τῷ with the infinitive signals an instrument, cause or manner as a satellite.
The infinitive, preceded by a preposition and an article, signals a satellite. The semantic role of the satellite depends on the meaning of the preposition in question.
From Thucydides onwards τοῦ with the infinitive (or accusativus cum infinitivo) signals a goal as a satellite.
The infinitive signals a goal as a satellite, usually with verbs of motion, striving, giving and receiving.
The infinitive, introduced by ἐφ᾽ ᾧ or ἐφ᾽ ᾧτε, signals a restrictive condition, and sometimes also a restrictive goal or result, as a satellite.
The infinitive, preceded by οἷος or ὅσος, signals a result as a satellite. This also applies to οἷός τε.
The infinitive, preceded by ὥστε (sometimes ὡς), signals a possible result as a satellite.
The infinitive, preceded by πρίν ‘before’, signals posteriority as a satellite. The main clause is usually affirmative.
The accusative signals a subject in an infinitive or participle clause.