prosthetic arm

i was wondering is it possible for one of my players to have a machanical arm and incorparate a sword or something into the arm so you can change from a hand to sword or is this not possible?

The DM word is final.  So if you the DM allow it it is fine.

This could be implemented on a purely flavour level. Mechanically go from unarmed to wielding a sword and just flavour it as the arm changing into a sword.

Since it'd be flavour and not mechanical, it's purely down to the DM*, as they try to police the feel and setting - if you're playing in a quasi-historical setting, you probably wouldn't want that. If you're playing something like Eberron etc, it should be fine. 

Since you appear to be the DM, you get to decide.

* Even if the DM had to change things mechanically to allow it, the DM still gets full discretion on the matter, but they'd have to consider the implications and whether it would be more or less fun for everyone.

There is a weapon called an armblade in Wayfarers Guide to Eberron, which is pretty much exactly what you're describing. By RAW, its only available to warforged, but I doubt it would be game-breaking to allow use by other species.

And, of course, there's the Prosthetic Limb magic item in the other Eberron book and also in the 24 DMG.

Seems like you could combine those into a homebrew item. The advantages I could see over a traditional weapon would be they can't be disarmed (but no one ever really does that, so no big deal) and they also would possibly be able to sneak a weapon into places where it might not be allowed, which campaign dependent may or may not be an issue.