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

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Another? 6dof Articulating Arm – ( The Figure Contains Frame Skelton) l2l2 l3l3 l4l4

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LP Table FramesLinkVar dl S C S C 0 → 11R 1 0S1C1 1 → 22R 22 0a200 01S2C2 2 → 33R 33 0a300 01S3C3 3 → 44R 44 0a4-90 0S4C4 4 → 55R 5 10S5C5 5 → 66R 6*6*d6000 01S6C6 * With End Frame in Better Kinematic Home, otherwise is ( ), which is a problem!

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Using MathCad:

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A Matrices, in Robot shorthand

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A Matrices, cont.

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Leads To: A FKS of:

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Solving for FKS Pre-process {A 2 *A 3 *A 4 } to collect angular terms They are the planer arm issue as in the previous robot model

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Then Continuing: Then Form: A 1 * {A 2 *A 3 *A 4 }*A 5 *A 6 Simplify for FKS!

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Simplifies to: n x = R 11 = C1·(C5·C6·C234 - S6·S234) - S1·S5·C6 n y = R 21 = C1·S5·C6 + S1·(C5·C6·C234 - S6·S234) n z = R 31 = S6·C234 + C5·C6·S234 o x = R 12 = S1·S5·S6 - C1·(C5·S6·C234 + C6·S234) o y = R 22 = - C1·S5·S6 - S1·(C5·S6·C234 + C6·S234) o z = R 32 = C6·C234 - C5·S6·S234 a x = R 13 = C1·S5·C234 + S1·C5 a y = R 23 = S1·S5·C234 - C1·C5 a z = R 33 = 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

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And Again Physical Verification:

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

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

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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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