An engine variable camshaft timing phaser (10) includes a sprocket (12) and a planetary gear assembly (14). The sprocket (12) receives rotational drive input from an engine crankshaft. The planetary gear assembly (14) includes two or more ring gears (26, 28), multiple planet gears (24), a sun gear (22), and a wrap spring (76). One of the ring gears (26, 28) receives rotational drive input from the sprocket (12) and one of the ring gears (26, 28) transmits rotational drive output to an engine camshaft. The sun gear (22) engages with the planet gears (24). The wrap spring (76) experiences expansion and contraction exertions to permit advancing and retarding engine valve opening and closing, and to prevent advancing and retarding engine valve opening and closing.