Convergent assembly

Note that in a practical design the size steps would be much bigger than mere doubling steps also it is not a necessity that the topmost convergent assembly levels have the same size as the whole factory device - like shown here. - Devices can be made thin and flat. - Coplanar layers are natural when equal operation speeds in all assembly levels are present.

Convergent assembly is the general process of taking small parts and putting them together to bigger parts and then taking those bigger parts and putting them together to even bigger parts and so on.

Convergent assembly must not be confused with exponential assembly (a concept for bootstrapping AP manufacturing).

Details

If applied int the bigger realm between micro and macro scale it does not speed up production. It may have other merits there.

In an advanced APM system the convergent assembly levels can be identified with the abstract assembly levels (including the more scale invariant ones lying further up). Stacking those levels to layers as a concrete implementation makes a nanofactory that's practical and easy to analyze. For optimal performance (in efficiency or throughput) deviations from a design with coplanar layers may be necessary.

• Convergent assembly is not a means to speed up production.
• Relation to recycling ...

motivations for convergent assembly

Specialisation

In today's non atomically precise production convergent assembly is the rule. In most cases it is just not fully automated. An example is the path from raw materials to electronic parts to printed circuit boards and finally to complete electronic devices. The reason for convergent assembly here is that for the separate parts there are many specialized production places necessary. The parts just can't be produced directly in the final product.

Usually one needs a welter of completely identical building components in a product - connection pins are a good example. Single atoms are completely identical but they lack in variety in their independent function. Putting together standard parts in place with a freely programmable general purpose manipulator amounts to a waste of space and time. General purpose manipulators are misused that way.

Even in general purpose computer architectures there are - if one takes a closer look - specially optimized areas for special tasks. Higher specialization is usually removed from the hardware and put into software.

(In a physically producing personal fabricator there's a far wider palette of possibilities for physical specialization than in a data shuffling microprocessor since there are so many possible diamondoid molecular elements that can be designed.)

Bigger assembly groups provide more design freedom and for the better or the worse the freedom of format proliferation. Here the speed gain from specialization drops and the space usage explodes exponentially because of the combinatoric possibilities. Out of this reason this is the place where to switch to software specialization.

Thus In a personal fabricator the most if not all the specialization is distributed in the bottom-most layers. Further up the assembly levels specialization is not a motivation for convergent assembly anymore. Some of the other motivations may prevail. Higher convergent assembly levels (layers) quickly loose their logistic importance (the relative transport distances to the part sizes shrink). The main distribution action takes place in the first three logistic layers.

---

Side-notes:

• In the obsolete assembler concept all parts of a product where thought to be mechanosynthesized right at their final place in the product.
• Consumer side preferences in possibility space may drive higher level physical specialization in beyond advanced APM systems.

Further motivations

• more simple construction of overhangs without the need for scaffolds (stalactite like structures)
• the automated management of bigger logical assembly-groups
• the simpler decomposition into standard parts that can be put together again in completely different ways
• the possibility to keep everything in a vacuum till the final product release - this should not be necessary and may decrease the incentive for the creation of systems that are capable of recycling

Logistics

The products of the lower assembly cells may be routed beyond the limits of the associated upper assembly cell if the geometric layout decisions allow this (this is e.g. the case in a stratified nanofactory design). In the crystolecule routing layer this e.g. allows the upper assembly cells to receive more part types than there are associated lower special purpose mill outputs.

Related

• Fractal growth speedup limit
• relation to data packages in electronic networks

[Todo: investigate this further]

External links

• https://en.wikipedia.org/wiki/Max-flow_min-cut_theorem and https://en.wikipedia.org/wiki/Approximate_max-flow_min-cut_theorem
• https://en.wikipedia.org/wiki/Maximum_flow_problem
• https://en.wikipedia.org/wiki/Flow_network
• https://en.wikipedia.org/wiki/Circulation_problem
• https://en.wikipedia.org/wiki/Mathematical_optimization