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Friction-induced energy dissipation impedes the performance of nanomechanical devices. Nevertheless, the application of graphene is known to modulate frictional dissipation by inducing local strain. This work reports on the nanomechanics of graphene conformed on different textured silicon surfaces that mimic the cogs of a nanoscale gear. The variation in the pitch lengths regulates the strain induced in capped graphene revealed by scanning probe techniques, Raman spectroscopy, and molecular dynamics simulation. The atomistic visualization elucidates asymmetric straining of CC bonds over the corrugated architecture resulting in distinct friction dissipation with respect to the groove axis. Experimental results are reported for strain-dependent solid lubrication which can be regulated by the corrugation and leads to ultralow frictional forces. The results are applicable for graphene covered corrugated structures with movable components such as nanoelectromechanical systems, nanoscale gears, and robotics.