A fair number of years ago I interfaced an early inkjet cartridge from HP (it was a 12 dot unit from the ThinkJet printer line) to a microcontroller. In that case the jet drivers in the cartridge were simply resistors in the cartridge. I connected the common connection to +12V and each of the 12 selects to a channel of a DS2003 darlington driver chip. Software then handled all of the timing of the drive signals to make the ink come out in dots at the right times.

The most complicated part of the project was trying to figure out the best way to connect to the cartridge itself. I suggest that you look inside the printer that is common with the cartridge you have selected. Study the HP cartridge carrier carefully and implement the cartridge clamp and contact cable design as similarly as possible (without infringing patents of course). (We did not follow that advice and had one heck of a time coming up with a relliable design).

I do not know if the same holds true today, but back at the time of the project I did I was able to obtain full data sheets and technical information (including mechanical drawings) for the ThinkJet cartridge from HP. They seemed "more than willing" to support any effort that promoted the sales of their cartridges!!

If you are doing a one-up home project out of interfacing to the cartridge then I would simply disembowel an old printer and connect your new circuit to the end of the existing cartridge flex cable.

Best of luck.
Michael Karas