Ring ATPases that translocate disordered polymers possess lock-washer architectures that they impose on their substrates during transport via a hand-over-hand mechanism. Here, we investigate the operation of ring motors that transport ordered, helical substrates, such as the bacteriophage ϕ29 dsDNA packaging motor. This pentameric motor alternates between an ATP loading dwell and a hydrolysis burst wherein it packages one turn of DNA in four steps. When challenged with DNA-RNA hybrids and dsRNA, the motor matches its burst to the shorter helical pitches, keeping three power strokes invariant while shortening the fourth. Intermittently, the motor loses grip on the RNA-containing substrates, indicating that it makes optimal load-bearing contacts with dsDNA. To rationalize these observations, we propose a helical inchworm translocation mechanism in which, during each cycle, the motor increasingly adopts a lock-washer structure during the ATP loading dwell and successively regains its planar form with each power stroke during the burst.