How does the Tooba's keyboard work?

The question I was most frequently asked when exhibiting the Tooba was about how the keyboard works. I was asked this by people who were obviously intelligent, and I have a deep understanding of it myself, so you would think there would be no problem in communicating it.

The short answer is, when you touch the copper contact, its effective capacitance increases, causing a change in an RC time constant which can be quickly measured with very simple electronics. The problem is that nearly zero otherwise intelligent people in our society understand capacitance.

I tried several different ways to explain this to people. Usually I said, "it works the same way as the touch screen on your phone", and that's true but it doesn't explain anything. It only gives people a known reference point to indicate that it's not physically impossible.


Capacitance is actually a pretty straightforward idea. You have two parallel metal plates. A battery or some other force pulls electrons out of one plate and pushes them into the other, so the first plate becomes positively charged and the second plate becomes negatively charged.

Opposite charges attract, so there is a force pulling the plates together, but they are mechanically held apart, usually by a layer of insulating material. The attractive force therefore acts upon the charges themselves, the excess electrons in the negative plate and the "holes" where electrons are missing in the positive plate. The negative and positive charges want to stay where they are, a bit like inertia, and this manifests as a measurable voltage difference between the plates. The only way to change that inertia is a current, a flow of electrons, into one plate and out of the other. A flow of 6.24x10¹⁸ electrons per second (or one coulomb per second) is one ampere.

Capacitors can be big or small. Capacitance is the size C measured in farads. Great, what the hell does that mean? Remember that the inertia of charge is measurable as a voltage V. The amount of charge is Q, the number of coulombs originally pumped into the plates by the battery. Then the magic formula is Q = C x V, or V = Q / C. How this pertains to the Tooba is that if Q is the same and C gets bigger, then V gets smaller.

Here is the touch-sensor circuit in the Tooba. The input on the left and the output on the right are I/O pins of the microcontroller. The left one is an output that drives electrons into and out of the capacitor, and the right one is an input to measure the voltage on the capacitor. It's a crude measurement, just a comparison to a threshold voltage that gives a zero or one.

BRIEF DIVERSION: In electronics, current is actually the direction opposite to how electrons are moving. This backwards convention is (no kidding) because Benjamin Franklin didn't have know whether the carriers of charge were positive or negative; the observable behavior was the same to him. He guessed, with a fifty-fifty chance of getting it right, and got it wrong. His mistake got codified into all of electronics, forever and ever, amen.

The output on the left is set to logical zero for a little while. The diode quickly discharges the capacitor to the same low output voltage representing a logical zero. Then the output is set to logical one, a higher voltage. The current flows to the right, against the direction of the one-way diode, so all the current flows through the resistor which slows down the movement of electrons. Here's the tricky part: if the capacitor is small, the voltage rises quickly, and if the capacitor is large, the voltage rises slowly. After a certain fixed amount of time, the voltage will just cross the zero-one threshold if your finger was not touching the copper, and the input will read a one. But if you touched the copper, the voltage will rise too slowly and the input will read a zero.

There is one more tricky bit to this. You may have been told in school that you always need to complete a circuit. Pushing current into the top of the capacitor would require that the bottom of the capacitor is connected to the ground in the Tooba. It turns out that capacitors are the one exception to this "complete the circuit" rule. You can (briefly) push current into a single plate and it will behave like a capacitor even without a second plate. That's why you can play the Tooba (or use the touch screen of your phone) without having a wire attached to you to complete the circuit.

Addendum - a friend read this post and wrote:

There's a missing piece in your explanation of capacitance: yes, the negative and positive charges do attract one another, but the charges in each plate also more strongly repel the same-sign charges in that same plate. That creates a restoring force that tries to push current back through the circuit to discharge the capacitor. 

The greater the capacitance, the smaller this net restoring force is. (You can think of a capacitor of higher capacitance as giving more room for the charges to spread out so they're not so crowded, or putting the plates closer together so that the "inertial" attraction across the gap is greater, or both.) 

If you touch one plate, a teeny bit of the charge can flow into your finger, or charges can become polarized in your finger so that some of the electric restoring force is cancelled out. Either way, it increases the capacitance by relieving some of the electric back-pressure through the circuit. And that's why you don't have to complete a circuit yourself.

The Tooba

Way back when, one of my friends in high school was a guy named Dave Wilson whose father got him into Moog-style analog electronic music synthesizers. Dave created a museum of historical synthesizers in his home in Nashua, New Hampshire. Through my high school and college years, we exchanged ideas and circuits and bits of lore for various synthesizer hacks. These synthesizer modules were implementing mathematical functions that could be implemented in digital electronics. So we both at various points and in various contexts wrote code to do that.

The Tooba is going to be some of that built into a short length of 3" PVC tubing. There will be a two or three-octave touch sensitive keyboard and some linear slide pots for various synth parameters. Sound will be generated in the same Teensy 3.1 controller board that scans the keyboard. Unless the poor little CPU gets overwhelmed, then maybe I'll put in a second Teensy for sound generation.

Here is a prototype, mostly testing the touch-sensitive keyboard. For this version the sound was generated by Timidity running on a Raspberry Pi, and the form factor is obviously different. The keyboard misbehaved in this video because of a sagging under-powered 12-volt supply.

UPDATE: Wrong! The keyboard misbehaved because of a programming error identified much later, now corrected.

I'll add more to this post as the thing gets closer to completion.

I had some confusion about the date for the Rhode Island Mini Maker Faire (last year it was a month after the NYC Maker Faire) so I had to hustle when I got the date correct. But I managed to pull it off and have got the thing working.

I also had to figure out how to mount the copper hexagons on the PVC tubing. Eventually my technique got good enough, but by then I had a mix of well-soldered and poorly-soldered hexagons, and the latter periodically pop off. So in the video below you'll see some missing hexagons that I need to replace before I head down to Providence.

So that's the gadget. There is a lot of clean-up to do on the mechanical design. Now I feel it's stable enough to justify laying out a printed circuit board. And the inside wires should be replaced by ribbon cable. But hey, it's working.

An overview of the 2014 printer

People have been asking for an overview of the 3D printer that I showed at Makerfaire NYC 2014. I designed it myself, borrowing a couple of ideas from other printers. My printer builds objects from a liquid resin that solidifies under ultraviolet light. Your dentist may use similar stuff to fill cavities. I get the ultraviolet light from an unmodified conference room projector that cost me about $350, the single biggest expense of the whole project. The most important design principle was that a person of very low craftsmanship like myself should be able to build the thing. It pretty much does not require precision at any point in the construction. There is a Github repository for all this stuff, including a DIY slicer.

The idea to use a projector rather than steering a laser came from the B9 Creator printer. The Peachy printer gave me the idea of floating resin on salt water and projecting the light onto the surface of the liquid. The idea to raise and lower the build platform using three threaded rods driven by a bicycle chain was my own, and it turned out not to be such a great idea.

Soon I plan to post some of my plans for a 2015 printer. Right off the top of my head I can think of four worthwhile goals.

• Bring it to both the Bay Area Makerfaire and the NYC Makerfaire.
• Replace the bicycle chain and those three threaded rods with something simpler and more reliable. The obvious candidate is GT2 belts such as are sold by Adafruit.
• Clean up the electronics and software so I don't need a laptop to control it.
• Replace the orange bucket with something with transparent sides, like an aquarium tank, so that people can watch the printing process.

With the bicycle chain not yet in place, the printer looks like this. Those gray sprockets engage the bicycle chain, which goes around in a sort of diamond shape. The orange bucket is one of the three-dollar buckets from Home Depot. The plywood, nuts and bolts, and threaded rods also came from Home Depot. At this particular point in the work, I thought I would suspend a mirror over the top of the bucket at 45 degrees, which is why you see a piece of wood in the upper right of the photo. But I didn't know about first surface mirrors then, and I lost enough UV going through the glass twice that I couldn't get the resin to solidify, so I then positioned the projector directly over the bucket, pointing downward.

The sprockets were designed using OpenSCAD and initially the teeth were too pointy - correct in theory but too sticky for real-world bicycle chain, so you can see where I cut off the points, and later revised the design. If you order sprockets from my Shapeways store, they should now work fine.

Here is the printer fully assembled. The bicycle chain is driven by a stepper motor. Each revolution of the stepper motor (200 steps) raises or lowers the build platform by 1/20th of an inch because the thread on the threaded rods is 1/4-20.

When it's printing, it looks like this. Only where the light is the strongest is the resin solidified. The resin happily ignores ambient diffuse daylight in the room where I'm printing, so I don't need to use dark room lighting.

Pictured below are some of the objects I've printed with the thing. I started out with a bottle of green resin and when that started getting low, I added a bottle of clear, so my things tend to vary between green and clear.

 

Previous blog posts discussing this printer in its earlier stages

• The very first prototype
• Initial 3D cad sketch, cost breakdown, ideas (not all of them workable)
• Moving from last-cut wooden gears to bicycle chain
• Bicycle chain details, particularly 3d printed sprocket design
• Final development work and first few really terrible prints
• A couple much better prints (also shown here)

A couple of recent 3D printing successes

With a few last-minute improvements I've been able to substantially improve the performance of the printer. I slowed the stepper motor to reduce vibration, and I allowed a settling time after each motor movement before exposing the next layer of resin. I cleaned up the build platform, it is now a sheet of aluminum epoxied to the plywood. (And of course, within a couple of prints, it has gotten covered with a sheet of cured resin. Best laid plans...) I had been trying exposure times that were too short, so I went back to 60 seconds per layer.

If you'd like to see these prints and others, and the printer that made them, come to Maker Faire NYC this weekend at the New York Hall of Science in Queens, NY.

Here is a chess rook. It has an interior spiral staircase. The windows are a bit misshapen and the bottom flat surface is covered with a big glob of cured resin. I don't know why those things happened, but the detail on the parts that came out well isn't too bad.

This is a dodecahedron, one of the five Platonic solids. In the days of ancient Greece, this shape was the cause of some controversy because it could be used to prove the existence of irrational numbers, which ticked off Pythagoras something fierce. This was posted on Thingiverse, as was the rook.

More shapes to come soon, if all goes well.

Finally, the thing is printing

Tomorrow I start a new job with Formlabs, a 3D printer company, and I'm psyched about that. Unfortunately, however, one of the conditions of my employment there is that I cease development on my own 3D printer. I spoke with their attorney and it all makes sense, it's the right thing to do, because my printer is entirely open source and they are selling a proprietary product. If I were to continue developing my printer, it would be too easy to unintentionally include pieces of their technology. So tonight I am putting the finishing touches on the Github repository.

Today was the first time I made a successful print with this printer design. I had hoped to print four dodecahedra at once. But I had some crud on the surface of my build plate, and I hadn't stirred the resin before printing, so only one of the four came out really well. Another was misshapen, and two of them never came together at all.

 Here are the two that were at least coherent solids. I think with a little more learning and practice, I'll get to where I can make four that all look as good as the one on the right.

Here is the setup I'm using. If you've followed this blog, you'll recognize the stuff on the bucket. The box-like thing overhead was quickly cobbled together when I realized that my mirror wasn't reflecting enough UV light to make the resin cure properly, because the mirror's glass isn't transparent enough in the UV range. To remove the mirror from the optical path, I needed to put the projector directly over the bucket, pointing down.

Of bicycle chain and sprockets

Here is the best video I've found for working on bicycle chain. I haven't looked extensively but this one gave me the information I needed, starting at the 34-second mark. I had to buy a length of chain and one of these tools shown in the video. I thought I might need a thing called a "master link" but that's really unnecessary. Bicycle chain is one example of roller chain, a mechanical engineering term for chains that follow the same principle.

The chain I'm using is 1/2"-1/8" single speed chain, also known as #410 chain. The first number (1/2") is the pitch, the distance between the centers of two consecutive rollers. The second number is the width, the distance between inner plates. These numbers, together with the roller diameter, determine the shape of the sprocket teeth. For #410 chain the maximum roller diameter is 5/16".

If you're going to build a gadget using bicycle chain as a drive chain, remember that you'll need a tensioner somewhere, something you can adjust to take up slack in the length of the chain. You'll need at least an inch of adjustment available (twice the pitch). In my design, I made the stepper motor moveable to take up chain slack.

On to the topic of sprocket design. The approach I used is basically guided by the red curves in the diagram to the left. Some sprocket designs truncate the teeth, which reduces friction but engages each roller for a little less time. I probably should have done that but it's not really necessary. The OpenSCAD code for my sprocket design appears at the top of the sprockets.scad source file in the Github repository for my printer. I tested the sprocket (Thingiverse, Shapeways) to make sure that in the absence of unreasonable friction, the chain could freely engage and disengage the teeth as it moved around at fairly high speed (much faster than it will move on the printer most of the time) and that worked fine.

There are a few different pieces, so let me step through it. The outer thing is a difference operation, which means that the first part (the union) establishes a block of stuff and the other parts are removed from it. So we begin with a rectangular solid stretching in the X direction from one roller to the next, with a Z height equal to the width of the chain. To that we add the "tooth" part, defined by the two upper red curves in the previous diagram. The first two pieces we remove are the cylindrical cutouts in which the rollers will sit when closest to the sprocket's center, defined by the two lower red curves. Finally, a couple of flat surfaces are cut out to taper the tooth in the Z direction, which allows the sprocket to still engage nicely when the chain isn't precisely coplanar.

module sprocket_tooth() {
    difference() {
        union() {
            translate([-1/4,0,-1/16])
                cube([1/2,3/8,1/8]);
            intersection() {
                translate([1/4, 0, -1/16])
                    cylinder(h=1/8, d=1-5/16, $fn=30);
                translate([-1/4, 0, -1/16])
                    cylinder(h=1/8, d=1-5/16, $fn=30);
            }
        }
        translate([1/4, 0, -1/8])
            cylinder(h=1/4, d=5/16, $fn=30);
        translate([-1/4, 0, -1/8])
            cylinder(h=1/4, d=5/16, $fn=30);
        multmatrix(m = [
            [1, 0, 0, -0.5],
            [0, 1, 4, -1.3],
            [0, 0, 1, 0],
            [0, 0, 0, 1]
        ])
            cube([1, 1, 1]);
        multmatrix(m = [
            [1, 0, 0, -0.5],
            [0, 1, -4, 2.7],
            [0, 0, 1, -1],
            [0, 0, 0, 1]
        ])
            cube([1, 1, 1]);
    }
}

POSTSCRIPT

I found with the design above that those teeth can easily get stuck if one of the links in the bike chain is stiff. I haven't done a lot of bike chain work, and I would imagine that people who do probably get better at avoiding or fixing stiff links, but I'm not there yet. So one thing I did was to make much less "aggressive" sprocket teeth. For my application, I get away with much shallower teeth, and have updated both the Thingiverse design and the Shapeways store accordingly.

I might have neglected to mention this elsewhere (though I think it's mentioned in both those places) that the sprocket for the stepper axle takes a 1/4-inch long 4-40 machine screw as a set screw.

Cleaning up the SLA printer design

The stereolithographic printer described in my last post works, but it has a lot of room for improvement. Two obvious improvements are to use a stepper motor to raise and lower the build platform, allowing for automated operation, and to accept standard input files such as the STL file format.

In this post, I'd like to look at improvements in the overall mechanical design, specifically intended to make this printer easy for other people to build. I envision this as a printer that could be easily and affordably built by an after-school club, at a price of less than $600. The projector I used cost me $350 and I'll assume that's the same price for others. Likewise I expect others would pay about $75 for a couple of bottles of UV-cured resin. That leaves $75 for everything else. You have a stepper motor, a stepper control board, and a Raspberry Pi. I have a little wiggle room left for laser-cut plywood, and a 5-gallon bucket from Home Depot. I get my laser-cutting done at danger!awesome in Cambridge, MA. The bucket is bright orange, and that's the color I've used in this design, where the plywood is yellow and green (the green pieces having gear teeth that mesh). The pale blue stick-things are 1/4-20 threaded rods, cheaply available at Home Depot. The brighter blue thing is the stepper motor. The three green gears surrounding the threaded rods have captive nuts, allowing the stepper to raise and lower the threaded rods in lock-step. I'm kind of pleased with this design and I think this is what I'd like to show at Maker Faire NYC this year.

 

Looking down into the bucket, we can see one more circular piece of plywood which is the build platform. When we raise the three threaded rods high enough, the build platform comes up out of the bucket, which holds a layer of resin floating atop a salt water bath (a trick I borrowed from the Peachy Printer). And in fact, you could use this setup with a Peachy Printer rather than a projector, and you'd save money by doing so.

These gorgeous pictures are courtesy of Tinkercad.com. It's a pretty wonderful thing if you're doing 3D design. One last picture, showing the projector bouncing light off the mirror to illuminate the resin.