That's not the gerund. That's its identical cousin, the participle. If it were a gerund, then you would use the genitive form "my":
- The likelihood of my doing this is small
In this example, "doing this" is a gerund phrase. "My" modifies the gerund phrase. The modified gerund phrase is the object of the preposition "of".
- The likelihood of me doing this is small
In this example, "doing this" is a participial phrase. Participial phrases can modify nouns. This participial phrase modifies "me". The modified objective personal pronoun is the object of the preposition "of".
Because there's no visible difference between the gerund and the so-called present participle, it almost looks like "me" and "my" are doing the same job. They aren't. The "me" acts as a modified object; the "my" acts as an object modifier. Of course, in both cases you end up with some modified object for the preposition "for". The overall meaning of each is much the same, and the choice between them is often no more than a question of stylistic convention.
If it helps, my personal preference is for the gerund construction. I prefer the action, rather than the person, to be the literal object.
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
Best Answer
I assume your confusion comes from failing to distinguish two different words spelled to.
The examples in your question aren't exceptions. They contain the preposition to:
In each case, the -ing form of the verb is what is traditionally called a gerund. When the verb is in its gerund form, the clause as a whole functions very much like a noun phrase.
Each of the bracketed phrases is a preposition phrase.
This should be distinguished from the infinitive marker to:
In each of these examples, the bracketed portion is a to-infinitival clause.
The word to in these examples marks the clause as infinitive; the -ing form is not possible here.