Thank you Adam. Very clear explanation! I'd like to ask one more question. Is it compulsory for pupils or students to hand-write clearly in their papers?

Americans love messy signatures! Most of the signatures in the image you posted actually look pretty tidy to me, compared to some signatures I've seen. When I sign my name on legal documents, I write the first letter of my name very big, but then I write the rest of my name quickly. Celebrities and famous people often practice their signatures so that it's nice and smooth every time. There isn't really ever a situation where your signature needs to be legible. 99% of the time, your name is printed or typed somewhere else on the page for when people need to know your name. The signature is like you marking that you agree with the document. If you showed me random celebrity signatures, I probably couldn't read them unless you told me whose they were!