Tailored Mail Sleeves
This 16th century mail shirt is on permanent display in the Medieval department of the Bernisches Historisches Museum . As you can see, its sleeves do not hang down straight, which you would expect if they consisted of simple mail tubes. Instead, they look exactly like sleeves of late medieval costume which feature a rather complex cutting pattern . They are tailored in such a fashion that they do not produce folds when a wearer lifts and bends his arms – like you do with the bulk of physical activities, be it eating, working or fighting. The biggest practical advantage of a costume like this is that, unlike with modern clothing,  arm movement does not result in any tear on the torso part of the garment. 

This seems to be the case with this mail shirt, too: One could move his arms freely without being restricted by the weight of the armour's chest part, even if additional armour, like e.g. a breast plate, was worn. And mobility is, of course, most important in fighting.

Also compare to this post.

See Daniel Jacquet work out in a perfectly reconstructed 15th century set of armour in this video .