It's a sort of four bar linkage which can be seen in this video (sorry aout the quality though) .

I have also made the linkage here (the lengths are all aproximate so have a play when designing your axe)
http://incredibots2.com/?robotID=dal...cff49.17217602

You could also try a chain based rack and pinion like the judge shown here:
http://members.toast.net/joerger/AskAaron/weapon.html
just Ctrl-F and paste this into the find box How were the chains attached to the weapon sprockets on 'The Judge' (without the speech marks).