1. Robotics, Fall 2006 Dr. Jennifer Kay Lecture 1: Coordinate Frames
Copyright © 2005, 2006 Jennifer Kay

2. Drawing 3 Dimensional Frames in 2 Dimensions
Y points to the right
Z points up
X points ???

3. Two views of the same cube
Viewed from below
Viewed from above

4. Now Overlay the 3-D Coordinate Framex y z x y z
Viewed from above
Viewed from below
X points away from you!
X points towards you!

5. We will always use a right-handed coordinate frame (x points out)z

6. We will not use a left-handed coordinate frame (x points in)z x y

7. Right Handed Coordinate Systems: Using the right hand rule
Given two axes, determine the direction of the third axis
Point right fingers along x
Curl fingers towards y
Thumb points to z

8. Right Handed Coordinate Systems: Using the right hand rule
Given two axes, determine the direction of the third axis z x y x y x y

9. Right Handed Coordinate Systems: Practicez y x y y x z x y z

10. Rotating Axes: Direction of Positive Rotation
If we want to rotate a frame, which way do we rotate it?
Example: Rot z (90 degrees) x y z y z x ? y x z ?

11. Rotating Axes: Another Right Hand Rule
Point right thumb in direction of axis you want to rotate
Fingers curl in direction of positive rotation x y z y x z
Rot z (90)

12. Plotting Points (Neatly) in 3-D
Example: Plot (5,3,4)
Step 1: Draw tick marks

13. Plotting Points (Neatly) in 3-D
Example: Plot (5,3,4)
Step 2: Draw two lines on the groundplane 5 3 4 3 5 3

14. Plotting Points (Neatly) in 3-D
Example: Plot (5,3,4)
Step 3: Draw a perpendicular with tick marks, and your point 5 5 3 4 4 4 3 3 5

15. Plotting Points: Example
Plot (1,3,5) on a coordinate frame where:
X points up and Y points into the paper
Y points down and Z points out of the paper

16. Working with Multiple Coordinate Frames
Tower Coordinates
Plane Coordinates

17. Working with Multiple Coordinate Frames
Location of the nose of the plane in tower coordinates?
Location of the origin of the tower in plane coordinates?
Location of the nose of the plane in plane coordinates?
50 meters 5m

18. Working with Multiple Coordinate Frames
Location of the nose of the plane in tower coordinates?
Location of the origin of the tower in plane coordinates?
Location of the nose of the plane in plane coordinates?