to be frank with you, to make a long story short（长话短说）, to be exact, not to speak of(更别说), to say nothing of(且不说) Eg:
To tell you the truth, I’ve never heard of the book.
To be honest, I don’t quite like the dish.
To begin with, it’s too cold. Besides, we’ve no money.
To be frank with you, I like you, and should be glad to
give you any help I can.
He’s a nice person, to be sure.
To cut a long story short, he beat them one by one.
You’ve wasted eight hours’ time, to say nothing of the material.
分词的表现形式是通过悬垂结构的句意来判断的，但是要请注意，悬垂结构中的逻辑主语一定是后面主句中的主语，检验的办法就是用主句的主语很分词结构还原成一个状语从句。如：
① 时间
Looking up suddenly, Robert saw a rainbow in the sky.
Floating on water, a ship displaces an amount of water equal to its own weight.
Hearing the news that her son was rescued, she felt greatly relieved.
② 原因
Not knowing how to pronounce the word “plough”, the Frenchman looked up it in a dictionary.
Considering the importance of the experiment, they checked the result again and again.
Living in a remote village, we rarely have visitors coming.
③ 条件
This same thing, happening in the peacetime, would be a great disaster.
Unless meeting with unexpected difficulties at the office today, I shall be home early tonight.
④ 让步
Granting the achievements to be great, we have no reason to be conceited.
Walking and sleeping, he has the plan in his mind.
The chemical composition of water is H2O, whether being solid, liquid or vapor.
⑤ 结果
Their car was caught in the traffic jam, thus causing their delay.
We introduced a lot of advanced devices, thus saving much time and labor.
⑥ 目的
The people are working hard, striving to realize our country’s modernization.
We held a meeting, marking the anniversary of his death.
⑦ 方式（也称伴随）
They stood by the roadside, watching the parade.
She stood motionlessly vacantly, looking at the sea.
They sat together, studying carefully the design of the new project.
有些分词短语并不表示句子主语的动作，而是表示说话人的态度,作句子状语。如常见的有下列短语：Seeing that（由于，考虑到）, considering that（由于，考虑到）, taking everything into account/consideration（把一切考虑在内）, judging from/by, given（假设，如果，考虑到）, generally speaking, frankly speaking, strictly speaking, roughly speaking（大约地说）,considering, talking of, supposing（假设）, providing, provided, regarding, respecting, concerning. Eg:
Considering all the possibilities, I really believe that I’d prefer to make any change now.
Women, generally speaking, live longer than men.
Strictly speaking, I should not be here.
Judging from what you say, he ought to succeed.
His acting was remarkable, taking into account his youth and inexperience.
Considering the distance, he arrived very quickly.
Supposing she doesn’t come, what shall we do?
Given the general state of his health，it may take him a while to recover from the operation．
It seemed bad-tempered to send him away，given that he only wanted to take photographs．
注意：有些过去分词短语作状语，并不表示分词与句子主语是被动的关系，而是表状态，如：be dressed in, be faced with, be devoted to, be surrounded by, be separated from, be seated, be
determined to等。Eg:
Dressed in white, he looks like a nurse.
Separated from other continents from millions of years, Australia has many plants and animals that
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