Chamber to part size ratio

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The chamber to part size ratio is the volumetric ratio between the assembly chamber
and the the maximal size of product that can be assembled in that chamber.

Sheet form-factor gemstone metamaterial on chip factories

In case of convergent assembly that stops at a layer which still has many assembly chambers inside
(convergent assembly that "stops short")
this last layer now must eventually fill up the whole volume of space above densely.

  • The (now virtual) "chamber to part size ratio" drops down to exactly 1 (or equivalently)
  • The "volume fill ratio" goes up to 1 (100% filled volume)

So given these "last assembly layer assembly chambers" needs to fill up the volume above to a 100% whereas
the ones below are designed to fill up the volume only to a much smaller "volumetric fill ratio"
(leaving enough space for the robotics of the next higher layer)
these "last assembly layer assembly chambers" need a lot more
parts per chamber per unit of time than the ones below (assuming the same branching factor across the last layers!).

In order to compensate for that the second to last layer assembly-chambers must:

  • either be stacked
  • inclusive or operate faster in terms of absolute speed
  • inclusive or have a lower branching factor

Conceptual but concrete example

Example robotics of a final convergent assembly layer that
still consists of a plane of many assembly chambers not yet a single cell
can be seen on the page about "part streaming assembly".

Here part streaming assembly:

  • allows for the last layer assembly cells to have the necessary overlapping areal reach (other methods could do that too)
  • makes assembly faster in a single layer without an necessary increase in absolute speed or reduction in branching factor
    additionally increasing the throughput-demands on the layers below.

More generally and more importantly Part streaming assembly:

  • allows to avoid support scaffolding complexities for smaller voids of problematic shape (e.g. stalagmitic shape)
  • allows for local speed variations in assembly (patches lagging behind)

Box form-factor gemstone metamaterial on chip factories

This is especially important at the macroscale end of convergent assembly with a single assembly chamber at the very top.
Just like with 3D printers it is inconvenient needing a giant machine only to produce minute parts.

Bigger chamber to part size ratios possible but not desirable at smaller scales

At smaller scales a high chamber to part size ratio is much less critical
as long as one can compensate with increasing speed of operations (or stacking same sized layers).
Higher speeds indeed are possible given the good characteristic-force to characteristic-stiffness ratio of gem-gum materials.
In the interest of minimizing friction losses stacking is to prefer over speedup though.

Higher factors may give more design freedom in design of robotics and other necessary subsystems.

Related

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