Sunday, January 31, 2010

Many useful little things...

Back in the late 1960s when I was very young and worked for IBM for a few years there was a magnetic tape that always lay beside the operator's console on the ancient IBM 360-40 computers labeled MULT. One day I worked up the temerity to ask the operator what it was and he said MULT stood for "many useful little things", viz, MULT. It was a compendium of utilities programmes that enabled the operator to maintain the old 360 and, given how reliable mainframe computers were in those days, was always kept very close at hand.

The projects that I've begun to undertake vis a vis Reprap reminded me of that old mag tape. Basically, I've been undertaking to explore technologies that might get the Reprap community into the next generation of Reprap machines. More to the point, I'm trying to crack some of the technical challenges posed by the Kartik M. Gada Personal Manufacturing Prize.  Mind, I'm not looking to compete for the prize.  The technical challenges, however, are very interesting.

Before the Gada Prize was announced, I was developing herringbone racks and pinions as a printable alternative to belts.  Once the prize was announced, the 90% printed by volume and the 60 watt power limit specifications drew my interest. Prior to the prize announcement, I'd bought all the pieces to build up a heated bed for my Rapman 3.0 printer.  It was obvious, however, that there was no way that a 3D printer with a heated bed was going to be possible using less than 60 watts.

At the time that I was thinking about all of this I was trying to develop a rail system to contain my herringbone rack so that I could use it to drive axes.  I wanted to build a Delta Robot something along the lines that Festo had done.




The Festo Delta Robot uses lead screws in the three columns that seat the arms that move the extruder.  I wanted to replace those with herringbone racks.  I also wanted to make the columns printable.  In that a usuable Delta 'bot is about a meter high, it was obvious that I wasn't going to be able to print a column in one piece.  That put me face to face with the question of how to make a large piece out of a bunch of little pieces.

The conventional approach is to simply bolt the small pieces together.  Frank Davies took this approach with his brilliant Sarrus Linkage positioning system.


Frank had avoided a lot of problems with printing larger parts by using relatively thin-walled, open structures. I shamelessly stole a lot of his techniques after having printed part of his Sarrus system.  While thinking about that it occurred to me that you get relatively little warping if your part's biggest xy dimension is less than about 50 mm.  Most of the parts I wanted to print had a cross section much smaller than that but were long and I needed them to be VERY accurate.

Then came the little epiphany.  Why not rotate the long dimension to the vertical and leave the small cross-section on the xy print surface?  Nophead {Chris Palmer} quite rightly pointed out that for a beam the extreme fibres on the upper and lower surfaces would be no stronger than the bond between two layers of printed plastic whereas if you printed the long dimension flat on the xy plane the bond between layers would only be subject to shear stress.  In spite of that I began designing a columnar rail system for my herringbone racks and began printing it vertically, reasoning that a bending stresses would not be as severe in a column as in a beam.

After half a dozen false starts I finally got a design I liked.  I rewrote the rack generation script for Art of Illusion so that it would put a flange on either side of the rack and then designed a cross-section that would seat racks on front and back sides.  One of the racks would carry the drive pinion while the other would seat a pair of unpowered bogies to stabilise the positioning assembly.

Here you can see a printing of a 100 mm long pair of these columnar rails.



Note that printing vertically allows you to create hollow structures, something much more difficult to do with present technology if you print them on their side. Also note how much like an extruded plastic or aluminum section this columnar segment looks.  That was intentional.  If some enterprising small Chinese factory starts paying close attention, it may be that this sort of section can become a very cheap vitamin instead of something that Reprappers in well served market areas have to print.  That cuts down replication time dramatically.

I'd originally designed the column elements to test whether the rack prints fit properly.  They did.


Before you start thinking that I'm some sort of design wizard, let me say that it took me four tries to get the fit right.  This sort of design thing is very hard work for me.

That accomplished I was beginning to design the connection between the columnar segments when it occurred to me that the rack prints already did that.



What is nice about this approach is that you can simply slide rack segments into the column until it is full.  I found as a practical matter that the segments dovetailed very accurately with just a touch of very fine grit sandpaper to knock off tiny bits plastic flash on the ends.

Just looking at the system one immediately realises that the join between segments is not what you would call a particularly strong.  That is where an old trick I learned in architectural and structural engineering design eons ago came into play, viz, post-tensioning.  In construction concrete is well known for being able to resist huge compressive loads but can resist virtually no tensile loading at all.  Plastic, the way I was printing it vertically, as Nophead rightly pointed out, doesn't have good tensile strength and will, given sufficient load, fail in bending.  In that way it is very much like concrete.

In building in concrete post-tensioning allows you to overcome this problem.  The method is quite simple.  You cast your concrete structure leaving channels through it.  After it has hardened {cured} you thread tendons through these channels and then use hydraulic jacks to put the tendons in tension.  The tendons are connected to either end of the beam you are building by face plates.  The tensioned tendons, usually made of either high strength steel rod or cable, compress the concrete beam strongly via the end plates to which they are attached.  Any bending forces put on the beam thereafter have to overcome this compressive force on the concrete before the beam can fail.  The method is very widely used.

I printed up some end plates and cut a piece of #8 studding {4.2 mm threaded rod} for the tendon.




Here you can see the end plate and tendon in place.


Finally, I point loaded the resulting post-tensioned structure with a 750 gram Mag-Lite.  The 200 mm column section weighs about 45 grams of which the steel and fixings account for 12-15 grams.


No visible deflection was observed.  This beam in this orientation is 18 mm deep, mind, and the top and bottom membranes are 1.75 mm thick ABS.  I will use this same approach for both columns and beams in the Delta Robot I am designing.

I think that by deepening the beam to 24-30 mm you could probably replace Rapman's 12 mm milled steel guide rods {and probably Darwin/Mendel's ...  I haven't checked the exact specification} with a post-tensioned, virtually entirely printed equivalent using about 6% of the steel {#8} as is presently used.

Keep in mind that the #8 studding tendon is massively overdesigned.  I bought #8 simply because, for some odd reason, it cost about on-third as much as #4 {2.8 mm equivalent}.  Using perfectly adequate #4 studding would bring that steel fraction down to 4%.  Heavens, even #2 would do the job!

One issue with this kind of development is creep, the tendency of plastic under stress to deform over long time frames.  It may be that we are simply not loading plastic to anywhere near the stress levels where this becomes a problem.  It warrants a hard look, however.  Unfortunately, the reference manuals on plastics creep are quite expensive, viz, hundreds of dollars and are rather spotty in the coverage of plastic types that they discuss.

15 comments:

Evan Clinton said...

awesome :)

Jacob said...

This is really beautiful stuff!

paul said...

Very sweet. Gives us a reason to think about vertical build dimensions.

Long ago in some structural engineering class I learned that post-tensioning works best if you shape your ducts in a sort of catenary so that the tendons want to flex the beam into the opposite of the curve that the loading would impose. It would be easy to put some guides in the construction to do this for, say, 4 symmetric tendons.

Other thought: can you use feedstock for the tendons? It would be particularly sweet (but impractical) if it could be threaded into the beams hot-but-not-soft, so that annoying shrinkage would provide the post-tensioning.

Forrest Higgs said...

"I learned that post-tensioning works best if you shape your ducts in a sort of catenary so that the tendons want to flex the beam into the opposite of the curve that the loading would impose."

Yes, I should have mentioned that. We tended to camber both the beam when I was doing that sort of thing at university. Of course, when you shipped a bunch of prefab beams by truck, if you hit a big hole in the road, the beams could flex upwards in the middle and fail. It was pretty spectacular when a whole load of beams broke like that, expensive, too. Mind, that was so far back that I think that there were mastadons wandering around at the time.

Given that the camber on a beam should be rather shallow we ought to be able to camber beams quite nicely when we print them vertically. Cambering a duct within the printed beam ought to be possible. It would have to be firmly connected to the beam structure, though, in order to transfer that force when the tendon pressed against the duct. Hmmm...

Gad, though. You've just told me that I have yet another Art of Illusion script to write. :-(

"Other thought: can you use feedstock for the tendons?"

Dale said...
This comment has been removed by the author.
Dale said...

Perhaps some sturdy wire (such as is used to hang pictures) could be used for the tendons, instead of threaded rod. A printable tensioning mechanism should be possible.

Forrest Higgs said...

Yes, I was thinking in terms of the woven wire that is used to hang pictures. It struck me, however, that the details of how to put it in tension and secure it properly to end plates was more than I wanted to involve myself with at just this moment.

Erik de Bruijn said...

Interesting progress. I though the iFab bot was appealing too. Especially since the axes are homogenous segments. You can optimize this subassembly and the rewards will be in threefold.

For a tie that will allow extra strength, this might be an option:
http://picasaweb.google.com/erikdebruijn1/RepRapDev#5433214095403015730
Especially, you could use standard bridge building techniques, but see it as a bridge on its side.
Making the profile rectangular instead of square will also greatly benefit its strength in two of the four directions.

Also, you could consider using a countering force to balancing the beams, since the beams will be loaded with the weight of the toolhead.

AKA47 said...

It is very much worth while cooking up a bunch of standard structural elements that can be used for a range of tasks.

T Slot extrusions but in plastic rather than aluminium are also another option, along with joining pieces, corners, inserts etc.

The tensioning is very reminiscent of some of the work done by Buckminster Fuller.

kpreid said...

Putting a wire in tension? Stringed musical instruments do that — perhaps some concepts to be found there?

What came to mind before that — and note I'm no engineer or real tinkerer in this sort of hardware — is wrapping a wire around a small metal plate. The 180° bends would retain it, and the plate could be set into a printed slot in the plastic to keep it in place. How to adjust the tension, I have no idea, but if this worked it would need no machined parts at all.

Forrest Higgs said...

http://technocraticanarchist.blogspot.com/2010/02/stepper-controller-for-delta-robot.html

Dale said...

Kpreid,

How to adjust tension? Assuming that you're created a loop over your end plates, just turn one of them a few times. As you turn the end plates, the two halves of the loop will twist around each other, taking out any slack before building tension. The end plates could be a printed item. This might even work with raw filament, if an easy way could be found to form it into loops.

Forrest Higgs said...

Anybody who wants to try the wire approach is welcome. I've got other fish to fry with the Delta Robot and the wire vs studding question just isn't important enough to matter for me right now. :-)

Dale said...

No doubt. Just for future reference maybe...

Can't wait to see how your Delta turns out, so keep going!

ArduinoM said...

Guitars can use nylon strings, so I can't see why filament does not work for tension. can possibly use those electrical connector tingies that are cramped on the ends of car electric wires and attach to a hook that is tightend with a butterfly nut.