Time your moves correctly. Always try to tap at the correct time. Also be careful about where you send the dots on each of the wheels. Eventually you will end up in very tight spots.

In many levels, it will seem that the wheels will turn at the same speed and have the dots placed at the same location, however this is not true. Spend time analyzing each level to view its details. When an opening appears on the lower wheel it also means that there is an opening on the top one.