Gday Donna,
Turret lathes sometimes-called capstan lathes because the horizontally rotating, indexing tool holder on the lathe bed resembles a ships capstan winch for hauling up the anchor (canvas sails, sweating sailors, Errol Flynn type movies)
As you see from the pictures at
http://www.machineryvalues.com/xdetails.cfm/QN/132016, turret lathes can be large ungainly pieces of machinery, but are still useful and cost effective if you have the space and the right sort of work for them. I have seen older electric-hydraulic, automatic turret lathes in good condition sell for as little as (Australian) $1000.00 because their peg-board programming system was considered too slow and inflexible.
I have seen, and used smaller hobby type lathes set up for repetitive operations; some even have turret type tailstocks available as accessories. This would be my recommendation, unless you wanted full automation.
Other options for jacket trimming, if you want to partially automate the process, would be one of the earlier desktop CNC training lathes, but I dont think they would be much faster than a dedicated hobby lathe set-up.
If you would like me to elaborate on anything I have mentioned, just ask.
Lots-a-luck,
Paul