OSU ECE 5463 - Homogeneous-Transformation-Examples (7 pages)

Previewing pages 1, 2 of 7 page document View the full content.
View Full Document

Homogeneous-Transformation-Examples



Previewing pages 1, 2 of actual document.

View the full content.
View Full Document
View Full Document

Homogeneous-Transformation-Examples

109 views


Pages:
7
School:
Ohio State University
Course:
Ece 5463 - Introduction to Real Time Robotics Systems

Unformatted text preview:

Homogeneous Transformation Examples and Properties Homogeneous transformation examples Consider the left foot of the walking robot as 2 foot 2 Foot Front 30o ZF 3 in Z XF 1 Foot What is B XB 5 ZB YF 5 XE 4 5 4 3 1 ZE YB YE 4 10 3 2 0 0 0 1 1 2 0 0 1 2 0 5 3 2 0 0 0 4 1 3 0 1 Leg Front View 0 2 3 XF YF ZF We need inverse To obtain 3 2 4 C1 5 3 2 0 0 0 1 0 1 0 2 3 1 6 33 4 C2 5 C3 3 1 2 1 2 0 0 0 96 1 3 3 2 1 2 0 0 1 2 3 2 0 0 0 0 1 0 6 33 0 96 3 1 5 4 3 1 4 6 92 0 1 Can you find the answer by inspection Relative compound transformation Since and We have 1 0 0 0 0 1 0 0 0 0 1 0 0 10 3 1 3 2 1 2 0 0 1 2 0 5 3 2 0 0 0 1 0 4 3 1 4 6 92 0 1 5 14 0 1 Use of Homogeneous Transformation To transform point vectors To transform a free vector free in the air no origin Use rotation matrix only Does not change magnitude 3 2 1 2 0 E g 1 2 3 2 0 0 0 1 To transform unit vectors Properties of Homogeneous Transformation Column of R are unit vectors n o a 1 Column of R are orthogonal 0 0 0 Dot product of any two rows columns i and j 0 when 1 when Cross product of any two rows columns give the components of the third row column



View Full Document

Access the best Study Guides, Lecture Notes and Practice Exams

Loading Unlocking...
Login

Join to view Homogeneous-Transformation-Examples and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Homogeneous-Transformation-Examples and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?