Peerless lathes, as far as I am aware, all have the same collet style that Paul has explained. I’m also a little confused as to why you would have to unscrew the collet when the draw bar has been removed 
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When you first entered the collet into the head stock, did you slide it in all the way with the groove in the correct mating position, then slide in the draw bar and turn it clock wise until it was tight, turn the draw bar, NOT the collet :