Scaling

From RepRapWiki
Revision as of 17:49, 18 March 2012 by DavidCary (Talk | contribs)

Jump to: navigation, search
Like most self-replicating systems, RepRap has fun built-in scaling issues.
Francois schuiten.jpg

Some of those issues include:

  • How can a machine build something bigger than itself?
  • quantity scaling: lots of RepRaps: what issues arise when everyone wants a RepRap, and we try to fulfill that demand for a RepRap in every home?
  • size scaling: what happens if we try to build larger or smaller RepRaps?

Contents

How can a machine build something bigger than itself

It would be very useful if a machine could copy itself. A typical milling machine has an enclosed "work volume". It's not possible for it to make any part bigger than that work volume, much less the size of itself (or bigger). This seems to make self-replicating machines impossible. (This seems related to the paradox discussed at Wiki:QuineProgram).

The main reason why these machines have an enclosed work volume is that milling machines (especially CNC Mills) need to be extremely stiff in order to rapidly move a cutting tool through the raw material at high precision. A "closed" work envelope is inherently stiffer than an "open" work envelope of the same size and materials. For example, gantry cranes are inherently stiffer than telescopic cranes of the same size and materials. (The enclosed work volume also makes it much easier to install safety interlocks).

There are a variety of work-arounds used to build large objects:

  • Make lots of small parts, each one easily fitting into the "work volume", and then later let the humans assemble the parts into one large object. (Humans are amazingly good at this, and it gives them a comfortable feeling that they are in control). This approach is used in the Darwin and Mendel RepRaps.
  • Make lots of long parts, each one with a relatively small cross-section, and then later let the humans assemble the parts into one large object. (perhaps use outfeed tables or roller tables to temporarily support the long part).
    • Make a "hole" in the concave hull of the machine somewhat larger than that cross-section, and allow the part to partially exit through that hole while the machine is still adding to the part still inside the machine. This is vaguely similar to extrusion through that hole. This approach has been proposed for the Open Air RepRap.
    • Make 2 holes in the concave hull of the machine, and slide long planks of raw material through the machine slowly enough that the machine can do whatever work is necessary on the section of the material inside its work volume. This approach has been proposed for Eiffel to make grid beam for the frame for the next Eiffel.
  • Using a flexible material, "fold" the design of the large object so it fits into the small work volume, then later unfold into the desired large shape. (Perhaps vaguely similar to the Sarrus Z Linkage). (This approach has been proposed for the Merkle Cased Hydrocarbon Assembler (1998-2000)).
  • Use a kinematic scheme that gives a work envelope larger than the machine itself:
    • a serial manipulator "robot arm", which unfortunately has the worst (lowest) stiffness of any kinematic scheme
    • a parallel manipulator "robot arm"
    • a small mobile machine that walks around on a large, but relatively thin slab of raw material and cuts into it appropriately, perhaps into all the pieces needed for a FlatPack RepRap. (Hexapod Robot CNC Router).
  • ...
  • ... other techniques ...
  • ... what other techniques am I missing? ...

Description

Data

Analysis

Model

Conclusion

scaling to lots of RepRaps

Main page: doubling time.

Timeline to World Domination

Please note. World Domination is not an official part of RepRap or RepRap Library policy.

Number of people living in Megaslums at <$2USD/day

RepRap Deployment in São Paulo Favela?

optimum constant-size RepRap

Assuming we want lots of more-or-less identical RepRaps, all the same size, how big should that size be?

Is "whatever size minimizes the doubling time" always the best answer?

  • Since it needs to be assembled by humans, the parts need to be "not too small" -- the whole part big enough for human fingers to pick up and manipulate; features on the part that need to line up with some other part big enough for humans to see and line up close enough.
  • larger is better: it needs to be "big enough" to make the *other* things a person wants to make -- cups, boxes, etc.; the larger the working volume, the larger the things that person can make.
  • It would be convenient if the entire RepRap was "not too big" -- small enough for one person to pick up and take to another city. See the "luggage" section of Bonsai_RepStrap#size_goals.
  • smaller is better: smaller beams deflect less under their own weight and inertia. And so smaller beams (for a given material) are more precise or (for a given precision) can be built out of cheaper, flimsier materials, or both.
  • smaller is better: smaller parts typically cost less because they use less raw material.
  • smaller is better: in some cases (such as when we use the same extruder nozzle and so get constant raw material flow rate, as on the Mini-Mendel) smaller parts take less time to produce, reducing (improving) doubling time.
  • larger is better for shaping: Some inaccuracies in the shape of each part are inevitable. Larger parts make those inaccuracies less significant; scaling it too small makes it impossible to make parts of the required accuracy.
  • larger is better for assembly: larger machines typically require less alignment tolerance. Assembly can go much faster, reducing (improving) generation time, if proper alignment can be seen "by eye" than if it requires precision measurement to verify. And in general, the looser the required alignment tolerance, the faster it is to line up two parts to adequate tolerance.
  • ...
  • ... other considerations ...

scaling to smaller RepRap

Some people want to build objects with much tighter precision than possible with a standard RepRap. Others want a smaller RepRap to reduce the generation time. The Mini-Mendel may be the first one designed with the goal of reducing generation time. The RepRap Breeder and Bonsai RepStrap and RepRapBreeding all attempt to reduce generation time even more.

It is simple to scale down every part of a model in a CAD system to any arbitrary scale factor. But you may need to tweak the design. Here are some things to watch out for:

  • making every part of the extruder smaller increases (makes worse) the surface-to-volume ratio. If this gets too bad, then heat energy leaks out faster than you can pump it in, and the filament never melts.
  • The "other parts" ("vitamins") of the RepRap that are not built by a RepRap need to be match up with this smaller RepRap.
  • It might be a good idea to make the outer frame of the small RepRep as a few large pieces (perhaps even one large piece?), rather than lots of tiny pieces that a human needs to assemble with lots of tiny nuts and bolts.
  • Some inaccuracies in the shape of each part are inevitable. If the desired final RepRap requires parts more precise than can be made directly from a standard RepRap, perhaps make a series of machines, each one scaled "a little smaller" from the last one, but large enough that the previous generation has enough precision to make the parts for the next.
  • ...
  • ... other considerations ...

scaling to larger RepRap

Some people want to build much bigger objects (say, automobile shells) than will fit inside the working space of a standard RepRap. Other people are printing out lots and lots of parts, and they want a bigger "tray" to so they don't have to manually empty the tray quite so often. The first few steps in this direction are devices such as the Mendel Apollo, BigRap aka MegaRap, 1X2 Tallcat, MegaMendel, and the Cubic Meter Bot.

There are several approaches to building a "scaled up" machine that is more-or-less compatible with the software and electronics of a standard RepRap:

  • Assemble a RepRap or RepStrap design as normal, using the standard parts and standard diameter long studding (threaded rod), except buy twice as much studding and cut each piece of studding twice as long as the original plan. Keep everything else the same size and shape and assemble them. (Was the Development:Mendel Apollo the first time this was done?).
  • Take some RepStraps design, scale all the parts up appropriately to a full-size design, then manually cut all the parts to that full-size design and assemble them. (Scale the wood/metal/whatever parts twice as wide, use studding with twice the diameter, etc).
  • Take some RepRap design, scale up all the parts appropriately, and print out on any available RepRap or RepStrap machine. (Scale the plastic parts twice as wide, use studding with twice the diameter, etc).
    • If the scaled-up pieces themselves are too big to fit inside the working space of the available RepRap, then change the design of those pieces: smaller sub-pieces that will fit in the available RepRap, and then snap or bolt together to form the large piece. Or,
    • If the scaled-up pieces themselves are too big to fit inside the working space of the available RepRap, then make a series of machines, each one scaled up "a little bit more" from the last one, but small enough that every piece can be made by the previous generation.

It is simple to scale up every part of a model in a CAD system to any arbitrary scale factor. But you may need to tweak the design; here are some things to watch out for:

  • Presumably you want to scale up the extruder nozzle so you get faster volume flow rate at each generation.
  • The "other parts" ("vitamins") of the RepRap that are not built by a RepRap need to be match up with this larger RepRap.
  • Scaling a solid beam bigger with the same proportions makes it deflect more and more under its own weight. Sufficiently large beams can't even support their own weight. You can delay this a little by non-proportionally scaling a beam (making it appear proportionally shorter and thicker and stubbier), or by changing the design (make it slightly less strong but *much* lower weight by removing lots of mass on the inside -- like animal bones, the Eiffel tower in Paris, the Hollow Mini-Mendel by MarcusWolschon, etc.), but eventually you are forced to switch to some other material with a better strength-to-weight ratio.
  • ...
  • ... other considerations ...