I selected the square threads to make more realistic steam engine.
To make square treads is not difficult..
Rule #1: Make the threaded hole first and next job will be easier to trim the threads with needle file on the threaded bolt.
The top slide on lathe is not in use, carriage only to form square treads.
keep all tools sharp, use pocket diamond grinder in both coarse and fine grade to smooth out cutting surface (both rake and end clearance).
Allways handcranking the spindle when you are working with the small threads to prevent the work is spoiled!
Part #34
1. Drill hole 3,5 mm root diameter
2. Make the threading tool of old drill grinded (i used the old HSCO drill, you can use high speed lathe tool too) to right size 10/1" pitch = 2,54 mm pitch : 2 = 1,27 mm wide and 1,5 mm deep tool and the tool must have place to go into the 3,5 mm hole.
3. Thread up the treads in the hole 0,04 mm each time until the right size in main diameter is 5 mm.
4. The last work: Thread up the threads without change the measure on handwheel on carriage until all swarfs is disappeared due the tool is a bit flexing under work.
Part #55
1. The main diameter 3/16" and root diameter 1/8" showed as in drawning.
2. The threading tool has a wide at 1,29-1,3 mm (1,27 wide is not necessary on the bolt due we need the clearance in threads without jamming)
3. Thread up the treads on the bolt 0,04 mm each time until the tool is touching on root diameter
4. Tread up the work without change the measure on handwheel on carriage until all swarfs is disappeared due flexing bolt.
5. In case the part #34 can not go into the threaded shaft due the threads on the bolt is too wide (if the wide of tool was smaller than 1,27) : Use thinn needle file to trim the wide of the threads and take a test to fit the part #34. You can polish the sides in the threads to make smooth moving the reverse link.
I has Sieg lathe who has 0,04 mm for each mark on the handwheel on carriage. Your lathe can have other size for each mark, find out how much marks you need for each threading.