The phrase to keep and bear arms contains a compound infinitive and the common direct object of both parts. The branching used for the compound infinitive is closed on the right to allow the diagram to show that both keep and bear have the same direct object, arms. 2. The participle being is a linking verb. A subjective complement, a.k.a. predicate adjective (in this sentence, the word necessary) is preceded by a diagonal drawn from upper left to lower right and stopping at the horizontal line.
The phrase beginning with "a well-regulated militia" and ending with "a free State" is an absolute phrase, a.k.a. nominative absolute. A nominative absolute consists of a substantive (a noun or noun substitute) and a participle and has no grammatical connection with the rest of the sentence. The nominative absolute is identical with the Latin ablative absolute, except that the substantive component of the latter is in the ablative case. An ablative absolutes usually consist of a noun and an adjective. The adjective is often a participle (present like running, or past like done). Example: God (noun) willing, (adjective) their freedom will be preserved.
Lesson over Common Core.