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.
(..) - Little green ghouls, buddy. Don't write ghouls! I'm not. I'm putting travel. - Jesus Christ! What are your dislikes? - People's knees. Come on! Come on! You gotta be kidding. You know what? We'll make it up. We'll make the whole thing up. Let's get out of here! We'll doctor the picture. We're not even gonna use you. Cover your knees up if you're gonna be walking around everywhere. Where are you? Come on. Bingo, bitch. - Hey! (..)2009 TvShow: It's Always Sunny in Philadelphia Title: The Waitress Is Getting Married Season: 5 Episode 5