Yours definitely looks correct, and the "grabbed" example is definitely a comma splice. But I don't think it's the tense change that makes it correct, I think it's the -ing verb which is maybe a gerund and maybe another thingy. If you said "I run for the door, grabbing my purse as I go" that would also be correct, I think.
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Ok, I dug a little, and the part after the comma is apparently a participle phrase--"grabbing" is a participle in this case (there's a wikipedia article about gerunds vs. participles that's not extremely illuminating), and it's not a dependent/subordinate clause because it has no object. Here's a good page about it: http://www.siskiyous.edu/class/engl52/reynoldss/n_participles.htm
"coordinate verb phrase" may be a linguistics superset that includes participle phrases as well as other things--google doesn't find that term in any grammar handy-notes stuff as far as I can tell, but does find it in a couple of language description docs, including this pretty interesting PDF about the Telugu language of India.
I had some formal grammar instruction, but it was 1000 years ago, so it's mostly slipped into the abyss of memory.
no subject
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Ok, I dug a little, and the part after the comma is apparently a participle phrase--"grabbing" is a participle in this case (there's a wikipedia article about gerunds vs. participles that's not extremely illuminating), and it's not a dependent/subordinate clause because it has no object. Here's a good page about it: http://www.siskiyous.edu/class/engl52/reynoldss/n_participles.htm
"coordinate verb phrase" may be a linguistics superset that includes participle phrases as well as other things--google doesn't find that term in any grammar handy-notes stuff as far as I can tell, but does find it in a couple of language description docs, including this pretty interesting PDF about the Telugu language of India.
I had some formal grammar instruction, but it was 1000 years ago, so it's mostly slipped into the abyss of memory.