Political machines created cycles that turned, like gears.
Assuming the underlined word is 'singing,' the correct answer is going to be A. participle.
A participle and a gerund look the same - they both end in -ing. However, participles are used as adjectives (as is the case here), whereas gerunds are used as nouns. Infinitives always have the same form, which is TO + verb.
B: Cortes and his army arrived in Mexico from Cuba!
Hope this helps! :D