Maker Faire is in New York Saturday September 25 and Sunday September 26, and NextFab offered to let me display something that I made with NextFab equipment on their table. So I decided to make a cheap version of a demonstrator model for the Logical Engine: a casing made out of acrylic, with only the insides being metal. Considering how long it took me to get some casing pieces out of aluminum, it was the work of under an hour to draw some parts in Illustrator and print them out in acrylic on the Trotec laser cutter. Some holes drilled through using the vertical mill, and we have a casing:
It’s a 3×3-rod cube which will allow me to have two inputs and three outputs: conjunction (AND), disjunction (OR), and exclusive disjunction (XOR). Hopefully I can get the rods completed by that weekend.
“Redmond C. Bagstock” is my steampunk name 
Considering the regular and simple nature of the parts of the Babbage-Boole Logical Engine, one has to wonder if Babbage ever considered binary operation for his Analytical Engine.
George Boole’s paper The Mathematical Analysis of Logic came out in 1847, and a copy indeed resided in Babbage’s library – in which copy Babbage wrote “This is the work of a real thinker.” (*) So Babbage was well aware of Boolean algebra. Nevertheless, there would have to be a very good reason for abandoning operation with numerical data in decimal form in favor of binary form.
Indeed, Babbage did at one point consider binary notation for digits. In On the Mathematical Powers of the Calculating Engine (1837), he writes about indexes to storage stored on Variable Cards, “The number of levers necessary for these purposes is not so large as might at first appear, consequently the Cards need not approach an inconvenient magnitude. For example fourteen levers and their equivalent fourteen holes will be all that is required … for eight thousand variables.” In fact, fourteen levers would be enough for 214 = 16,384 Variables, but perhaps one lever was reserved for something else, leaving 8,192 addressable Variables.
Babbage later abandoned the idea of binary representation for a certain mechanical simplicity. His later designs specified a single hole per Variable. Also, having three decimal wheels in place of (approximately) ten binary devices no doubt decided him.
Nevertheless, my argument is that it is mechanically simpler to use binary than decimal. So perhaps Babbage was simply attracted to having fewer (yet more elaborate) parts.
(*) Hyman, Anthony, Charles Babbage: Pioneer of the Computer, 1982, p. 244.
The first two parts for the Babbage-Boole Logical Engine are finished!
These are 3-rod wall parts. They fit together like this:
I need to make five more of each part, and then I can put some rods in and prototype some logical functions. I made these parts on the manual vertical mill. I haven’t yet gotten to the point where I can make these on the CNC mill at NextFab. The Roland CNC mill uses a proprietary program called SRP Player which is actually good for milling complex 3D objects, but not so good for simple shapes whose surfaces are essentially 2D. I will likely create my own toolpath using GCam, and see if the Roland accepts that.
Note that I also decided to change the name from Babbage-Boole Rodulator to Babbage-Boole Logical Engine. It is really an Analytical Engine, but works with logical data rather than arithmetical data. Or, put another way, base 2 instead of base 10.
Back at the beginning of this year, I wrote about how the brass 1/8″ bar stock that I purchased was not straight. While the steel 1/8″ bar stock was straighter, it also was not straight:
You can see light through the 0.06″ gap (about 1/16″) between the table and the bar. The bar itself is 18″ long.
Since I took the metalforming class at NextFab, I realized that the slip roll machine might be used to straighten the stock.
These machines are normally used to bend sheet metal into a tube:
Normally the thickness of material going into the rollers is limited by the machine specs. In this case, the limit is 20 gauge steel, or 0.036″. However, Dan at NextFab agreed that although my bar stock is 0.125″ thick, the machine should easily handle it because (a) it is only 0.25″ wide, so the force required to bend it is vastly reduced, and (b) I’m not bending into a circle, but only to an extremely large (and hopefully infinite) radius.
After running one bar through and adjusting the bending amount, I was able to reduce the bend to nearly nothing:
Now, theoretically, if I turned the bar around and fed it through, I should end up with a similar amount of bend going the other way:
Oh no, what happened? I believe that what we have here is a case of internal stress. Machining produces internal stress in metals, which can cause distortion. In the bar stock, imagine that there is an invisible rubber band pulling on the ends of the bar, thus causing the bar to bend. That represents the internal stress. Applying a force opposite the distortion is resisted by the internal stress, but applying a force in the same direction as the distortion makes the metal bend even more because the internal stress helps it along.
Ideally, I would “process anneal“ the stock to remove much of the internal stress. This, however, involves heating the metal to about 650 degrees C for an hour, which is impractical. I will just have to take the risk that straightening the metal will cause just enough internal stress to balance out the existing internal stress, and that after straightening and machining the metal, it will not significantly distort.
One has to be careful when using the slip roll machine. Its rollers can eat your fingers:
NextFabber Dan showed me another warning sticker on some other device, which made me burst out laughing when I saw it:
A few days ago I wrote about the mechanical sequencer built by Tim Robinson out of Meccano. I emailed him for some more details, and here is what I found out.
Using a differential, Tim is able to apply constant rotation to the crown gear and switch the rotation to one shaft on or off. Here’s a picture of a differential from Wikipedia (by user Wapcaplet):
In this diagram, the red shaft on the left goes through a hole in the large crown gear; it is not attached to the crown gear. When the crown gear is rotated, then assuming that both shafts are free to move, there will be no drag on the central bevel gear, and so both shafts will rotate in the same direction at the same rate as the crown gear.
If, however, one of the shafts is prevented from moving, then the central bevel gear has to rotate, and the other shaft continues to rotate, this time at twice the rate of the crown gear.
Now imagine a finger extending radially outwards from each of the shafts. I can stop the rotation of a shaft by blocking the movement of that finger with, say, a rod. By pulling out the rod and letting the finger go, the shaft can move again. If I move the rod into position again, the shaft can only complete one rotation, and then the finger hits the rod and the shaft stops.
By timing the blocking rod movements correctly, I can choose when and how many rotations the shaft may make. This is the essence of Tim’s sequencer. The movements of the blocking rods are controlled by a drum with bumps on it.
Again, being Meccano, these things are hellishly expensive. The cheapest bevel gear sold by meccanoman.co.uk is £4.94, or nearly USD 8. And they’re made of brass. That’s just nuts.
In “A better drive mechanism”, I looked for springs that could exert a force of 0.25 lb when compressed 5/16″, and whose uncompressed length is 1.316″. I had determined that McMaster-Carr did not have any such springs, but that Associated Spring Raymond did. It turns out that Associated also does not have a spring that fit the requirement.
Let me first review the calculations for McMaster-Carr’s springs. We need a spring that will fit around a 1/8″ x 1/4″ steel rod. The diagonal of such a rod, that is its largest dimension, is 0.280″. For a spring whose outer diameter is 3/8″ (0.375″), we need to subtract twice the spring’s wire diameter, and that must be greater than 0.280. Thus, our first criterion is that the wire diameter must be less than 0.0475″, and preferably significantly less than that, since we don’t want the inner side of the spring to scrape against the rod.
There are four continuous-length springs that meet this criterion. They are listed in the table below.
| Item | Length | Wire size | Constant (lb coils/in) |
n (coils/in) |
Force = 0.3125C/1.316n |
Fully compressed length = 1.316n x wire size |
|---|---|---|---|---|---|---|
| 9662K19 | 36″ | 0.035″ | 54.7 | 7.7 | 3.37 lb | 0.355″ |
| 96565K39 | 12″ | 0.041″ | 109 | 6 | 8.64 lb | 0.324″ |
| 9663K56 | 20″ | 0.032″ | 32.3 | 7.7 | 1.99 lb | 0.324″ |
| 9663K23 | 20″ | 0.041″ | 95.4 | 9 | 5.03 lb | 0.486″ |
So clearly, none of the springs exert a gentle-enough force. The weakest spring is at least eight times as strong as we need.
Taking a look now at the springs from Associated Spring Raymond (downloading the catalog PDF gives more information about the springs than the online tables do), the spring rate given is in lb/in, and the formula for computing the force is a bit easier, being 0.3125RL/1.316, where R is the rate and L is the original length of the spring (10″ or 18″). This makes it much easier to solve for R. For 10″ springs, R must be less than 0.10, and for 18″ springs, less than 0.058.
Looking only at springs whose outer diameter is 3/8″ or higher, we quickly find that not a single spring meets the force criterion.
Quickly checking a few other manufacturers of springs shows that nobody makes a weak compression spring.
What about expansion springs? I could reverse the drive and have the spring pull the rod in, at the expense of attaching the spring to the rod and the wall (instead of just sticking it on the rod and letting it push against the wall).
McMaster-Carr again, this time using the unexpanded length in the denominator for the force equation. The fully compressed length is always 0.691:
| Item | Length | Wire size | Constant (lb coils/in) |
n (coils/in) |
Force = 0.3125C/0.691n |
|---|---|---|---|---|---|
| 9664K51 | 36″ | 0.028″ | 21.1 | 35.71 | 0.27 lb |
| 9664K19 | 36″ | 0.035″ | 54.3 | 28.57 | 0.86 lb |
| 9665K24 | 20″ | 0.032″ | 31.3 | 31.3 | 0.45 lb |
| 9665K25 | 20″ | 0.041″ | 92.7 | 24.4 | 1.7 lb |
We have gotten much closer!
Now, if we remove the constraint that the spring must fit over the rod, we can go with a smaller diameter spring. The reason we wanted the compression spring to fit over the rod is that such a spring needed an axial piece to remain straight. Expansion springs do not need that, so let us try 1/4″ instead of 3/8″:
| Item | Length | Wire size | Constant (lb coils/in) |
n (coils/in) |
Force = 0.3125C/0.691n |
|---|---|---|---|---|---|
| 9664K46 | 36″ | 0.018″ | 12.2 | 55.56 | 0.10 lb |
| 9664K47 | 36″ | 0.023″ | 34.8 | 43.48 | 0.36 lb |
| 9665K84 | 20″ | 0.015″ | 5.3 | 66.7 | 0.036 lb |
| 9665K16 | 20″ | 0.017″ | 8.2 | 58.8 | 0.063 lb |
| 9665K57 | 20″ | 0.020″ | 20 | 50 | 0.18 lb |
Here we have four candidates to choose from, ranging from 0.036 lb to 0.18 lb. Any of these springs should do.
Now, using an expansion spring will change the drive. Instead of the drive preventing the rod from being pulled in, now the drive must prevent the rod from being pushed out, unless we put the spring back on the drive side, and connect it between the follower bearing (the thing on the rod which follows the contour of the drive) and the wall. Thus again, the drive prevents the rod from being pulled in.
However, the dimensions of the rod on the drive side are different than those on the other side. The distance the rod moves is the same, 0.3125″, but the spring at full compression is now 0.816″ instead of 0.691″. Looking at the force equation, we can see that this increase in the denominator only serves to decrease the force further, so we can remain with the same choices for springs.
Babbage included microcode in his Engine, meaning that he could control and sequence the individual elements of the Engine within a single cycle. While searching for ideas on how to sequence groups of rods in the Rodulator, I found that Tim Robinson, who created a Difference Engine out of Meccano, also created a mechanical sequencer. Listening to it is hypnotizing. But more importantly, it is reliable. I would like to achieve that level of reliability for the Rodulator.
But without using Meccano. My personal feeling is that if I can fabricate the basic parts myself, I don’t have to be limited to the architecture and conformation that Meccano provides. And while that limitation is a boon, it is as much a hindrance because I want to make my mechanisms as small as possible. That, and Meccano is hellishly expensive.
A few days ago I was watching Rough Science, a TV series about several scientists “stranded” in a remote location, and given various tasks to perform using the natural resources around them plus a chest of junk. The tasks involve performing measurements, creating chemicals, and building devices. And oddly enough, this was the push I needed to continue my work on the Babbage-Boole Rodulator. Just seeing people work on things was inspiring.
Given that I’m having a crisis of confidence in my X2 mill converted to CNC, I figured, why not find a makerspace that already has at least a guaranteed working CNC mill, and makers making things so that I can exhort myself to making things too? A quick online search, and local to me, in Philadelphia, I found NextFab Studio, located at 37th and Market.
NextFabbers: please keep me honest. If I misreport something, let me know and I’ll edit.
The very open storefront for NextFab on Market Street
NextFab opened its doors in January 2010, after locating space provided by the University City Science Center (a technology incubator) in the new (completed 2008) building at 3711 Market Street, and obtaining financial backing by angel investors. After they secured the location, huge crates of new equipment started to arrive, and the NextFabbers were driven (to exhaustion) to install and set it all up.
And I have to say that they did a fantastic job of utilizing the space. Let’s go on a tour.
This is the entrance to NextFab and the front desk, with 2′x2′x2′ lockers in the background:
Makers can pay for access to NextFab equipment, lockers, and training courses, or they can purchase monthly or yearly memberships to get reduced prices. Currently NextFab has about 40 members. NextFab also offers consulting and contracting services where anyone can pay for design and prototyping expertise.
Here is a variety of things that were made on NextFab equipment. The materials range from MDF, to aluminum, steel, acrylic, wood, fabric, and so on.
There is a computer room with six computers, 4 PCs and 2 Macs. This is Lewis, one of the NextFabbers. Everybody say Hi, Lewis!
Users can access software such as Adobe Suite, Solidworks, Maya, Rhino, and VisualMILL.
This is the electronics room:
There are soldering irons, desoldering stations, oscilloscopes, DMMs, power supplies, generators, etc. The picture only shows one bench, but there is a similar bench on the other side of the room.
Members get access cards which give them access to the various rooms, and you will not be able to enter a room until you have completed the prerequisites for that room. In addition, you cannot use the equipment until you have taken the course and have been checked out on the equipment. Kind of like leveling up. The prerequisite for most machines are the Orientation and Workshop Safety Training (included with membership), and Machine Shop Safety Training (also included). These are only one-hour classes, so they are not at all stultifying.
NextFab is not only a makerspace, but a shared space. Members are encouraged to share, and here we see the “take a part, leave a part” bins.
NextFab also has a materials exchange. I’m not sure how it works, but presumably you can bring in materials for NextFab, and they will let you use a certain amount of materials they already have.
This and the take/leave was the perfect opportunity for me to dig through my closets and find all the things and stuff that I had collected and no longer needed, but didn’t want to give to charity or throw away.
The Roland CNC mill is in the tool room:
It is a four-axis machine, and has a little under 20″ x 16″ of travel, and 6″ in the Z-axis. Due to the spindle speed, this mill cannot handle ferrous material, which includes the mild steel I was planning to build the Rodulator out of. Oh well, that’s what aluminum is for.
Next to the mill is a Stratasys Dimension 3D printer, which prints using ABS plastic, the same plastic that LEGO is made of.
This 3D printer has the interesting feature that it can print support material also, so if your part arches up into the air, it is still printable. Here is a propellor blade made on the printer, which rests on the support material:
The material can be dissolved with a solvent, leaving the ABS piece intact. One of the NextFabbers, Dan, was telling me that you could print a transmission with gears, dunk the whole thing in the solvent, and then the transmission is ready to work.
There is another 3D printer in this room, a Z-Corp Spectrum.
This is an inkjet printer which uses gypsum to construct your part. It is also full color! For example:
Being gypsum, the parts are fragile, but can be infused with a glue to make them very solid.
Also in the tool room are… tools. Things that screw, bang, twist, twirl, and so on, with and without power. This includes a small desktop drill press.
In the next room, which is the machine room, this huge mangler greets you:
It is a lathe. I admit to being totally ignorant about lathes, knowing only that they can be used to construct any other machine in a machine shop, including itself. Warrant Officer Leonard A. T. Beckett built a lathe when he was a POW during World War II at the Batu Lintang Japanese internment camp. Using the lathe, he was able to build a radio and a generator. I have to learn how to use this thing.
There are other woodworking tools here: a bandsaw and belt sander, complete with dust collection vacuums.
Here is also a compound saw, and a huge table saw:
The table saw has Saw Stop, which theoretically means you can stick your hand in the rotating blade and it will sense the capacitance difference and stop the blade instantly, giving you just a nick instead of a missing finger. Saw Stop is typically demonstrated with a hot dog, but I’m sure that someone had to eventually test it with a real live finger. I would like to shake that person’s (hopefully five-fingered) hand.
Not shown is the drill press, metal former, metal cutter, and manual mill, and probably a few others I forgot about.
All these machines can bend, spindle, mutilate, rip, cut, and kill you, and make you cry. NextFab has a very clear set of safety rules, which are not at all onerous. They make sense. Do not ignore them.
You must always wear protective goggles (included in membership) and long pants (not included in membership) in every room other than the computer room, main room, and embroidery room.
In an area in the machine shop is the welding room:
These are Tiggy and Miggy, the comedy welding pair. OK, I made that up, but what else do you call a TIG and a MIG welder? Welding safety equipment is provided.
There is also a big, scary plasma cutter:
Sitting on the plasma cutter was what appeared to be a 1-1/2″ thick steel plate into which a huge hole had been cut out. The plasma cutter isn’t really for such thick materials, but the fact that it could be done at all was impressive and a bit emasculating. Um. Forget I said that. Moving on!
Also in the machine room is a laser cutter. It cuts and engraves wood, acrylic, felt, cork, marble and granite. Just don’t put anything containing chlorine in it (which includes PVC and vinyl), because the resulting chlorine gas will wreck the machine.
As shown above, do not lean. That makes laser cutter ANGRY! It has a 75 W CO2 laser at the business end, and is vented by a blower. Here is the inside, which I call “the grill”:
This thing is very precise. Here is a sample bit of plastic that was part of an architectural model. The piece is 1/2″ by 1-1/2″. Wowzers.
The final piece of equipment in the machine shop is the ShopBot CNC router:
Wood and foam typically go into this thing.
With all the machines that are in the machine room, you’d think the room was huge, but it isn’t. The space is well-utilized, though. Since not everyone is going to use all the machines all at once, many of the machines can be moved around a bit.
Back in the main room, we have two large plotters:
These sit next to another row of computers, these for general use: two PCs and a Mac.
Not shown is the library and the huge central table where you can eat, read, doodle, or hold meetings (or eat, read, and doodle during a meeting).
This alcove contains a computer-controlled embroidery machine, and a serger, which presumably serges. These are yet more machines that I need to learn to use. There is also a comfy sofa.
We also have a 3D scanner:
This takes your small object and measures it using a laser, but also takes photographs so that you can immediately turn it into a renderable 3D object in your 3D programs, or you can turn around and cut it on a ShopBot or one of the 3D printers.
There is another room, the wet room, in which all the chemical things lie in wait. I am assured it contains a fume hood, a spray booth, and oven, a vacuum pump, and an ultrasonic cleaner. Presumably this room is where one would pour molds and mix up foam.
That’s pretty much it. Just by being there, I am inspired to make things, and this is where I will be constructing the Rodulator.
If you are ever in Philadelphia, be sure to drop by for a look (except Mondays and Tuesdays when they are closed).
See you at NextFab!
Tags: cnc, makerspace, nextfab, rodulator, tools
