A distinctive feature of mechanically interlocked molecules (MIMs) is the relative motion between the mechanically bonded components, and often it is the functional basis for artificial molecular machines and new functional materials. Optimization of machine or materials performance requires knowledge of the underlying atomic-level mechanisms that control the motion. The field of biomolecular NMR spectroscopy has developed a diverse set of pulse schemes that can characterize molecular dynamics over a broad time scale, but these techniques have not yet been used to characterize the motion within MIMs. This study reports the first observation of NMR relaxation dispersion related to MIM motion. The rotary (pirouette) motion of alpha-cyclodextrin (alpha CD) wheels was characterized in a complementary pair of rotaxanes with pirouetting switched ON or OFF. C-13 and H-1 NMR relaxation dispersion measurements reveal previously unknown exchange dynamics for the alpha CD wheels in the pirouette-ON rotaxane with a rate constant of 2200 s(-1) at 298 K and an activation barrier of Delta F-double dagger = 43 +/- 3 kJ/mol. The exchange dynamics disappear in the pirouette-OFF rotaxane, demonstrating their switchable nature. The C-13 and H-1 sites exhibiting relaxation dispersion suggest that the exchange involves "macrocycle breathing", in which the alpha CD wheel fluctuates between a contracted or expanded state, the latter enabling diffusive rotary motion about the axle. The substantial insight from these NMR relaxation dispersion methods suggests similar dynamic NMR methods can illuminate the fast time scale (microsecond to millisecond) mechanisms of intercomponent motion in a wide range of MIMs.