Some questions regarding ~てくる (edited)

Question

Up to now my understanding of ~てくる has been very vague. No matter how many explanations I read, in practice my translations always feel uneasy. Here are a few unresolved doubts I have:

• From what I understand ~てくる　signifies inception or continuation depending on the verb with which it's used. How can I tell which verbs entail which meaning? From what I understand the former meaning is more aligned with changes in state (なってくる, 分かってくる, 太ってくる, etc.), wheres the latter comes in to play with verbs that involve activity (like 押してくる　and 運動してくる).

  My first question is regarding "state verbs". When てくる　(as opposed to other tenses) is attached to words of this class of verbs the meaning is always "start to ~", correct? So "あなた、　いつか私を愛してくる” means "You will come to love me in time"; and "私は義理を感じてくる” translates to "I start to feel a sense of duty"? Can "感じてくる" not mean "continue to feel", that is, without the implication of inception?

  My questions concerning "activity verbs" (not really sure of the correct terms here) are much the same. "運動してくる" means "continue to exercise" and "押しこんでくる" means "continue to push in", I think. Is the concept of inception altogether absent? Would it be incorrect to translate those lines as "start to exercise" and 'start to push in" respectively"?

• I'm under the impression that when てくる is attached to a verb which indicates a process of change, inception is signified; whereas when it is attached to a verb that doesn't involve change (like　押す or 泣く) the indication is continuation. Could someone better explain the difference between verbs which entail either inception or continuation?

• When it comes to verbs which involve change ~てきた is usually translated to English as either has~ or has begun to~, for example, "私は太ってきた" is translated as either "I have begun to get fat" or "I have become fat". To me, those two translations offer two different meanings, yet I often see such translations used interchangeably regarding that verb and others like it. The former translation indicates a change has started and is continuing in the present, right? The latter states a change has completed and the results of said change are persisting in the present. Clearly I'm misunderstanding this kind of usage of ~てきた. Why are these differing translations used seemingly interchangeably?

While these aren't are all my doubts concerning ~てくる, they are the largest. Please help me better understand.

Answer 1

Note:I cannot guarantee the accuracy of the information below so take it with a grain of salt. Any comments that point out inaccuracies would be appreciated.

While I can't fully answer your question because I'm still learning myself, I can still provide some information that you don't know. I haven't found a textbook that goes into depth about the usage either which is very annoying.

Maggie does explain some concepts of the usage but in my opinions doesn't go into enough detaillink

I'm not sure how much Japanese you can read but anyway.

link 「～てくる」は、物理的に、また、心情的に、ものごと・状況などが話の中心点（ときに話し手であったり聞き手であったりします）のほうに近づくという意味合いを表します。

意志動詞（食べる、見る、する、など）に「～てくる」が付くと、「ある動作をして、また、話し手／聞き手のところに戻る」（見てくる。聞いてくる。上例（５））という「順次的動作」を表します。

また、（９）や「これまでずっと我慢してきた。」のように「動作の継続」を表すこともできます。

一方、(11)のように無意志動詞（落ちる、なる、など）に付くと、発話時までにおける「状態変化の出現」（例：寒くなってくる。少し太ってきた。世の中が変わってきた。）を表します。

The gist if you can't follow the above is that the different uses depend on whether the verbs are 意志 or 無意志 with verbs like 食べる、見る、する being 意志 and 落ちる、なる being 無意志. With 意志 verbs the usages would correspond to usage (2) and (4) from below and 無意志 would correspond to (3) and (5).

Here's the definitions from Excite. Try to read these definitions and then understand which usage these examples fall under(you can check which usage is which because it shows them on their website)

「台所で変な音がしたからちょっと見てくるよ」

「生まれてからずうっとこの村で暮らしてきた」

「いつも，ひとに迷惑をかけるな，といってきたはずだ」

「眠くなってきた」

「少年がこっちへ走ってきた」

「いけない，大事な書類をうちに忘れてきた」

「蜂が飛んできた」

「うちへ帰ってカバンを置いてきます」

「生まれてくる子供のために」

「出るとき玄関の鍵はきちんと掛けてきたはずです」

(1) 話し手の方へ向かって動作が行われ，その話し手の方へ近づく意を表す。

(2) （すぐに現在地に戻ることを前提にして）別の場所へ行って動作を行う意と，現在地に至る前に別の場所である動作を完了・実現した意を表す。

(3) ある事態が出現し，またある現象が現れる意を表す。

(4) 動作が継続・反復されて現在に至るまで続く意を表す。

(5) 事態が進行してある段階に至る意を表す。

I hope this comment will at least benefit you in some way although it won't fully explain the usage.

Answer 2

～てくる has those meanings.

1. to do something and come back here
2. someone does something toward the speaker
3. gradual change ([edit] or accumlation of acts)

So, 運動してくる makes sense only when it's used in the meaning of 1.

As for difference between ～てくる and ～てきた, the former means the gradual change progresses from now on, and the latter indicates a gradual change that started before now. If you stand in the course of the change, you can say either, though the focus is different.