A six-wheeled Automated Guided Vehicle (AGV) with a center drive wheel has been widely proposed for logistics applications in hospital settings, as it can maneuver with zero turning radius through narrow corridors. However, this configuration is prone to losing traction at the drive wheel when crossing a ramp, because the load distribution becomes concentrated at a single contact point. The common approach in prior research is to add an extra actuator to keep the drive wheel's normal force adequate. This paper proposes a different and mechanically simpler approach: a passive rocker mechanism, with no additional actuator or sensor, that connects the drive wheel to one of the caster wheels, pivoting on a single fulcrum point on the main frame, similar to the walking-beam principle used in truck-trailer couplings. Through action-reaction analysis and a two-stage Free Body Diagram (FBD) (main frame, then rocker arm), a relationship is derived between the drive wheel's reaction force (FrC), the center of gravity (CoG) position, the rocker geometry, and the ramp incline angle. The analysis results are used to derive a traction sufficiency condition, namely whether the reaction force reaching the drive wheel, after being split through the rocker, is still enough to produce traction capable of moving the AGV up the ramp. Experimental verification on a physical prototype shows that this mechanism consistently maintains ground contact for all wheels and drive wheel traction at inclines up to 6°, in line with the hospital ramp standard.