Using Mathematica for Matrix Math -- as it Applies in Robotic Kinematics

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# Using Mathematica for Matrix Math -- as it Applies in Robotic Kinematics - PowerPoint PPT Presentation

Using Mathematica for Matrix Math -- as it Applies in Robotic Kinematics. A Lecture Supplement R. Lindeke, Ph. D. UMD - MIE. Starting A worksheet -- . Use Subscript input Icon Matrices are A i. Choose Create Table/Matrix … to add one. We need 4x4 matrices – this can be set!.

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## Using Mathematica for Matrix Math -- as it Applies in Robotic Kinematics

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### Using Mathematica for Matrix Math -- as it Applies in Robotic Kinematics

A Lecture Supplement

R. Lindeke, Ph. D.

UMD - MIE

Starting A worksheet --

Use Subscript input Icon Matrices are Ai

Choose Create Table/Matrix …to add one

We need 4x4 matrices – this can be set!

#5 here:
• Then we will Form the FKS: T0n = A1*A2*A3*A4*A5
• I’ll use a software: Mathematica (or DERIVE5/6 on another day!)
After All the Matrices are entered:
• Lets Verify the accuracy of our input – We will set each angle and length (temporally to 0 units – degrees or mm)
Physical Verification (A1)

4th Column states O1 same place as O0

Implies X1 parallel to X0

Implies Y1 ‘anti-parallel’ to Z0

States, Z1 Parallel to Y0

This Symbol (equal period) is “UnSet” – returns variables to original condition for symbolic math (after Physical Verification is complete)

After Variables are “UnSet”
• We must “Pre-process” Parallel Z –Revolute – Consecutive Joint Matrices using FullSimplify
• Then we Develop FKS solutions with the proper order of the Ai’s
Simplifying A2A3

Great News: Simplify is NOW SMART Too!

Use FullSimplify to capture Proper Solution

… And MatrixForm to display!

Period to indicate Multiply

Again with the MatrixForm!

Physical Verification of FKS (TOO!) :

It Agrees with my Model (at least at the Home Position!

(Xn  X0; YnY0; ZnZ0; Origin is at:6,-.5, 4.25)