Assume I want to say something like :
I called you to go out.
How a sentence with the same structure would be translated? Is there like a certain pattern or rule to it?
「出かけるためにでんわしました」 or 「出かけるのによびました」 ought to both be valid translations of that. It depends a little on the kind of going out that you're doing, but you can generally say "I did X in order to Y" with ために and のに.
http://okwave.jp/qa/q4740693.html has these descriptions (English translations mine):
「ために」は目的の理由？ - ために states the reason why, or the goal, directly.
「のに」は説明？ - のに explains the reason for the call.
I would interpret this as shifting the emphasis, with ために being weighted towards the goal and のに being heavier on the action that was actually taken rather than the reason it was taken.