Usually, infinitives with 'to' are used to indicate adverbials of purpose.
e.g.
- I go downstairs to collect my parcel.
- In order to keep warm, my dog curls up on the rug beside my bed every evening.
Can we use present participles as adverbials of purpose, as shown in the following sentence:
She telephoned saying that she was not coming this evening.
Is 'saying' an adverb of purpose, or an accompanying circumstance(attendant circumstance)? In other words, the action described with 'saying' is happening at the same time or to be on the safe side, roughly at the same time as the action 'telephone' .
Same confusion with the following example sentences regarding whether the present participles indicate purpose or just accompanying circumstances:
Tom has gone meeting his girlfriend. He wrote a letter inviting me to his party.
I'm grateful for your help!