To bend something is to make a curve become straight or a straight line become a curve, either with a material or one’s body. The past tense of this verb is bent.
Bended is the archaic past tense of bend. Currently it is mainly used in the phrase on bended knee. This phrase means to be kneeling, usually in front of someone to ask either forgiveness or to propose getting married.
Outside of usage in that specific phrase, bended is an error and bent should be used.
The phrase on bent knee is seen very rarely. While not technically incorrect, the preferred way to describe the same action is using the word kneel as a verb.
Yet over the years the EU has often bent the rules for a higher cause, such as the single currency (the debt criterion for membership was egregiously fudged for Belgium and Italy) or expansion to the east (Romania and Bulgaria were let in before corruption had been properly tackled). [The Economist]
Abbott obligingly went down on bended knee to secure a private tête-à-tête with the mogul, because why on earth would a multi-time zone eminence like Murdoch stand up to greet a mere politician on the cusp of the prime ministership? [The Guardian]
However all was righted when twice-married Geoff got down on one bended knee for a very public proposal at Melbourne Cup in November. [Daily Mail]
Police said the gun owner was carrying the pistol legally but that its safety switch may not have been on when he knelt to pray at the Cathedral of the Blessed Sacrament in the town of Altoona. [The Independent]