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.
(..) Well, maybe just a cigarette more Never such a pleasure before I've got to get home But, baby, you'll freeze out there Say, lend me your comb It's up to your knees out there You've really been grand I thrill when you touch my hand But don't you see How can you do this thing to me? (..)2003 Elf