This is a YouTube video from Chuck Bommarito (aka, outsidescrewball) showing a Leinhard Rose Geometric Chuck in use. The video is a bit long, but does show the chuck well, as well as a piece made on it.
Frank Dorion gave this lecture on the design and functions of a geometric chuck. He also built an oversized wooden model of one, helping to explain it's function. This is one of the best overviews presented to date.
More Information
Published Articles
Geometric Turning: The Manufacturer and Builder, by (unknown). OTI Newsletter, Volume 20, No. 1 - Spring, 2013, pg. 5
The details are difficult for me to explain, and are far better explained by John Edwards' document. John captured this and more in what he calls the "Holtzapffel Volume 6", which you can get from the The Society of Ornamental Turners.
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.