PURPOSE: FOR + noun phrase, (IN ORDER) TO + infinitive clause, etc.

There are three basic "a por, para,  para que" (purpose) structures in English. The most important thing: for to do is a typical mistake, but it simply doesn't exist! Look:

[a] I went to the market for some fruit.

[b] I went to the market to buy some fruit. 

[c] I went to the market so that he could buy some fruit: he didn't have enough money.

[a] is not followed by a subordinate clause, but just a noun or noun phrase;

[b] is followed by the infinitive in Spanish;

[c] is different in that there is a new subject, and so that is used in English, and "para que" in Spanish.

It is more complex and varied, but these above are the 'three basics'!

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In order to and so as to are the common,  more formal equivalents of to in this context.

I got up early in order to have time to pack.

We went via Worcester so as to miss the traffic jams.

He stopped for a minute in order to rest.

In negative sentences, in order not to or so as not to are used; the infinitive alone (not to + base form) is not usually correct when you want to convey purpose.

I’m going to leave now, in order not to miss the beginning.

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So that can also be used, secondarily, with the same subject.

James took my golf clubs so that he could play at the weekend.

(= in order to be able to play …)

The that in so that can be omitted in an informal style, and in this case the ‘appearance’ is that of the typical so (the common, informal equivalent of therefore, consequently, as a result …). In other words: so that never means consequently, but so usually means consequently and sometimes so that (purpose, not result).

We ought to write to him so (that) he doesn’t/won’t feel we’re hiding things from him. [purpose]

We’ve already written to him so I don’t think he feels we’re hiding things from him. [result]

So that is followed by thre Present or Future Simple when the meaning is future, and by a past modal verb form (normally, should, could or would) in past sentences.

I’m going to make an early start so that I don’t/won’t get stuck in the traffic.

We talked to the shy girl so that she wouldn’t feel left out.

He really hurried to the meeting so that we shouldn’t have to wait.

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The 'second' "para" + infinitive is for + -ing. This is used for expressing the specific purpose of something, what something is used for, etc". 

I came here to show you [the typical structure] that this machine is for improving our production.

It is also possible to use ‘to improve our production’ here, anyway.