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I found an example from an online dictionary as follows.

> 彼は私の手伝いをするのを露骨にいやがった。
>
> He showed a great reluctance to help me.

Because の in the relative clause「私の手伝いをする」 can be replaced by が, so

> 私が手伝いをするの

can mean "the help I do".

# Question

Can 私の手伝いをするの mean "the help I do"?

In other words, can the original sentence

> 彼は私の手伝いをするのを露骨にいやがった。

be translated as follows?

> He showed a great reluctance to receive my help.
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grammar translation relative-clauses nominalization
Can 私の手伝いをするの mean "the help I do"?
No, it can't. You can't replace が with の in your first example without
changing the meaning of the sentence.

That is to say, 私の手伝いをするの means "to help me" and 私が手伝いをするの means " the help I
do".
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> "Can 私の手伝{てつだ}いをする **の** " mean "the help I do"?

No, it cannot regardless of the context.

「私（の/が）する手伝い」 can.

> "Because の in the relative clause「私の手伝いをする」 can be replaced by が..."

But 「私の手伝いをする **の** 」 is **_not_** a relative clause in the first place; It is
only a nominalized verb phrase. Therefore, whatever works in relative clauses
is irrelevant here.

Let us take a look at a real relative clause here. How about:

> 「私 **が** 手伝っているお店｛みせ｝」 ("the store I help out at")

Since it is a 100% genuine relative clause, that 「が」 can correctly be replaced
by「の」.

> In other words, can the original sentence
>
> 「彼は私 **の** 手伝いをするのを露骨{ろこつ}にいやがった。」
>
> be translated as follows?
>
> "He showed a great reluctance to receive my help."

No, that would be an incorrect translation. The correct Japanese sentence that
would mean that would be:

> 「彼は私 **が** 手伝うのを露骨にいやがった。」
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One exception of so-called " _ga_ - _no_ conversion" is that you cannot use の
in place of が if there is を. Such ～の will be taken not as the subject but as a
modifier of the object marked with を. According to [this
answer](https://japanese.stackexchange.com/a/12829/5010),

> But you can't replace が with の if there's a direct object marked with を:
>

>> ジョンが本を買った店  
>  *ジョンの本を買った店 (ungrammatical)  
>  The store where John bought the book

As mentioned in the comment in the link, ジョンの本を買った店 will be taken as "the
store where someone bought John's book".

私の手伝い can mean not only "my help" but also "help for me" depending on the
context.

Therefore:

  1. 彼は私 **の** 手伝い **を** するのを露骨にいやがった。 → He did not want to help me. 
  2. 彼は私 **が** 手伝い **を** するのを露骨にいやがった。 → He did not want me to help him.
  3. 彼は私 **の** 手伝うのを露骨にいやがった。 → He did not want me to help him.
  4. 彼は私 **が** 手伝うのを露骨にいやがった。 → He did not want me to help him.

1 ≠ 2 = 3 = 4.
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