Ron,

I need your help on the use of participle modifiers. As per your posts on manhattanGMAT forums, you have pointed that the participle modifiers modify the subject and the action of the main clause. Here is the link to one such post -
https://www.manhattangmat.com/forums/pos ... tml#p46255

However, my doubt is that if a participle modifier does not accomplish the two requirements that you state in the above post, what does the participle modify? The noun before the comma or the main clause noun without any reference to the action of the main noun?

Listed is one such example for which I believe the rules do not apply and thus the participle modifies the preceeding noun

OG Q30 -
For members of the seventeenth century Ashanti nation in Africa, animal hide shields with wooden frames were essential items of military equipment, a method to protect warriors against enemy arrows.

A. a method to protect
B. as a method protecting
C. protecting
D. as a protection of
E. to protect

OA is C. How is 'protecting' modifying the entire action of the main clause? - there is no action!!!
I believe in this case protecting is modifying items of military equipment, the noun preceeding the comma.

These are a few examples to help me understand the usage of having(participle) modifier -

Ron substitutes for the absence of Stacey, having worked in the MGMAT for years.
I slept for three hours, having finished my homework.

The first example - Having clearly modifies Ron but does not seem to modify substitute - the main verb, as having worked means a completed action and not an ongoing action and thus this example would be a wrong use of having.

Second example - having finished clearly modifies I and the action of the main clause.

Could you please validate the use of having in these two cases and also whether having modifier always implies a completed action?

Thanks in advance.