A transmission mechanism includes a planet gear, a set of sun gear teeth and a set of ring gear teeth. The planet gear is configured to be mounted to a synchronization ring for rotation relative to the synchronization ring about a planet gear axis. The set of sun gear teeth are meshed with teeth of the planet gear. The set of sun gear teeth is configured to rotate and drive motion of the planet gear in a circumferential direction about an axis of the set of sun gear teeth. The set of ring gear teeth are meshed with the teeth of the planet gear. The set of sun gear teeth and the set of ring gear teeth are spaced apart from one another.