Un coup de main

Every once in a while, you come across a word with a lot of potential. The French word coup is one of them; it is used in a wide range of expressions that seem mostly unrelated to each other, and sometimes even contradictory.

On its own, un coup just means a blow, a punch, or a bang.   Two very common expressions with coup are un coup de poing (a punch or "strike of the fist,") and un coup de pied (a kick or "strike of the foot.")   But here comes the confusing part: coup doesn’t always refer to violence.  As it turns out, donner un coup de main, (litterally to give a blow with the hand,) has nothing to do with slapping someone's face.  Quite the opposite: it means giving a helping hand.

If you want to minimize the level of help you need or would like to offer, you can also say that you're giving a helping thumb instead of a whole hand: donner un coup de pouce.

Really?  How can one word be used in such opposite ways?

Origin

We find references of prêter la main (lending a helping hand,) as far back as the 17th century.  At the time, there was clearly an expectation that the lucky recipient would return the favor down the road.  The expression developed into a more generous donner la main (giving a helping hand) in the 18th century.  What about un coup de main? Well, un coup was added in the early 19th century whenever you wanted to stress that the kind of help you needed would be a quick affair.

And that's why we hear so many expressions using un coup de in French today: they all refer to something quick.

Un coup d'oeil is a glance, un coup de foudre is love at first sight, un coup de tonnerre is a clap of thunder, un coup de téléphone is a (presumably quick) phone call, boire un coup means having a drink (again, presumably a quick one,) and tout-à-coup means all of a sudden.  The English word coup, from the French coup d'état, similarly refers to a sudden overthrow of a government. 
Totally unrelated expressions, all referring to something happening quickly or suddenly.

Examples

Tu peux me donner un coup de main pour mon déménagement demain?
Can you give me a hand with my move tomorrow?

Il a eu besoin d'un coup de pouce pour finir son travail.
He needed a push in the right direction to finish his work.