It is common to hear people say “used to” to indicate that they did something in the past but no longer do; for example, “I used to play basketball.” How would “used to,” used in that context, fit into a sentence diagram? What part of speech is it?
This is more of a theoretical question, and so the answer depends a lot on what framework you prefer. “Used to” in this context is sometimes called a “quasi-modal” along with “want to”, “ought to” and so on. Some linguists consider them the result of a historical process called grammaticalization, in which common collocations take on their own somewhat idiosyncratic grammatical properties.
I think there are tests you can use to demonstrate that quasi-modals don’t behave the same way as infinitive structures (by making them questions, for instance), but this is not my specialty. However, I think a real infinitive use of “used to” would be as in:
(1) The saw was used to cut the wood.
I can’t find a good article for this right now, unfortunately. Maybe someone else knows of one?