A patient transport apparatus transports a patient over a floor surface. The patient transport apparatus comprises a base and support wheels coupled to the base. An auxiliary wheel is coupled to the base to influence motion of the patient transport apparatus over the floor surface to assist users. A wheel drive system is operatively coupled to the auxiliary wheel to rotate the auxiliary wheel relative to the base at a rotational speed. A throttle assembly having a throttle operably coupled to the actuator. The throttle is movable in a first position, a second position, and intermediate positions between the first and second positions. The rotational speed of the auxiliary wheel changes in a non-linear manner with respect to movement of the throttle.