There used to be quite a few in the past, and
this website will tell you all you need to know about the practicality. For theory read below here.
Basically for normal use the sidecar has to be a banking design, hinged alongside the bike, otherwise left turns with a light sidecar are impossible. In the past there were some common exceptions to this rule, for example many window cleaners used them, the sheer weight of the ladders and bucket etc keeping the sidecar firmly pinned down so rigid linking to the bike was practical.
The bike in the photo of the kids only succeeds because of the weight of the kids in the box and the lean in of the bike. That lean in is wrong though as it makes right turns extremely difficult. Sidecar geometry requires that the sidecar should toe-in a little at the front to ensure straight line travel is ok, and the bike should have slight lean-out for best handling, not practical for pushbikes with light sidecars.
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