We combine experiments and distinct element method simulations to understand the stability of rings and rackets formed by single-walled carbon nanotubes assembled into ropes. Bending remains a soft deformation mode in ropes because intra-rope sliding of the constituent nanotubes occurs with ease. Our simulations indicate that the formation of these aggregates can be attributed to the mesoscopic mechanics of entangled nanotubes and to the sliding at the contacts. Starting from the single-walled carbon nanotubes, the sizes of the rings and rackets' heads increase with the rope diameter, indicating that the stability of the experimental aggregates can be largely explained by the competition between bending and van der Waals adhesion energies. Our results and simulation method should be useful for understanding nanoscale fibers in general.