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

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## Homogeneous-Transformation-Examples

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## Homogeneous-Transformation-Examples

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

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