A rotary drive mechanism for use with a timer/sequence switch in an appliance is presented. The mechanism converts linear motion from a cam tracker following a programmed cam track to rotary motion to drive a vent damper in an appliance. The rotary motion output is derived as a multiple of the input linear motion through a gear set. This input linear motion is translated to rotary motion imparted to a tracking rod, which is coupled through the gear set to an output actuating rod. Tracking by a tracking lobe is accommodated by a spring bias force applied though a bias lobe that counteracts the force applied by the cam track. Alternatively, tracking by a tracker is accommodated by a spring bias force applied through a torque arm of the tracking rod that also counteracts the force applied by the cam track.