The rope trick works very well.
1. Remove nut and washer that holds sprocket onto shaft.
2. Remove center screw from tool and oil the threads on center screw.
3. Oil the threads on the tool and carefully thread it all the way in until it bottoms out inside the sprocket. Take your time as it is easy to cross thread the darned thing and you do NOT want that to happen.
4. Install the center screw of the tool back into the part you have threaded into the sprocket and tighten it well. The sprocket should either pop off or just slide off of the shaft as the center screw is tightened.
Keep a watchful eye out for the woodruff key (a half moon shaped bit of metal) and don't loose it. You will need to reinstall it when you install the new sprocket.
Edit:
Also, the tools have a hex on the outside of the portion that threads into the sprocket, gear or clutch to let you hold it with a wrench, preventing it from turning, while you tighten the center screw.
Using this feature of the tool allows you to use it without using the rope trick.