Seatpost: At least one make of cycle trailer (Cycletote) attaches here. We didn't look closely to this, but we can't help but think that being attached at the seatpost makes it more likely the trailer would tip over if the bike came down.
Rear Wheel Skewer: Most of the quality trailers seem to attach through the rear wheel skewer (quick release). You get a special hitch bracket that slides onto the skewer.
Whatever type of hitch, the pole from the trailer is supposed to be attached or unattached relatively easily.
I said "relatively easily", it does depend on manufacturer.
The standard Burley hitch (see manual) To be honest, I looked & looked, and I still don't quite understand how the Burley hitch works. I think it requires turning something (a knob?) to tighten down to the chainstay; there is no need to buy a separate hitch for each potential towing bike, at least, this is a big plus. But I have problems (weakness) in my hands; tightening down a hitch in cold weather is really difficult for me. Burley do an alternative hitch (which you pay for, of course) rather like the Wike one (see next); you would need one alternative hitch for each bike to use with it.
The Wike hitch has a lock bolt on thin metal (bail wire) rings; I would expect these to wear quickly, possibly break & certainly hurt my fingers after a while. At least 2 hitches come included with the basic price of a Wike trailer, though.
Chariot: like the Wike hitch, but bless 'em, they don't use bail wire for the locking bolt, they use a canvas strap; bliss!
Also, you need one of these special hitch brackets for each bike you tow the trailer. The brackets can be moved from one bike to another, but it's a faff; for instance, the bracket may come with its own long skewer (quick release). Not sure but I would imagine when you take the trailer bracket out, the skewer is too big for what's left of your axle, might render the rear wheel non-functional unless you get some big spacers in there. Am not sure about all this!
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