Rotating the coordinate system for the payload

Hi,

I got the weight, payload center and payload inertia for my EOAT. However, my EOAT is rotated 75 degrees around the z axis relative the robot coordinate system

To translate the payload center to the new coordinates is straight forward:

x' = x.cos(v) - y.sin(v)

y' = x.sin(v) + y.cos(v)

z' = z

What I can't figure out is if this formula is valid for the payload inertia too. Using it gives reasonable values but I think it is wrong.

Help would be appreciated.

Thanks for the answer.

Sure, but my question is still valid.

My problem is that the EOAT has been rotated on the z axis of the robot, i.e. in the xy plane. I do not have access to a CAD model of the EOAT.

If the EOAT had been rotated a full 90 degrees it would have been simple to just swap the x and y axes. But 75 degrees requires some trigonometry skills that I lack.