workholding chuck for DIY lathe?

So im building a treadle lathe, which will also function as a disk sander by sticking a 9inch sanding disk on it.

Only thing i cant figure out is work holding. I can buy a machined chuck for a lathe of course but then it costs $100 which i figure is almost half what i could buy a used lathe for.

Is there a DIY alternative or should i look for a parts lathe to grab the chuck from?

Treadle lathes normally hold the work between centres , the drive end has the drive 'dogs',  and one end has the 'loose' centre.

Thanks, John. Sorry, but I guess I'm not enough of a woodworker to understand your reply. I don't understand what centres and dogs mean in this context. I'm used to dogs being pegs in a work table concept but I have no idea how to apply that to a lathe in my head. Centres is totally new to me.

Here's a diagram that might help:

Here's another:

Here is a diy lathe chuck.

Well that explains it all perfectly, thank you!