According to Spinball Sports, there are several rolling utility carts that you can purchase from WalMart that should do the trick. Many people use them for shopping carts or for bringing equipment onto ball fields.
According to the manufacturer, the machine with the legs attached is about 5 1/2 feet tall. Unattached, the legs are about 40 inches long.
It is three feet wide with the legs attached and about 16 inches wide without the legs.
The depth would also be 3 feet with the legs attached but approximately 1 foot without the legs.
Frankly, I would purchase the machine and see if the inexpensive WalMart carts work before going to the trouble of engineering something, myself.