1. Rotation of Objects about Two or More Axes Module 8

2. Session Topics ● Rotations about Two Axes ● Order of Rotations ● Equivalent Rotations

3. Review: Rotation of Objects ● Rotation: turning an object about a straight line (axis of 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 Edge in Contact Point in Contact

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 Y X 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.

7. Order of Rotations ● Final orientation of the object depends on the order in which the rotations were performed.

8. Order of Rotations ● Object rotations about two or more axes are not commutative! X Y Y X

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

10. Equivalent Rotations ● Sometimes one set of rotations can be replaced by a simpler set. X Z Y X X Y

11. Course Software….. ● Work through the Rotation of Objects about Two or More Axes software module

12. Rotation of Objects about Two or More Axes Homework … ● Complete the following pages in Module 8 ● rot2- – 1 - 2 – 5 – 8 – 11 – 12 – 15 - 16