Twice the frequency of half sized machinery

This is about keeping operation speeds in terms of length per time constant over all size scales.
This would make operation frequencies rise linearly with falling size, and lead to massively higher throughput of smaller machinery.
This is a crude and bad approximation for what one would actually want to do in a gemstone metamaterial factory.
See: Deliberate slowdown at the lowest assembly level.

A reasonable macroscale reference speed is between 10mm/s and 100mm/s (seen in todays fused filament fabbrication 3D printers)
Proposed speeds for macroscale style machinery at the nanoscale in Nanosystems are about one to two orders of decimal magnitude lower.
~4mm/s? (to check!)

That is: The proposed macroscale style machinery at the nanoscale operates well below "scale natural frequencies" in the sense that
the speeds are not limited by overswinging vibrations and resonances from inertial mass. (Assuming no very high Q factor structures are built).
The limit for the speeds is rather set by an attempt to minimize energy dissipation from friction.

Related

• Unsupported rotating ring speed limit – this follows scale natural frequencies at the upper physical limit