An engine variable camshaft timing phaser (10) includes a sprocket (12), three ring gears (26, 28, 30), multiple planet gears (24), and a sun gear (22). The sprocket (12) receives rotational drive input from an engine crankshaft. One or more of the three ring gear(s) (26, 28, 30) receives rotational drive input from the sprocket (12) and rotates with the sprocket (12), and the remaining ring gear(s) (26, 28, 30) transmit rotational drive output to an engine camshaft (62). All three of the ring gears (26, 28, 30) engage with the planet gears (24). And the sun gear (22) also engages with the planet gears (24). In operation, relative rotational speeds between the sprocket (12) and the sun gear (22) causes the engine camshaft (62) to advance or retard engine valve opening and closing.