrices, cont.

  7. Leads To: • A FKS of:

  8. Solving for FKS • Pre-process {A2*A3*A4} to collect angular terms • They are the planer arm issue as in the previous robot model

  9. Then Continuing: • Then Form: A1* {A2*A3*A4}*A5*A6 • Simplify for FKS!

  10. Simplifies to: nx = R11 = C1·(C5·C6·C234 - S6·S234) - S1·S5·C6 ny = R21 = C1·S5·C6 + S1·(C5·C6·C234 - S6·S234) nz = R31 = S6·C234 + C5·C6·S234 ox = R12 = S1·S5·S6 - C1·(C5·S6·C234 + C6·S234) oy = R22 = - C1·S5·S6 - S1·(C5·S6·C234 + C6·S234) oz = R32 = C6·C234 - C5·S6·S234 ax = R13 = C1·S5·C234 + S1·C5 ay = R23 = S1·S5·C234 - C1·C5 az = R33 = S5·S234 dx = C1·(C234·(d6·S5 + l4) + l3·C23 + l2·C2) + d6·S1·C5 dy = S1·(C234·(d6·S5 + l4) + l3·C23 + l2·C2) - d6·C1·C5 dz = S234·(d6·S5 + l4) + l3·S23 + l2·S2

  11. And Again Physical Verification:

  12. And Finally of the FKS: Remember – these “Physical Verifications” must be checked against the robot’s Frame skeleton – not just prepared!

  13. You should Develop Frame Skeleton for each of the Various Arm Types • SCARA • Cylindrical • Prismatic • Gantry • Cantilevered

  14. And Proceeding from the text • It is often possible to find that robots are assembled from Arms and various Wrist • Thus Arms ‘control’ the Positional issues of POSE • And Wrist ‘adjust’ the Orientation Issues of POSE • Hence these POSE issues can be treated separately • See text for Wrist Details • Spherical • RPY of various arrangements

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