How do I setup an Axis System by Euler angles?

[Tetragrammaton]

Hi all,

I am having a quite challenge here to measure and setup a complex, compound axis system (in Catia V5.19)

I have an existing axis which is explicit / isolated.

The challenge is to redfine it by using Euler angles since it has three distinct angles from absolute.

First I tried measuring each axii, starting with X axis of the isolate axis against the respective plane and/or axis of the absolute axis to determine the delta values to put in my Axis System Definition dialog, Angle 1, 2, & 3 fields (though the logic escapes me here somewhat).

EG: Measuring my x axis against the XZ plane it measures 72,613deg and 11,132deg up from the XY plane; when I check this in the top view i can immediately see it is not correct, there is a slight misalignment.

Measuring the isolated X axis against the absolute X axis i get a different measurement of 76,816deg; which now looks to be correct.

After which i cannot set another angle and get the 2nd and 3rd angles correct to bring next axis to match the original isolated axis??

It is not clear what the points of refences are even looking at the documentation under Common Functrionalities-Defining and Axis System
(A description from online help though lacking any significant substance or a working example to help clarification)
[ul]
[li]Euler angles: defined by three angle values as follows:[/li]
[li]Angle 1= (X, N)a rotation about Z transforming vector X into vector N.[/li]
[li]Angle 2= (Z, W)a rotation about vector N transforming vector Z into vector W.[/li]
[li]Angle 3= (N, U)a rotation about vector W[/li]
[/ul]


How do I measure the angles correctly and input those values in the Anlges 1, 2, & 3 fields?

My question is how do you determine the 3 angles initially, meaning what do you measure against what, what are your points of reference?
Do I measure the isolated axis/i or plane(s) against the respective axis/i or plane(s) all before I input any values into the axis definition dialog?
Alternatively do I measure one input the angle then measure the next as no matter what way I try it seems to always alter the axis (start with X) when i input the 2nd angle not matter if it is Y or Z?

Any constructive suggestions, tips advice that can help me with this dilemma would be most gratefully appreciated.


Best Regards

Tetragrammaton

 

[DaSalo]

Take a look at the wikepedia article on Euler angles. It gives a pretty thorough explanation and some diagrams. The key is that the sequence of rotations is critical. To take a rotated csys (csys B) and return it to the fixed (csys A) you do the following:

- Rotate about the Z axis of csys B by the angle between the X axis of csys B and the XY plane of csys A. This returns the X axis of csys B to being coincident with the XY plane of csys A.
- Now rotate about the X axis of csys B by the angle between the Z axis of csys A and the Z axis of csys B. This returns the Z axis of csys B to being coincident with the Z axis of csys A.
- Now rotate about the Z axis of csys B by the angle between the X axis of csys B and the X axis of csys A. This returns the two X axis to coincidence and completes the transformation.

So you have an X rotation followed by a Z rotation and then another X rotation. This is the most common convention for Euler angles. If you play around with it enough I'm sure you'll work it out.

CATIA V5 R20
PC-DMIS 2011 MR1