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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)**

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LP Table Frames Link Var d l S C S C 0 → 1 1 R 1 90 -1 S1 C1 1 → 2 2 2 a2 0 S2 C2 2 → 3 3 3 a3 S3 C3 3 → 4 4 4 a4 -90 S4 C4 4 → 5 5 5 S5 C5 5 → 6 6 6* d6 S6 C6 * With End Frame in Better Kinematic Home, otherwise is (6 - 90), 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 {A2*A3*A4} to collect angular terms**

They are the planer arm issue as in the previous robot model

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

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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

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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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JOINTS CS 490.006/582.001 KINEMATIC LINKAGES PAGE 36 REVOLUTE JOINT (1 DOF) TRANSLATIONAL JOINT (1 DOF) CYLINDRICAL JOINT (2 DOF) SPHERICAL JOINT (3 DOF)

JOINTS CS 490.006/582.001 KINEMATIC LINKAGES PAGE 36 REVOLUTE JOINT (1 DOF) TRANSLATIONAL JOINT (1 DOF) CYLINDRICAL JOINT (2 DOF) SPHERICAL JOINT (3 DOF)

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