Gerund with and without "of" preposition

Question

Could you please explain the difference between using of a gerund with and without "of" preposition?

For example what is the difference between following sentences:

1. I've worked on improving of the article.
2. I've worked on improving the article.

Answer 1

With "of" before a logical object, an "-ing" form is not a gerund, but is rather a derived noun. A gerund, being a verb, does not allow an article, but the "-ing" noun does, and your first example, which is not grammatical as it stands, is improved by adding an article:

?I've worked on the improving of the article. ("improvement" would sound better)

However, if you try adding an article before the gerund, the example gets much worse (because verbs don't take articles):

*I've worked on the improving the article.