using mathematica for matrix math as it applies in robotic kinematics n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Using Mathematica for Matrix Math -- as it Applies in Robotic Kinematics PowerPoint Presentation
Download Presentation
Using Mathematica for Matrix Math -- as it Applies in Robotic Kinematics

Loading in 2 Seconds...

play fullscreen
1 / 16

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


  • 179 Views
  • Uploaded on

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!.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Using Mathematica for Matrix Math -- as it Applies in Robotic Kinematics' - jariah


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
using mathematica for matrix math as it applies in robotic kinematics

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

A Lecture Supplement

R. Lindeke, Ph. D.

UMD - MIE

starting a worksheet
Starting A worksheet --

Use Subscript input Icon Matrices are Ai

choose create table matrix to add one
Choose Create Table/Matrix …to add one

We need 4x4 matrices – this can be set!

5 here
#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
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 a 1
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

before proceeding we must unset all the variables angles and length
Before Proceeding we must Unset all the variables (angles and length)

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

after variables are unset
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 a 2 a 3
Simplifying A2A3

Great News: Simplify is NOW SMART Too!

Use FullSimplify to capture Proper Solution

… And MatrixForm to display!

Period to indicate Multiply

physical verification of fks too
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)