Broken Knoll Pollock Chair Help  

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That could be repaired -- either by welding (maybe) or by applying a ring or wire or other annular (circular) hardware to each end of the broken cylinder. Take it to a metalworker or machine shop.

my exact thought SDR

Beat-up, cheap Pollocks sell...
Beat-up, cheap Pollocks sell on ebay/craigslist daily for little $. Buy one local and cannibalize the part that you need. If you are in/near an urban center it should be fairly easy. If not, you may have to wait a big longer.

Pollock - Goodwill
I actually saw a Pollock Executive (beat up fabric) the other day at a Goodwill for $6.50
Good luck!

Thanks guys. My buddy is a...
Thanks guys. My buddy is a welder and he said cast aluminum can't be welded. There is an aluminum alloy that may work. I guess you heat it up with a propane torch and it kinda solders the joint. Maybe I'll give it a try. The rest of the chair is mint so I'd really like to get it fixed. I'll post my results when repaired.

A new (used) part
would be better than a repair, no doubt -- and maybe cheaper, too, if another chair could be acquired for $6.50 ?

They come up all the time in...
They come up all the time in Austin. I have a brown leather one whose leather cracked and buttons pulled through finally. I was able to find another brown leather one with a broken arm and missing wheel for cheap so I could mix the parts into one working chair.
These chairs are so underrated. Super comfortable.

Yeah
You should be able to find a beat-up and/or fabric upholstered one for quite cheap.