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.