https://m.youtube.com/watch?v=V1IMmLDa1Po

This maybe how it works and should help you program it

I know this is an ancient thread, but I am working on a similar machine, just with a 6 tool umbrella.  Did you get this working?  If so, can you post the code? 
I'm modifying the code that CNC4PC has on their site and have the basics down, I think, but I need to get the umbrella rotation and counting worked out.  Also, it'll need to be homed in the machine homing script, but I don't think that'll be too bad.

Thanks!

Mike

I used to do the programming for one of those back when they were new! It was challenging to load large tools because the distance from the tool load button to the spindle was just about the length of both arms stretched out straight. I hope you manage to resolve that issue.