Rotation of Objects about Two or More Axes Module 8.

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Presentation transcript:

Rotation of Objects about Two or More Axes Module 8

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

Review: Rotation of Objects ● Rotation: turning an object about a straight line (axis of rotation)

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

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

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.

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

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

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

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

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

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