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Basics of Coordinate Metrology
Unit 3: Coordinate Systems in Space - Transformation |
Step 4 of 5
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Coordinate systems can also
be translated and rotated in space:
- In a translation, the origin is
simply shifted in the x, y and z directions. The associated (x,y,z) number
is called translation vector.
- In a rotation, the coordinate
system is rotated around the x, y and z axes.
- The translation and rotation of
coordinate systems is also called transformation.
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Here the coordinate system "ks1" is transformed into the coordinate system
"ks2" by moving in +x, +y and +z and by revolving on the y-axis (with a
positive angle).
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| Tip: For the sake of clarity, it is
recommended always to translate coordinate systems first and then to rotate
them.
Tip: Right-thumb rule:
 In
rotation, the following trick helps you to determine the positive direction
of rotation around an axis: Shape your right hand as if you wanted to stop a
car. Now grab towards the axis of rotation, for example
towards the bottom screen edge such that the thumb points in the positive
direction of the axis (in most cases towards the right), in which case the
fingers point in the mathematically positive direction of
rotation. |
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