Dale Larson shows how to turn an oval bowl in this video.
How it works
David Springett (author of Woodturning Wizardry) describes this device best in this video.
Elliptical Turning: An Introduction presented by David Springett [Woodworkers Institute]
Wes Pilley made one and showed pictures along the way on his Instagram page.
This is not a project that I would recommend for the weekend machinist.
More Information
Web Sites
John Edwards' web site, OrnamentalTurning.co.uk, really does a far better job explaining these devices than I could ever do, and there is also a lot of great information there which is worth reading.
Understanding the historical devices really helps make one far better at understanding and using today's rose engines. The newer designs for devices like a spherical slide still draw much from what was done more than a hundred years ago. And this is why so many books that were written up to 200 years ago are referenced in the section, How to Get More Information.
Disclaimer : eMail comments to me at OTBookOfKnowledge @ Gmail.com. The process of woodturning involves the use of tools, machinery and materials which could cause injury or be a health hazard unless proper precautions are taken, including the wearing of appropriate protective equipment.
Ellipse Chuck