1. Rotation of Objects About Two or More Axes
ENGAGE
Rotation of Objects About Two or More Axes
Prepared by: Sheryl Sorby, Ph.D.
Amy Hamlin, Ph.D.
Norma Veurink

2. Rotations about two axes
Order of Rotations
Equivalent Rotations
Computer Module

3. Review: Rotation of Objects
Rotation: turning an object about a straight line (axis of rotation)
To visualize a rotation, imagine a door turning about its hinges. The axis of rotation is a line passing through the hinges.
The portion of the object that lies along the axis of rotation before rotation remains on the axis of rotation through the rotation.

4. Rotation About Two Axes
Objects can be rotated about two or more axes the same way they were rotated about a single axis

5. Rotation Origin
When objects are rotated about two or more axes, only a single point remains in its original position

6. Arrow Coding in Multiple-Axes Rotations
Arrows are placed in the order in which the rotations are performed
Positive 90° rotation about the z-axis followed by a negative 90° rotation about the x-axis. Z X
Positive 90° rotation about the y-axis followed by a positive 90° rotation about the x-axis followed by a negative 90° rotation about the x-axis. Y X X

7. Order of Rotations
Final orientation of the object depends on the order in which the rotations were performed. X Y
If the rotation can be switched and still achieve the same orientation, it is commutative. Y X

8. Equivalent Rotations
Two sets of rotations can result in the same final orientation of the object

9. Equivalent Rotations
Sometimes one set of rotations can be replaced by a simpler set. X X Z
is equivalent to Y Y X

10. Demonstration Y X Z Y X Y X Z Y Z

11. In-Class Exercise X Y Z Z X Y

12. Computer Module – Rotation about Two or More Axes
Launch the Spatial Visualization software.
Complete the module on Rotation of Objects about two or more axes

13. Rotation of Objects about Two or More Axes Homework …
Complete the following pages in Module 8
rot2-
1 - 2
5 – 8
11 – 12