For many years our units had a home on brackets mounted on an internal wall, kept in their "sets", but this was quite labour intensive when it came to changing them. They had to be taken manually from the wall to the machine, and then the removed units hung back up. Although greens units are not super heavy they are a bit awkward to carry. To overcome these problems I decided to mount the units on a trolley, the trolley can then be taken to the machine, the units changed with minimal carrying and the trolley then parked back in it's place or taken to the workshop for attention.
The trolley need not be "industrial strength or Russian built" and should be as small as possible with a "wheel base" wide enough to maintain stability. The ones manufactured in the workshop here are made mostly of 40mm box mild steel in the basic framework and 25mm box for the upright that the units hang on (see photographs); the brackets themselves are made from 30mm x 4mm flat bar. The wheels are not super duty and plastic is good enough on our very smooth concrete floors but you may want to go for slightly better quality if your floors are not as good.
You may be able to "recycle" the wheels from a super market trolley or similar, they are ideal and come with 2 fixed and 2 swivels, which is what's needed on your trolley. The lowest unit sits on the H frame chassis to keep the centre of gravity as low as possible.
You can see from the photo that the trolley is simple and skeletal in construction, nothing fancy; it incorporates everything that's needed and nothing more to make it heavier to move.