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.
(..) - Which hospital? - Whichever one Jim Gordon's in. - I have seen worse cartilage in knees. - That's good. No. That's because there is no cartilage in your knee, and not much of any use in your elbows or your shoulders. Between that and the scar tissue on your kidneys, (..)2012 The Dark Knight Rises