There are many possible options for making a lathe. Typically, a lathe is run by a spindle at the head stock (which you can find here https://buildyourcnc.com/SpindlesAndAccessories.aspx) which will rotate the object rather than a fourth axis, however you will need to create or buy the clamp mechanism of a regular lathe to hold the object in place. You will be able to control the on/off either manually or via software, but the speed (RPM) will have to be controlled manually.
You can create a more indexed alternative to a lathe by using our rotary axis at the head stock (found here https://buildyourcnc.com/item/axes-4th). either way, the tail stock center can be found here https://buildyourcnc.com/item/axes-4th. This will give you full control of the turning via software.
You will want to use linear rails and their associated bearing blocks (found here https://buildyourcnc.com/item/mechanical-rails-HIWIN-Linear-20mm and herehttps://buildyourcnc.com/item/mechanical-rails-linear-guide-rails-20mm) to run along the length of the item being turned and you will need linear rails to be run perpendicular (towards and away) to the object being turned that would hold either the blade (for a traditional lathe) or a spindle (for the indexed version containing the rotary axis).
Where you have linear rail, you will also need lead screw (found here https://buildyourcnc.com/item/mechanical-leadscrews-lead-screw-!5-5-starts-10-tpi) to transmit motion using motors (and drivers) of your choice also with various options (found here https://buildyourcnc.com/category/nema and here https://buildyourcnc.com/category/driver). You will need 2 - Drivers (either 3.0A or 6.0A, the 6.0A driver will be for our larger motors hence you will have more torque available) and 2 - Motor's (either our Nema 24's or Nema 34's, the Nema 24 will work with our 3.0A driver while the Nema 34 will work the 6.0A)
To control these motors, you will need a parallel breakout board and Mach 3 software to control the two axes (or three with the rotary axis) found here https://buildyourcnc.com/item/electronicsAndMotors-parallel-breakout-relay and https://buildyourcnc.com/item/control-SOFTWARE-mach3.
You will need couplings to couple the lead screws to the motor shafts (found here https://buildyourcnc.com/couplings.aspx). All of the miscellaneous hardware you need can also be found here https://buildyourcnc.com/Hardware.aspx.
Click the link to respond:
CNC Wood Lathe project - Would like to have the guts to a 2 axis DIY lathe. Can you let me know of a possible one stop shop solution? Would like it to be at least 40" on the X axis.