Basics of Coordinate Metrology
Unit 3:  Coordinate Systems in Space - Transformation

Step 4 of 5
  Next

       

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.
       
      
  
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).
 
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.