Brushless motor control doubt....

Hi guys... Sorry, i'm newbie in electronics... Here are the details and pics.

My motor is a prosthetics lab brushless one, complete kit. Kind of a mini Dremmel. Bought over ebay. Meant to be built in (in one of my workbenches)

As I'm no expert, what exactly mean complete motor details, so I can try to find out more.

Attached are some pics of the control box and it's manual.

There's also a button to invert the rotation, and I'll also control it with the arduino through a 4066 CI. And of course, an on/off switch, on/off led... But the speed control is my goal now.

It needs 24V AC, so I bought a huge 12-0-12 6A transformer

I don't know how much of this 24V AC inside the control box gets transformed into DC, and how much of it powers the bldc..

Does this help? If not, tell me exactly what I should look for then I'll try to provide the details... I've got a small oscilloscope if needed.

I've got one more question...

As arduino is one circuit... And the motor set is another... When using the pwm-to-low pass filter set-up, I would need to make the grounds of both circuits commom, right? I mean, I would need to connect the arduino ground to the ground terminal where the motor's pot is.

Is this possible? Two different circuits, powered differently (even though they are dc at the connections points to the pot) sharing the same ground?

Thanks again for your help! I'm still learning at an older age...