Planar Assembly of Loose Parts

Way back in June, Tom Craver asked a question that deserves an answer. After much procrastinating, here's the answer.

The question was: How could planar assembly make a loose part that was not bonded to its neighbors, such as the rings in chain mail? Tom suggested that removable scaffolding could be used to hold loose parts in place. Though that should work, I don't think it will usually be necessary - in many cases, the problem will solve itself.

To review, planar assembly is a process of fabricating large objects by attaching small building blocks to one face of the product. If you stopped the process in the middle and pulled the product away from the assembly station, you would have a nice cross section through the interior of the product.

Planar assembly isn't perfect - there will be seams or joint lines between the building blocks. But there are very strong ways of mechanically joining blocks - I described one of them in my nanofactory paper. And it should be possible to make adequate seals simply by pressing together atomically precise surfaces.

The nice thing about planar assembly (which was developed by Eric Drexler and John Burch, and is illustrated in their nanofactory animation) is that the linear deposition speed remains constant regardless of the scale of the blocks, as long as the deposition machinery scales with the blocks. So you can use very small blocks - sub-micron, even - and still "extrude" your product quickly - perhaps as fast as a centimeter per second [ originally stated as a meter per second - see comments ]. Sufficiently small blocks will mostly evade damage from background radiation; will be buildable by a single mechanosynthesis workstation in a reasonable time (say, an hour); and will not be significantly affected by gravity, so can be picked up simply by touching them.

Anyway, back to Tom's question: If your 2D array of block-deposition machines is trying to build chain mail, and it builds a ring that (although interlocked) is not rigidly fastened to any other ring, won't the ring just flop around once it's built?

The answer to this depends on several factors. Probably the most important is the size of the ring (or whatever you're building). If it is small enough to be dominated by surface forces rather than gravity, then it will be stuck in place regardless of whether it's mechanically fastened.

Another factor is exactly how the block deposition machines interact with the product they're building. It seems likely that they will need to remain in contact with some recently-deposited blocks, so that the product doesn't just slip sideways out of alignment. Or, looked at another way, surface forces should make it easy to transfer a sub-micron block from one manipulator to another, assuming the manipulators and surfaces are precise, but difficult to let the block loose entirely, so the machinery will need to remain in contact with some blocks until they deposit others to grab instead.

So my picture of planar assembly is that growing products will be "stuck" to the surface until the fabrication is finished. The same applies to loose sub-parts of products. It's no harder, in general, to grow a loose sub-part within a product than it is to grow two products side by side on the same planar assembly surface.

There are, of course, exceptions. If there's some force that will torque the loose part sideways with enough force to pull it away from the machines, then the part will have to be supported. For large parts, the force might be gravity. For small parts, it could be surface forces - if the part is very near, but not touching, nearby parts. (Of course, if it is built to be touching, then it's somewhat fastened in place by the surface forces even if there's no mechanical or chemical joint.)

So there may, in some cases, be a need for support scaffolding, but in many cases it will be unnecessary - just build the parts unconnected to the product but attached to the planar assembly surface, release them from the planar assembly surface when they are completed, and continue building the rest of the product underneath them if you want.

Chris Phoenix

Comments

[Baughn]

While I understand that this is only if the parts have previously been stockpiled, the "one meter per second" number is considerably more than I expected.

If you don't mind, could you point me at some reference for that?

[todd]

Agreed

So you can use very small blocks - sub-micron, even - and still "extrude" your product on the order of a meter per second.

I do not recall this production rate noted before although I like that number :) .

[Chris Phoenix]

Well, that's my own estimate, and I don't really have a lot of calculation to back it up.

To tell the truth, I did the thinking about this a while ago, and it's possible that I misremembered my conclusion. It might be a centimeter per second or a meter per minute.

I'm thinking of snap-fit fastening and conveyor-belt placement. Automated factory machines can move things around at much higher rates of speed - but the things are smaller. Picture a belt with decimeter cubes - the end of the belt scans across the product face and slaps the cubes into place - each belt end covers maybe 2 square meters, the cubes are spaced a few decimeters apart on the belt, moving at say 2 meters per second...

So you're delivering maybe 1 cube per second, and you need 400 cubes to make a decimeter layer - that's 4000 seconds for a meter. Ugh, 3 orders of magnitude off! OK, I'd better do more thinking about this. Of course, if you can pack the belts more closely or move the cubes faster, you can probably save an order of magnitude or more.

I'll adjust the post after lunch. Thanks for raising the question.

Chris

[JJ]

Agree with Baughn, thanks for post.

[Chris Phoenix]

JJ, I don't understand - Baughn's comment no longer applies - I've corrected the number he questioned. See my comment, above, from Sept. 18.

Chris

[jim moore]

The main problem I see with the Planar Assembly technique is that the plane of assembly is a bottle neck and a place with very limited redundancy.

But a Scaffold Assembly Technique would able to extrude an obeject at the speed of the conveyor belt plus a fixed amount of time because the system is bigger. It is also easier to add redundancy to this system. The scaffold can be very simple - an array of ribbons all in tension.

(To model your example)
You have 100 ribbons 2 cm wide 1 mm thick.
Each ribbon moves past a series of cube deposition stations at 2 meters per second.
The 3 d array of deposition stations is 3 x 3 x 8 meters.
As the ribbons (covered with cubes) funnel down to a one cubic meter box, the cubes snap together forming the object.
Total distance traveled ~12 meters or 6 seconds to extrude a 1 cubic meter sized object.

[Tom Craver]

I'd guess that either stuff doesn't stick enough to secure it while the deposition workstation applies pressure (i.e. it might rock or twist) and has to be held in place - or it sticks enough and thereby makes the parts essentially bonded instead of freely moving. For some materials, that'll be OK - eg a rubbery material.

Deposition workstations could probably hold the product in place - however, that adds a new dimension of complexity. For a non-moving product, you just had to create a static design and fill it in, maybe picking the right type of block for each position. Now you need to compute the forces needed at each step to maintain the product in position, OR have a process that always holds the product in position.

Figure you need at least three points of contact to lock the product against roll/pitch/yaw. And their positioning needs to be programmable (not necessarily dynamically so) to adapt to products with different hole positions. I.e. visualize the difference between pinning down a ring shaped product and a spherical product that would fit through the ring, but both of a size that a single or few deposition workstations would produce them.

I'm thinking that there may be a fuzzy "design limit" on complexity, and if the overall design has a lot of mobility (e.g. cloth, rubber-like) it probably has a highly repetitive design that allows a handful of pinning processes to suffice.

[Chris Phoenix]

Answers to both Jim and Tom...

Tom, there will definitely be a fuzzy "design limit" on complexity - just as there is for software.

As to things sticking together by surface forces: we should distinguish what happens during construction from what happens once each part is constructed. During construction, the part will be held by the deposition machinery, and will probably be either in close contact with neighboring parts, or sufficiently separate from neighboring parts that surface forces aren't very strong. Everything that's constructed will have to be held by the construction machinery, so I don't see added complexity from having multiple parts that don't apply much force to each other.

Once the part is constructed, and released by the construction machinery, it may flop sideways if it's not already in contact with another part. As long as this motion does not interfere with the handling of other parts that are still under construction, then there likely won't be a problem. But this is something to be determined for each class of product and/or part. Of course, if the part was fabricated in contact with another part, it won't move when released, and there's no problem.

Jim, I suspect that there's a topological equivalence between the scaffold assembly you're picturing, and the planar assembly that I'm picturing. If you deform the plane into an elongated pyramid, don't you basically get a scaffold assembly system?

And if you folded the belts over so that instead of running parallel to the product path, they simply deposited the blocks as the belt did a U-turn, wouldn't you be able to place them all in a plane?

It may be that stretching out the plane is a good way to deal with fault tolerance issues. There are at least two other ways to deal with these issues. One is to build the machinery big enough that each workstation can have fault tolerance built in. This probably means the blocks have to be quite a bit larger than a micron, which would then require two stages of assembly as in the Burch/Drexler animation. Another approach is to make the machinery flexible enough that adjacent workstations can fill in for a non-functional workstation.

Chris

[Tom Craver]

Chris - if you haven't seen it - this is kind of cool and sort of relevant :

Lego Digital Designer"

Now they just need to provide a way to automate assembly... And maybe work with the Play-doh folks to let you automatically extrude your own custom blocks around a Lego blank...