This paper addresses the deterministic translational-rotational motion of a freely-draining rigid dumbbell that is freely suspended in pressure-driven Stokes flow through a periodically corrugated pore or channel. As is demonstrated by numerical integration of the coupled, nonlinear equations of motion within a sinusoidally corrugated, axisymmetric pore, passage of the dumbbell through successive converging and diverging local flow environments engenders rotary fluctuations relative to the local streamlines that gradually increase in amplitude, over many pore wavelengths, until it eventually flips over. Then the dumbbell slowly realigns itself with the flow, with diminishing fluctuations-whereupon the whole cycle begins again.