Learn English – ny reason why we can’t use “I hope you to buy me a doll.”

“We use for + the -ing form of a verb to talk about the function of something or how something is used.”

This dictum from English Grammar Today might have two very different meanings:

• “To talk about the function of something or how something is used we must use for + the -ing form of a verb.”

  This is simply wrong. There are other ways of talking about these functions, even if we restrict ourselves to the constructions licensed by the verbs use and need: a marked infinitive, a subordinate clause introduced by in order that or so that or to the end of or for the purpose of. In fact, the quotation itself uses a marked infinitive with use for exactly that purpose: to talk about the function of, &c.

• “A use of *for + the -ing form of a verb is to talk about the function of something or how something is used.”

  This is quite a different matter. This talks about what the construction is good for—or one of the things it is good for, since it has other uses, such as specifying the reasons for an award or an arrest.

Context, context, context!

Sometimes the gerund and infinitive forms are interchangeable; sometimes they are not. Your examples above ("travelling", "dancing", "getting") are all examples of interchangeable usage. Here are examples where interchanging alters the meaning of the sentence:

"Travelling" vs "to travel":

• He remembered travelling to Canada. (He has traveled to Canada, and now remembers that.)
• He remembered to travel to Canada. (He was supposed to go to Canada, and then he did.)

"Dancing" vs "to dance":

• She stopped dancing. (She never danced again.)
• She stopped to dance. (She interrupted an activity to begin dancing.)

How do you know when the gerund and infinitive are interchangeable? Generally, gerunds are best for talking about completed actions, and infinitives are best for talking about incomplete or future actions.

Gerund: I was getting up earlier last week. (The getting up already heppened.)

Infinitive: I want to get up earlier. (The getting up hasn't happened yet.)

Still, knowing which form to use requires some memorization and intuition. Here is a list of common verbs from http://www.gingersoftware.com/content/grammar-rules/verbs/gerunds-and-infinitives/:

Followed by a gerund:

admit, advise, avoid, be, used to, can’t help, can’t stand, consider, deny, discuss, dislike, end up, enjoy, feel like, finish, forget, get used to, give up, go on, have difficulty, have problems, have trouble, imagine, it’s no use, it’s worthwhile, keep, look forward to, mention, mind, miss, recommend, remember, quit, spend time, stop, suggest, understand, waste time, work at

Followed by either a gerund or an infinitive without causing a change in meaning:

begin, continue, hate, intend, like, love, prefer, start

Followed by a gerund or infinitive but with a change in meaning:

forget, remember, stop

Followed by an infinitive:

afford, agree, appear, arrange, ask, care, decide, demand, expect, fail, forget, hope, learn, manage, mean, offer, plan, prepare, pretend, promise, refuse, remember, seem, stop, volunteer, wait, want, wish

Followed by a noun or pronoun and then by an infinitive:

advise, allow, ask, cause, challenge, command, convince, expect, forbid, force, hire, instruct, invite, order, pay, permit, program, remind, teach, tell, urge, want, warn