Bateson

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Bateson

Release status: Concept

Bateson Frame.png
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Page started by DGoncz 20170805 after a creative winter and particularly July and some hospital time.

The Bateson Family of Machines

Bateson is cyclic: Each Machine makes a Feature of a Part of a Machine Under CNC Post Operator Setup and There are Essential Parts Purchased and Essential Features Completed by the Operator

We don't call them vitamin parts any more. Sorry. There have to be vitamins and minerals and more. It gets complicated.

Firstly, Bateson is a RepStrap design concept and at this writing no Bateson has been built. Also, Bateson is a concept for how to build, not what to build so there may be many bootstrapped Batesons which may replicate to varying degrees of success. Bateson is designed, unlike all other RepRaps to my knowledge, to array densely such that each Bateson supports the others. So it's a cube, or rather, the Bateson concept includes a design rule: a Bateson should fill allspace when arrayed.

Secondarily, all the axes in a most Batesons are not indistiguishible but are functionally identical. Pairs of secondary struts join pairs of primary axes and a tertiary strut joins those secondary struts, reducing the input of as many as 24 motors in 12 primary cube defining struts on 3 perpendicular sets of 4 parallel axes moving synchronously along the 4 parallel axes to motion in 6 face-bound secondary struts on 3 perpendicular sets of 2 parallel axes moving synchronously along the sets of 4 parallel axes and normal to the 2 parallel axes to 3 position defining interior tertiary struts moving normally to the sets of 2 parallel axes. The 3 tertiary struts either cross at a folllower block to which is mounted effectors oF any type or a bed holding a part being composed, or interesting in a follower block of 6-symmetric hex cruciform. Nonintersecting tertiary struts limit the work envelope to X < Y-t < Z-2t, and telescoping strust are actually most suited to zero G, although on the diagonal, the forces may balance. The construction is symmetric. The tertiary struts are not shown in the logo picture nor is the follower block.

Leadscrews can drive a heavy bed, which would not be very fast. An advantage for that option is the Bowden tube wouldn't move. For a direct welding machine with MIG technology, FFF Metal to Metal, this might be a significant advantage. Also, for the floppier, hard to drive filaments, the Bowden tube not moving might be an advantage in that the reliability of the filament drive might be increased. There are conceivable uses for an inverted bed, also, topsy-turvy, if bed adhesion is high, because some infill specifications require in-free-space infill and heaping melted plastic on itself doesn't really work all that well; if you want to draw an octet truss inside your part, you would do that from below.

Thirdly, a Bateson hangs on a diagonal or sits braced within an octet truss, allowing, if desired, threaded rod leadscrews to be used, subject to yet another design rule: accelerationss are below 0.707 G to avoid backlash; all the parts are biased downwards by gravity, but it's oriented diagonally; it isn't a squat cube. The symmetry is taken to the extreme.

A fitment opposite the hangpoint supports various worktables for 3D printing or a lathe tailstock and die chasing head that allows sturdy Batesons to make their own leadscrews. The platform defines the work envelope by blocking certain positions of travel of the tertiary struts. If it's a small platform, printed work can grow long. It it's thick and inverse conical, it can support a larger piece with a flat round base. It can be half the height of the Bateson and as wide as a diagonal for self-reproducing the axes across the main diagonal or support work that would probably warp, replicating along the main diagonal.

The Bateson concept includes a an auxiliary foundry and a head for extruding its own machinable wax stock which can be contained in a Rubik.

See Wolfram and other sources for the Prince Rupert problem of the largest square that fits through a cube. It's larger than the side of the cube, making Bateson a RepRep that can, ignoring its own infrastructure, print parts larger than itself, and build a larger Bateson, not just from joining pieces, but from frame parts. This figure of 115% needs some study.

There is no name for a Prince problem of the largest line that fits through a cube; it's trivial. The diagonal is about 1.7, the cube root of three. Bateson can, once again ignoring its own infrastructure, double its size in two generations (1.7^2>2) by arranging a bed not normal to the hanging axis, but from a lower corner to an upper corner.

An array of 3 x 3 x 3 Batesons is a Rubik. Such a Rubik would strengthen and support the central Bateson and would, like just one Bateson, be amenable to being surrounded by an octet truss to further strengthen the array at low mass cost. Post such rigidification, a Rubik's central Bateson will be fitted with an effector ballast attachment allowing heat for the melt effector to be taken from a surround of water and from motors for milling. The water would turn to ice supplying needed ballast for milling to resist vibration. 27 Batesons with 4 axes each fit into the 127 node USB design space including a boot drive for the machine.

An array of 5 x 5 x 5 Batesons is a Kubik and is notable in that there are fewer blocks needing extension by octet truss than there are in use as joiners between cube legs, and this is true as scale grows to 6 x 6 x 6 and beyond.

Bateson arrays to billions; cubes fill allspace as mentioned.

One Bateson with octet truss is an octagon and can sit on a desk. It can be small or large. The larger a Bateson is the more it looks like a cube; the octet truss conforms to the cube surface.

A cubical Bateson can be small, large, or huge. An ironwork frame building can be made up with a Bateson in each room of a pyramidal building.

DGoncz has contacted America Makes about Bateson.

DGoncz is building a model Bateson of 21 pieces 3/4 inch OS aluminum tubing, 5/8 inch IS, roughly 12 inches long, with analog drive, and may or may not inbuild potentiometers from resistive sheeting. The first try will probably use stall for endstop with no sensors and coordinated motion of all 3 axes. It will probably use 14 gage bicycle spoke wire, taxidermy wire, in pairs of tension members, to conduct the power and hold together, inside the tubing. It will probably be seen onstage somewhere as a prop one day because it will not do much. It will probably use magnets inside the tubing to transmit the motion. It will be hand fitted just to prove that there can be a symmetric Cartesian machine. You might want to base your Bateson on 2 inch OS aluminum tubing inside IS 1.75 inch fitting the very popular NEMA 17 frame stepper, 1.7 inches square faced. You'll want to slot the tubing and arrange positive drives, not use magnets.

A Basteson can be built with care and concern, a bit at a time, by assembling RepStrap style a single axis, and instructing it to facilitate the manufacture of 3 more, assembling them in a pyramid, a cube corner, with non-Bateson supports, to form a plotter or printer with limited capacity. That concept is called Stix.

3 Edges.jpg

Adding 6 more Batesons to form an unfinished cube adds some capacity. Adding three further to complete the 12 axis cube completes the capacity. Multiplying by 4 (repeat 3) adds some rigidity, but 27 offers a central position rigidified greatly by Batesons on every possible face: a Rubik. This can be configured to 3D print machinable wax, to bend, rivet, and otherwise form the wax in mass-neutral processes requiring large forces in the central stiffened cube, to mill and turn the wax, tap and drill it, to thread mill it, for assembling in left-hand / right-hand pairs that mate to simultaneously tighten opposing faces of joining parts with a given torque and orientation, and these wax parts can be cast, formed, subtractively finished, and used to form Batesons, Rubiks, Kubiks and more, as well as in applications requiring superalloy parts like turbogenerators.

Once a Kubic has been used to reproduced 27 Batesons, it can be disassembled into 27 more Batesona.

That's an important point; we do not have here 27^x, a new basis for the exponent of a deployed population of machines, but we do have a 27 * 2^x, a useful development. In one generation, x=0, 2^0=1, there is (was) one Rubik, but disassembled, there are 27 Batesons, which would have taken 5 generations 2^5=32>27, to generate, and we find, or I observe, and I may not be correct, that with revisions, most RepRaps do not generate 5 times without serious revision.

So this is a concept of geometry relating to machine reproduction we as RepRappers can use.

Any RepRap that arrays to fill allspace, co-suppporting the others in the array, lending stiffness most to the inner machine(s) in the array, is subject to development in multiples advantaged by this assembly/array/disassembly protocol. Bateson, being a design taking symmetry to an extreme, is well suited to this advantage, as it incorporates an additional factor of 12 times the 27, since all 12 axes are identical.

There are more than three possibilities for orientation of a cube--three relevant orientations are: a short "diagonal" (face to face) can be vertical, and so the others become horizontal; a long diagonal can be vertical; or, long sought and relevant to replication, two long diagonals can be horizontal: this allows printing parts large relative to the cube size.

A Bateson can be externally trussed in layers of octet truss to any needed degree of rigidity but only the selection of prehardened drill rod for the tertiary rods and careful control of their length controls the critical stiffness there. The addition of mass to the follower block with ballst blocks or by water pumped in an frozen, and melted and pumped out when not needed, can ameliorate some of the vibration concerns associated with contour milling. The success of applying that process to this highly parallelized motion control frame is not known.

The end connectors would look something like this:

Bateson Block.jpg

Another way of setting it up is this:

Contact Tensegrity Cube.jpg

Nonintersecting tertiary struts are shown in this rendering:

Open Cube v1.png

...and this one:

Open Cube 2.png


Bateson is the macromaterilistic rebuttal to the nanomaterialistic quest for matter that does our bidding; as every apprentice knows, we already have such matter.

References:

http://blogs.sccs.swarthmore.edu/julianleland/engineering/academic-projects/e90-senior-design-self-replicating-mill/