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The biologically inspired Sprawl family of hexapedal robots has shown that fast and stable running is possible with only open-loop control. Proper design of the passively self-stabilizing leg structure has enabled these robots to run at speeds of up to 15 bodylengths/s and over uneven terrain. Unlike other running robots built to date, the Sprawl robots' front and rear legs are designed to preform distinct functional roles. Like the cockroaches that inspired them, the front legs of the robots act to lift and decelerate, while the rear legs provide the primary forward thrust. This paper uses a dynamic simulation to investigate the effect that changing the robot's leg structure and posture has on its performance. The simulation results support our hypothesis that the use of a differential leg function induced through postural adjustments effectively trades efficiency for stability. [DOI: 10.1115/1.2168477]