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.
For a specific reference speed there are different scale natural frequencies for different sizes. Halve size double frequency.
These scale natural frequencies keep the acceleration loads from inertial mass constant over all scales.

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.

Deviation from scale natural frequencies in proposed nanosystems

A reasonable macroscale reference speed is between 10mm/s and 100mm/s (seen in todays fused filament fabbrication 3D printers)
(And 1m/s to 10m/s for fast delta style pick and place robots.)
Proposed speeds for macroscale style machinery at the nanoscale in Nanosystems are about one to two orders of decimal magnitude lower than for macroscale 3D printers.
~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