No common purpose between Germany and Japan? Other than adding territory, which was what they were both very keen on doing.

Both countries saw themselves as the dominant nation in their area and it was their expansionist policies that led both of them into conflict with their neighbours - Germany with France and the UK over Poland and Japan with the USA because (initially) of the desire to secure their eastern flank while taking over former French Indo-China and the Dutch East Indies.

The common pupose was that there were countries which would not agree to their expanding into any territories they thought they had the right to - namely the USA, the UK and France, and, of course the countries themselves - China, Poland, the Soviet Union.

Tha amount of actual co-operation between Japan and Germany was limited by the distance between the countries and the communications difficulties. But the Germans did send military secrets to Japan (rocket engines, radar) in exchange for strategic materials (rubber, tungston) by submarine.