Local to global transformation; end rotational displacments

[aa2105]

Hi
I am analysing some piping which starts off as being aligned with the global axis system (X Y Z). So axially its X, laterally is Y and Z is vertically upwards. Due to bends etc. the end of the pipe is in a different orientation though still in the same plane - now the local axis system is x y z. However, the software I'm using can only accept global values. I need to impose displacements and rotations at the ends of the pipe. For displacements, this is easy - its simply the displacement multiplied by the cosine of the angle which the pipe makes (lets call it theta) with the global X-axis.

However, I am unsure what to do for rotations. Clearly, as the pipe remains in the same plane the Z axis and z axis will remain unchanged. But X and Y have been rotated by theta.

Now if I want to apply a 1.5deg rotation at the end about the local y and z axes - how can I get the equivalent rotation in global terms?

I hope this makes sense... if not I can add some more detail.

Thanks in advance.

Kind regards,

Adders

 

[viscousflow]

If you could provide some sort of sketch for your setup that would be helpful.

This sounds like a simple DCM (direction cosine matrix) problem, with angles as a function of angles. The easiest way to start is to define axes from your point of interest and make fundamental rotations until you get to your global axes.

 

[aa2105]

Thanks for the early response - but are you sure one can apply the DCM for rotations?

I've attached a diagram anyhow.

Cheers.

A