Definitely Swiss Screw Machine Collets. check out the Hardinge Tooling website.
www.hardinge.com I have no idea as to what size or machine configuration, but definitely Swiss Screw Machine. More than likely an old Nakamura-Tome early 80's. Could also be a Cam style Brown&Sharp Swiss too. Now I miss my Tsugami and Star even more.
What your seeing in the front where the tools are is a Guide Bushing, about 3-4 inches behind it(depending on the Z Axis Stroke) holding the bar stock is the Spindle Collet. The Guide bushing is stationary and so are the tools X and Y are in and out A and B are up and down. The Z is always Positive respectively unless you want to position a tool in front of the Bar Stock without cutting it is Z(-) Negitive. Fun Machines really as all parts are complete with out any secondary operations. Turning, Milling, Cross Drilling at any angle you can imagine. You setup/program/proveout/walk away and check every hour. Holds .0001 all day even in Inconel X750.