I was wondering where the forearm handshake came from. I found absolutely nothing in wikipedia, so I have no idea if this is really historically based or just a recent popular greeting. I was led to believe that it may have been used by european pre-roman age tribes.
The earliest reference I can find comes from a 1937 commentary on Shakespeare's "Julius Caesar", although there are many later references that this handshake was taught to the actors by Lawrence Alma-Tadema in a 1898 staging of the play. It seems to have been often used in this play since, and I could find an example from a 2005 staging.
Almost all references to it is from 2010 and later, which probably is because "cool" teenagers seldom go to watch Shakespeare in a theatre. So this handshake didn't become a "thing" until it popped up in TV and Movies. It seems it is the TV-series "Spartacus" we have to blame/thank for this.
However, there are no Roman era depictions of this handshake that I can find, and there are plenty of depictions of ordinary handshakes from the Roman era, so we have to conclude that it's attribution as a roman handshake is a later invention. That probably goes for the handshake itself as well, although that's less certain.
It's probably invented in the theatre to make the handshake look dramatic, and the prime suspect is Alma-Tadema himself, although this is pure conjecture.
The history section of the wikipedia article on handshakes suggests that the Greeks were familiar with the custom at least since the 5th century BC (because we have a sculpture showing Hera and Athena shaking hands that has been dated to the 5th century BC).
Romans also used handshake. It was depicted on Roman coins to symbolize agreement and compromise.
Here are two (not very good) references that attribute the forearm handshake to the Romans, if not earlier, along with other interesting background regarding the forearm handshake and similar variations on the common modern handshake:
Shaking hands is a relic of our ancient past. Whenever primitive tribes met under friendly conditions, they would hold their arms out with their palms exposed to show that no weapons were being held or concealed. In Roman times, the practice of carrying a concealed dagger in the sleeve was common so for protection the Romans developed the Lower-Arm-Grasp as a common greeting.
Unfortunately, these references don't bring reliable sources for their contentions, although I personally can attest to witnessing in NYC the variations cited by Jim Kent in the '60's and the Vietnam War era, and noting that they were new for that period. I always understood that such gestures are related to the gesture of reassuring or encouraging someone to be strong and stalwart by firmly grasping their arm or shoulder. The two parties exchange such a gesture, encouraging each other to be strong and united. This makes sense, given that this sort of greeting was particular to groups that considered themselves "comrades in arms", etc., and so perhaps this sort of thing hearkens back to some ancient form of warrior greeting. Admittedly though, this amounts to nothing more than interesting speculation.
I suppose I can lay claim to being a "primary source" on such a thing, and IMO, when we encounter such forms of greeting today, they date back to those 1960's forms, just as do many other contemporary customs and fashions.