He was forced to ask for their help 'on bended knee'. [=he was forced to beg for their help; he was forced to ask for their help in a very humble way]
If you want to clean the floor properly, you have to 'get down on your (hands and) knees' [=you have to kneel down on the floor] and start scrubbing.
She 'dropped/fell/sank to her knees' [=she knelt down] and begged for forgiveness. = She 'got down on her knees' and begged for forgiveness.
(..) Come here. Please, son. He still has the one good eye. I suppose he's lucky... ...not to be completely blind. We get down on our knees and thank God for that much at least. Right, Caleb? Okay, go on in now. That dog attacked my boy for no reason. (..)1999 The Green Mile
(..) TOOT-TOOT: Walking the Mile, walking the Mile... ...walking the Mile, walking the Mile, walking the Mile... ...walking the Mile. I'm getting to my knees. I'm praying, praying. Lord is my shepherd and so forth and so on. I'm sorry for all the bad shit I've done and people I've tramped on. (..)1999 The Green Mile