This creative coupling solution comes from another generous user of the site. He has devised a way to couple the motor to the leadscrew with standard aluminum tubing. Marc has graciously allowed me to show you this creative idea.

From Marc K.:

As I said it's now time to mount the steppers and lead screws to the machine. I've developed the poor man's coupler using aluminum tubes of different diameters. Those found at a local store fitted perfectly together. I've taken 3 tubes of 6, 8 and 10mm inner respectively 8, 10 and 12mm outer diameter. I've cut 2 short pieces of the 6 and 8mm tubes and a longer piece of the 10mm tube. The stepper shaft is 1/4" so I had to bore the 6mm up to 6.4mm. The lead screw I use is M10. The 3 tubes are put together. 2 holes taped at M4 with 2 srews hold the plate part of the steppers shaft. 1 hole taped at M4 goes all through the big tube and the end of the leadscrew. Voilà!.

The fit on the stepper shaft is perfectly tight. The leadscrew fit is very little loose which helps compensating alignment errors. An upgrade I immediately foresee before installing the couplers is to bore up the lead screw to 6mm and putting a small piece of rubber or plastic tube in that hole. The M4 screw then goes through the rubber tube. That should add damping and reduce the noise.

The screws I use here are all refurbished, that's something I've learned from my dad ;-) ... "Don't throw that away son, You might regret it".