One disadvantage of replacing the leadscrew on a lathe with a
hydraulic cylinder would be that the length of the lathe would
probably need to be doubled (close). I tried to find details of how
the Sheldon tape lathes were made, but was unsucessful. Finding
details about how such machines are constructed is difficult, but I
was happy to find out that they exist.

As far as the criticism of stiffness between mechanical and hydraulic
systems, I believe that one only has to compare mechanical and
hydraulic presses. I think it's a matter of proper design to get what
you need.

Finally, I found a 2006 description of a CNC machine made by a German
company (Schutte) using electrohydraulic axes with a bed resolution of
0.1 microns (1 micron accuracy at the tool).

Here's a link:

http://www.productionmachining.com/a...lti-world.aspx

Here are excerpts:

... In 1996, Schütte made the decision to go with electro-hydraulic
axis drives for all end-slide and cross-slide actuation, replacing
cams. Speed, power and accuracy were the motives for this decision and
fit into the company’s multi-spindle philosophy.

As the name implies, electrohydraulic drives use a combination of
hydraulic fluid and electronic control to move an axis. Hydraulic
fluid provides the motive force, and electronics, in the form of valve
control and linear feedback, provide precision control of the
motion.....


A key to successful use of electro-hydraulic drives is precise control
of the valve that allows hydraulic fluid into and out of the cylinder.
It controls the force, speed and distance traveled.

The valve, in turn, is regulated by a processor. The valve and
processor system was created in conjunction with Bosch to give finite
measurement of fluid movement in the shortest period of time. In
addition to the hydraulics and electronic processor, each slide is
equipped with a linear scale to give actual position feedback to the
processor. The digital feedback loop operates at 800 Hz, feeding back
the slide position 800 times per second.....

“Multi-spindle applications have always been associated with high
cutting forces,” Jim says. “Form tools and drilling operations are two
prime examples of where feed power and cycle time intersect. The idea
is to rough out the part as fast as possible and then bring in the
semi-finishing and finishing operations. We believe the machine must
be capable of power for the roughing and finesse, such as single-point
turning for finishing. Electrohydraulic actuation gives us both.”

Also, the system is capable of delivering the close-tolerance
specifications necessary for shops to be competitive. “Our
electrohydraulic axes have a resolution of 0.1 micron. That resolution
delivers a usable repeatability of 1 micron at the tool,” Jim
explains. “That tolerance is necessary because of the changing nature
of the work being run across the multi-spindle. Close-tolerance
machining capability, along with processing flexibility, is in demand
to eliminate the need for secondary operations. Customers want to drop
parts off the machine complete, and that ability starts with
accuracy.”