A machine includes a single power source 18 for asynchronously operating dual indexing conveyors 12 and 14. The single power source 18 is part of a drive system 16 for the conveyors 12 and 14 and may be a reversible servo unit 18 operatively connected to gear sets 80 and 82 and one-way clutches 38 to drive the conveyors 12 and 14. Alternatively, the power source may be a uni-directional rotating driver with a linkage to reciprocate a rack operatively connected to gear sets with one-way clutches. Each of the conveyors 12 and 14 advances liquid-filled open-topped containers C and is configured to engage the containers C releasably. The drive system 16 schedules conveyor motion according to a predetermined motion profile. The motion profile comprises sequential indexing periods, each indexing period comprising a move portion and a dwell portion. Each move portion comprises a generally discontinuous acceleration profile that includes generally instantaneous acceleration changes of a finite value.