I'm not an authority on this but the way I heard the story told at least was that the shaking motion was meant to dislodge any knives or other weapons hidden up the sleeve. So if someone had a knife hidden up the sleeve of a robe or tunic and you were to shake their hand and therefore arm and they did the same to you, it would ensure that neither of you was armed and trusted the other to check you. You often see Romans doing a handshake where you grip the forearm rather than the hand (http://alison-morton.com/wp-content/uploads/2015/04/Roman-handshake-300x169.jpg) because the forearm is the perfect place to hide a knife (http://www.trueswords.com/images/prod/c/TS-CA2NDG2B_540.jpg). So it's a trust thing and proof that neither is carrying a knife.