[Olivier]

If I understand correctly, you want to rotate the local reference frame around the robot base while keeping its absolute orientation?

1. Create a frame on the robot base.
   
2. Left click on the local reference frame holding the targets and do "change support" to the newly created frame.
   
3. Rotate the newly created frame 60 degree.
   
4. Rotate the local reference frame -60 degree to keep its absolute rotation value.
   
5. Left click the local frame and "change support" to its original parent.