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Materials such as graphite exhibit step edges that affect their frictional behavior. Recent experimental studies found that an atomic force microscope tip can experience either an assisting force that facilitates sliding or a resistive force that impedes motion as it scans down a step. Here, an atomistic model is used to show that tip shape affects its trajectory on a graphite step edge, which determines the potential energy, and thus the frictional behavior. The relationship between trajectory and potential energy is confirmed using density-functional theory, which provides insight into the origin of the energy barrier at a step edge.