A camera dolly has a steering unit which provides conventional, crab, and round steering modes, selected by the operator via use of a single steering/shifting handle. The steering unit includes first and second transmissions and a differential. Chains link sprockets on the transmissions and differential, to steer the wheels of the camera dolly to appropriate angles, so that the dolly can roll easily and without wheel scrubbing. A dolly leg position compensator adjusts the amount of steering angle correction provided by the differential, to compensate for changes in the dolly wheelbase/tread dimensions. Sprockets in the differential are locked into offset positions, during conventional and round steering, to maintain proper steering angle correction, even under heavy loads. Active idlers are mechanically linked within the steering unit to automatically maintain appropriate chain tension, in all steering modes.