This is a 3 string instrument I designed that is similar to a soprano ukulele, but even smaller.

These models will fit on a Prusa Mini+ with minimal supports needed.

I recommend printing the body facing up with using supports only at the base of the body. You might be able to print the body with zero supports, but I used supports for that. The neck does need supports, but only on the connector part. gcode files will be included. 

Parts needed: 

• Soprano ukulele strings or similarly sized strings. The smaller the gauge the better. 
• You need a M4x20 bolt and a M3x16 bolt. One for the side of the neck and the other bolt for the back of the neck. You could use a 6mm steel rod, but its not needed. If you use a steel rod it needs to be around 230mm long.
  You will also need 4 - M1.7x6 self tapping screws. Two for the nut and two for the bridge. More if your geared tuning pegs don't come with screws.
• Generic geared tuners for ukuleles. You will only need three out of the 4.
   

The body and neck are both 180mm long so this instrument will fit perfectly on a Prusa Mini+ build plate with almost zero supports. Print time was around 12 hours for a complete instrument. No glue needed. 6mm rod optional, not needed.
 

How to assemble: 

• Insert the nut near top of the neck at the headstock. There should be two screw holes. Screw the nut into place and do the same for the bridge. You want the flat side of the bridge facing the sound hole. Slot the neck and body together.

• Connect both the neck and body. Make sure your tolerances are correct or things might break.

• Optional step: If you decide to use a steel rod, make sure its 6mm x 230mm and insert it from the neck into the body. Be careful and make sure the rod will fit in both the neck and body. Having a properly calibrated 3D printer is key. You do not want to break the instrument or harm yourself, especially if the tolerances for your printer are incorrect. 
   
• Screw both bolts into the instrument.
   
• For the headstock, you will want to have one geared tuning peg on the left side, one on the center, and one on the right side. Make sure the tuning pegs don't bump against each other or you will have a more difficult time tuning. You can use a small screwdriver to help make pilot holes. Again, be careful. Screw in the tuning pegs, one at a time.

After you are done, you can start stringing your instrument. If you are using ukulele strings, the strings may take a while to stay in tune, but that is normal for ukulele strings.

I also recorded a quick sound demo. I tuned this instrument in a open tuning, GBD (G major):
https://soundcloud.com/grhmhome-583373264/pico-size-3-string-instrument-sound-test-001-tuned-to-gbd

Update: fixed the bridge area by extruding the bottom by 2mm