Infinitive Constructions with um, anstatt, ohne zu
There are also a few infinitive constructions which are not linked to a particular main-clause verb or impersonal construction; they can be used in almost any situation where the secondary verb, that is the one in the infinitive, is contrasted with the main verb in one of three ways:
um .... zu + infinitive (in order to)
(an)statt .... zu + infinitive (instead of + gerund)
ohne .... zu + infinitive (without + gerund)
Again, these infinitive constructions could be replaced with subordinate clauses starting with the subordinate conjunctions ohne dass, anstatt dass, or damit (in order to). An infinitive construction of this type serves as a free adverbial addition to the main clause.
In all cases where the subject of the main clause and the subject of a subordinate clause is the same you may use the infinitive construction. To put it another way, it is only correct to use this construction when the subject of the main clause is the implied subject of the infinitive.
Look at the following sentences:
Sie gibt uns ihr Auto, damit wir nach Heidelberg fahren können.
Unsre Freunde haben uns besucht, anstatt dass wir sie besucht haben.
Er hat eine Geburtstagfeier organisiert, ohne dass ich davon etwas gewusst habe.
The subjects are not the same and no infinitive construction is possible.
Sie kauft sich ein Auto, damit sie leichter reisen kann.
The subjects are the same and there are two possible ways to use the infinitive construction:
Sie kauft sich ein Auto, um leichter reisen zu können.
Um leichter reisen zu können, kauft sie sich ein Auto.
Unsre Freunde haben uns besucht, anstatt dass sie ins Museum gegangen sind.
The subjects are the same and there are two possible ways to use infinitive construction:
Unsre Freunde haben uns besucht, anstatt ins Museum zu gehen.
Anstatt ins Museum zu gehen, haben unsre Freunde uns besucht..
Er hat eine Geburtstagfeier organisiert, ohne dass er mir etwas gesagt hat.
(same subject: two possible ways to use infinitive construction):
Er hat eine Geburtstagfeier organisiert, ohne mir etwas zu sagen.
Ohne mir etwas zu sagen, hat er eine Geburtstagfeier organisiert,
You see that the infinitive construction can precede or come after the main clause. The main clause does not change!
Although we do not use exactly the same constructions in English, good style also depends on being sure that the subject of a subordinate construction is the same as the subject of the main clause:
Good style: Without letting go of the rope, Marie climbed the cliff.
Bad style: Without letting go of the rope, the cliff was climbed by Marie.
Good style: She drove at top speed to get home for her father's birthday.
Bad style: The speed limit was broken time and again to get home for her father's birthday.
In English the first example of bad style is the famous "dangling participle"; so I guess the second would be a dangling infinitive. Do not allow your infinitive constructions to dangle without a clear subject!