How did the United States government happen to take the shape established by the Constitution?

historical influences on American ideas regarding: purpose of government, the form of government, and the concepts and ideals they wished to preserve.

I suggest you read the Federalist Papers. This book should give you an idea of the thought processes behind the Constitution. Sorry that is the best help that I can give to you.

http://www.foundingfathers.info/federalistpapers/

Read a history book, or look on History channel.com! Please educate yourself