TO不定式用法  to belong to?

似乎這題目的焦點不在於研究 dummy-it 或 empty-it 的結構, 而是探討 belong to 這 phrasal verb 的不定式的用法.

[動作的主詞] to belong to [動作的受詞]
這裡的不定式表示了動作的目的(purpose)或意圖(intention).
   [the dogs] "to" belong to [families]  ~ 狗隻 "去/要/想" 屬於家庭
= [families] "to" own [the dogs]        ~ 家庭 "去/要/想" 擁有狗隻

看看這句意思比較貼切的句子, 就會明白:
It is not so hard to find food for me to eat.  (to eat 就是尋找的目的)
~ 尋找我要吃的食物並不困難。

為什麽尋找想擁有(領養?)狗隻的家庭這樣困難?  (families that want to own the dogs)
 所以 to belong to 的詞性是副詞, 用以修飾動詞find.

(題外話, 我想補充一點,看來to find families似乎是形容詞hard的補語, 詞性屬副詞; 多於是名詞作為句子原本的主詞哩!)

infinitive--n,adj, is the form of the verb that can used after other verbs and with to before it., such as to in belong to; to in to find.
We can identity the same meaning of the sentence Why is it--->It is from their meaning and their introductory word=It is.; grammatically:-eg:-
It is so hard----S+vt
to find families-----noun/inf.phr.(a verbal)
for the dogs----O, a phrase
to belong to----to-infinitive is the object of the verb "is" of reason/cause; purpose, result, condition, concession.( also a verbal)belong to vi means be the property of; be a member of' be connected with; have as a right or proper place of the adopted owner of the DOGS.

to find families是「不定詞片語」，作為本句的「延遲主詞」（delayed subject），屬「名詞」性質，因為它加上後面的「受格補語」（to belong to）後，太長了，所以用「虛的主詞」it代替，將真正的主詞延後，以免句子結構頭重腳輕，不易閱讀。

比較下列兩句：
不改裝的敘述句：To find families for the dogs to belong to is so hard.
改裝的敘述句：It is so hard to find families for the dogs to belong to.
改裝後的句子焦點可提早出現：主詞補語so hard是上面兩個句子的焦點。

families和dogs的關係也類似下面的狀況：
to find someone something: Will you find me my tennis racket?（兩個受詞：人＋物）
to find something for someone: Will you find my tennis racket for me?（一個受詞;物）
即：To find the dogs families to belong to is so hard.（兩受詞＋受格補語）
To find families for the dogs to belong to is so hard.（一受詞＋受格補語）

整個不定詞片語的結構：
to find xxx to belong to
不定詞（不完全及物性質）＋受詞＋受格補語
在上面這個不定詞片語當中，不定詞片語to belong to是「受格補語」（屬形容詞性質）。
介系詞片語for the dogs是用來帶出這個不定詞片語在邏輯上的主詞（dogs)，在文法上它是修飾不定詞片語to belong to的「修飾語」（將後面不定詞片語的語意範圍加以約束，屬副詞性質）。

下列的不定詞片語均是句子中的「受格補語」：
I want him to leave now.
The man begged the judge to change his mind.
They like him to help them in the garden.
You don't expect me to do such a foolish thing.

「修飾語」才有修飾的功能。「受格補語」只是補充「不完全及物動詞」（或動狀詞）的語意，使其完整（及物動詞雖有受詞，但整個語意不完整）。不定詞屬於「動狀詞」，保有動詞的這種特性。