A steering system for a vehicle adapted to travel on a track or a guideway includes a drive shaft having a rotational axis and first and second substantially semicircular gear elements provided on the drive shaft and adapted to engage first and second racks, respectively. The first and second substantially semicircular gear elements are offset along the rotational axis of the drive shaft and are located about a common end of the drive shaft. The first substantially semicircular gear element engages the first rack when the drive shaft is rotated in a first direction while the second substantially semicircular gear element engages the second rack when the drive shaft is rotated in a second direction, the second direction being opposite to the first direction. Both first and second substantially semicircular gear elements engage the first and the second rack, respectively, when the drive shaft is in a neutral position.