How did balance of power affect the american revolution ?

The American Revolution made huge changes, but indirectly.

France got involved to kick the British while they were occupied with the Americans, and get back some of their losses from the previous war in India and the Caribbean. Instead, they lost even more in India and the Caribbean, and they went bankrupt, which led directly to the French Revolution and then Napoleon.

Although the European monarchs tried to put things back the way they were before, they had to fan the flames of nationalism to do so. This led directly to the unification of Italy and Germany, which drastically changed power politics. Also, Spain went into decline due to losing her American colonies (which was due to colonial reactionaries breaking away when Spain implemented Napoleonic reforms around 1820). So the European great power structure of Austria - Britain - France - Russia -Spain changed to Austria - Britain - France - Germany - Italy - Russia.