A drug delivery device drive that includes a single shape memory alloy wire actuator to advance a lead screw via a ratcheting mechanism and method thereof are disclosed. In one embodiment, a shape memory alloy wire is operably connected to one of a pair of ratchet wheels and configured to drive incrementally the rotation of the connected ratchet wheel via a contraction, which in turn drives the rotation of the other ratchet wheel about a rotational axis which moves a lead screw and advances a plunger to dispense a liquid drug from a drug container. A drug delivery device using the shape memory alloy wire actuator in combination with the ratcheting mechanism to incrementally rotate a shaft, a lead screw or a sleeve provides for a more compact an less complicated design.