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Convert from unit vector to (maybe) special euler angles on a machine tool

  1. Mar 13, 2009 #1

    I am trying to extract the 3 angles from a unit vector to position a part on a 5 axis milling machine:

    This machine has 3 linear axes (x,y,z), direct coordinate system
    It has 2 rotary axes:
    A turns about the x (called 'tilt')
    C is carried on the A axis (called 'rotary')
    See picture of an example of such machine.

    I want to machine a feature (ex: drill a hole) on a randomly oriented face
    My CAD software gives me the unit matrix of the 'local' coordinate system:

    x1 x2 x3
    y1 y2 y3
    z1 z2 z3

    See the 2nd picture:
    - blue face is the face (local xy plane) that has to be positionned parallel to the machine (brown lines) XY plane
    -The machine only has 2 rotations so the best it can do is to make the local coordinate system Z axis parallel to the machine's Z axis (spindle)
    Then I need to add the 3rd rotation by rotating (or mapping) the local coordinates around Z to express them in the machine's XYZ.

    I am able to extract the 'A' value:
    A=atan2( sqrt(z1*z1+ z2*z2),z3)

    In the example picture, the cube is 2x2x1
    In this particular case:
    A = 35.264
    C= 135

    That brings the blue face (or the local z axis) parallel to the machine's Z axis.
    But the part is rotated 180 degrees around z.
    I can easily rotate the coordinates with a rotation matrix. This is the 3rd angle that is not physically there (like an Euler type machine) but can be implemented via matrices.

    How do I extract the 'C' move?
    How do I extract the 3rd angle?

    Thank you,

    Attached Files:

  2. jcsd
  3. Mar 16, 2009 #2

    I found the answers, pretty easy actually after a few good nights thinking about it.

  4. Sep 28, 2010 #3
    I have this exact same issue. Could you, or someone, show how this is done? I can find the rotation of the A axis fairly easily, but I'm stuck trying to determine the C rotation.

    Thanks in advance,

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