I recently got an old Kenmore Ultra Wash II (model number 665.1761591).
I tried to hook it up to my sink but discovered I could not. The
hookup mechanism won't grab onto the kitchen sink's faucet. I assume I
have to replace it with something.
Here's the faucet:
http://jbeall.com/personal/washer/Dscn0856.jpg
Here's the hookup:
http://jbeall.com/personal/washer/Dscn0860.jpg
The machine originally came with the adapter for the sink faucet.
You'll have to get a new one.

Bring the faucet screen screw-on thingie and the hose to a plumbing or
home improvement store. They'll get you the correct male/female quick
connect adapter for the faucet.