Bateson

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

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.

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 Bateson are identical. Pairs of secondary struts join pairs of axes and a tertiary strut joins those struts, reducing 8 motors in 4 axes to 2 secondary struts and 1 position defining tertiary strut. There are 3 tertiary struts, crossing in a folllower block to which is mounted effectors oF any type.

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 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 up and outwards. 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.

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 3/4 inch square aluminum tubing, 5/8 inch ID, roughly 17 inches long, with analog servo drive, and may or may not inbuild potentiometers from resistive sheeting. 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.

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. Adding 6 more 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.