Fig.: to improvise, to talk or make remarks without prior preparation or planning, which implies saying whatever comes to mind at the moment

Quel giovane politico è un bravissimo oratore; riesce a catturare completamente il pubblico parlando a braccio: niente gobbo elettronico e niente copione

That young politician is a great speaker. He can totally capture his audience speaking off the cuffs in his own words; no teleprompter and no script

When the reporter asked the politician about an unfamiliar subject, he didn't lose confidence and readily gave an interesting reply straight off the cuff 

Quando il giornalista ha fatto una domanda su un argomento non previsto, l'uomo politico non si è perso d'animo e ha risposto in modo molto interessante, andando a braccio

The actor, suddenly struck by a memory gap, couldn't recall his lines, so he had to play it by ear and improvise

L'attore, colto da un vuoto di memoria, non ricordava la sua parte e dovette perciò andare a braccio

The office manager, called in by the director to deliver an unscheduled presentation to new clients, was taken completely by surprise and started speaking off the cuff, improvising the whole thing

Il capo ufficio, convocato dal direttore per fare una presentazione non programmata a dei nuovi clienti, è stato colto totalmente di sorpresa e ha dovuto andare a braccio 

When someone is asked to speak on short notice and doesn't have the time to write down a formal speech, he would scribble some notes on his shirt cuffs. Originated in the U.S.A., this expression dates from at least 1938