You're in EU? Do all countries there really have unarmed police? I really found that surprising and baffling at the same time. I live in a third world country and none of our police here would be caught dead without a gun. (Whether the gun actually work properly is a different issue.)
Yes, many countries have special cops that sometimes do the job of a traffic warden and a kind of peacekeeper. These cops have tonfas, pepper sprays, handcuffs and in case of a real emergency call for backup. They're usually dealing with bums sleeping on benches, people urinating or drinking in public places and such stuff.
Different countries have many different types of policemen. For instance when I was in Germany there were a lot of patrols with dogs and automatic weapons.