# Robot Modeling and the Forward Kinematic Solution

## Presentation on theme: "Robot Modeling and the Forward Kinematic Solution"— Presentation transcript:

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)

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!

A Matrices, in Robot shorthand

A Matrices, cont.

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

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

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

And Again Physical Verification:

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

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

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