Here's a homemade wooden pivot lathe, made for polishing the arbor pivots of clocks. The clock wheel is held between centers. The left center is a fixed (dead) center made of steel,while the right center is a wooden half-bed center, made from a dowel stick.
A wooden driver pulley with an internal brass bushing turns on the left fixed center, which has a cone machined in the end. The driver drives a crank, which fits through the windows of a wheel; or it can also drive a pin which pushes a dog attached to the clock
arbor.
The open half-bed center permits filing and burnishing the pivot with a pivot file. The half-beds are merely dowels drilled to pivot diameter, then cut down to half-thickness, or a little less, on the end.
Details for working pivots using wooden half-bed centers can be found in the writings
of JM Huckabee.
The tailstock can move along a groove in the bed, and is locked in place with a through-bolt and a wing nut.
This adjusts for different clock arbor lengths. The dowel half-beds are held in
the tailstock with a thumbscrew, which permits changing dowels which have different-sized
half-beds. Half-beds for small pivots must be made from brass.
It has a counter shaft made of a piece of 5/16" steel. The counter shaft has male cone centers cut on the ends which run in female cone centers cut into the ends of threaded beaings. The threaded bearings are threaded into the oak of the supports and so are adjustable. (You can make good threads in oak.) There is a locknut threaded onto each bearing.
The pulleys are wooden, home made.
The motor is screwed to a piece of plywood, which is hinged on the front, thus using the weight of the motor to keep the belt tight. There is a wooden wedge under the back of the motor board, which permits belt tension adjustment. The belts are leather bootlaces.
The entire countershaft is mounted on a piece of 1/4" plywood, which can be
adjusted forwards and backwards to adjust tension on the front belt.
The motor is an ordinary sewing machine motor. I use it with a rheostat for speed control.
I used this little lathe exclusively for several years to polish pivots on American clocks. It's fast,
and works well.No doubt, with some imagination, a hollow center could be made which would permit using this little lathe to re-pivot and perform other operations. Likely, the lathe is too springy to permit turning -- but perhaps not! I haven't tried it.
It has a small, built-in drawer for keeping centers and other items.