You may be searching for a replacement Dyson DC14 cyclone top handle. You may call it a bin handle or a canister handle.
It is the handle you tend to lift the Dyson with. It is also the handle you would carry the cyclone unit with when it is removed from your Dyson.
These handles do not break as often as the ones on other machines, and when they do break, it is typically where the hinged housing that contains the pre-motor filter is situated. See the photo below for the bit that breaks.
You can see on the photo there is a bit of the handle missing. The bit at the front that locks the filter housing closed.
Dyson refuse to sell this handle on its own. They insist on selling you a full cyclone unit instead. This isn’t an unusual tactic for Dyson; they do the same with other models of machines with some parts that could be easily replaced by those with a practical inclination.
The Dyson DC14 handle comes in several colours; they are all interchangeable.
So, if you want to buy one, but don’t want to buy a full cyclone unit from Dyson, your only option is to buy one used. This will not only save you money, but it is green too. Get in touch with Manchester Vacs, the used and recycled Dyson parts specialists. They might just have one in.