Hi,
Regarding the falchion, taken from "The Archeology of Weapons" (Oakeshott)....
"One of these weapons is the falchion. This is a development from the old Norse sax, particularly the long Norwegian sax, which was popular all over Europe during the eleventh and twelth centuries, as we can see by its frequent appearance in manuscript paintings. During the thirteenth century its form altered considerably: the blade became extremely broad at is "optimal striking point." ............ The blade of the falchion from Thorpe differs from the Durham and Chatelet ones for it is very similar to a sabre blade. How this blade form developed is not clear; we rarely see it in manuscript pictures before 1290, and it seems to have no direct kinship, like the Durham type, with the old Norwegian long sax. It may have developed under an Eastern European influence, for it is very closely akin the the Sword of Charlemagne - the Hungarian one - in Vienna, a type which had been in use in Eastern Europe since the ninth century. Whatever the origin of its particular form, as a falchion it is still a direct descendant of the sax, the Greek kopis and the ancient Egyptian kopsh, and its form remained in use from the early fourteenth centruy till the mid-eighteenth, with modifications, while the Durham type (the machete on steroids) is seen no more after about 1300."
Hope that helped,
Lamont