An Eccentric Chuck is used for holding an object off-center from the axis of rotation. On high speed lathes, great care must be taken to balance the work when running eccentrically, but, on an rose engine lathe, the rotation is significantly slower so this is not an issue. That is why home made versions are so easily made.
The eccentric chuck shown to the left could also be inclined as shown, making it somewhat like an oblique chuck.
Jon Magill demonstrated the eccentric chuck shown below at the 2016 AAW International Symposium in Atlanta.
Some modern eccentric chucks designed for higher speed lathes include the ones left and right, but they can certainly be used on a rose engine lathe.
Bill Ooms made one using Corian. This video shows how he did it.