Robot wheels

The robotics club has continued building their automated foam-dart shooter (which I won’t call a Nerf gun any more—not because I fear trademark infringement, but because it won’t take Nerf-brand foam darts, needing the ones for the NXT generation crossbow).  After getting a Lego prototype of their pan-tilt mechanism working, they’ve been building a sturdier one out of PVC and plywood.  For the pan mechanism they wanted a wheel that was runnable off the 12v battery and controlled by the HexMotor board. Initially they built something using a small 12v motor I had (a Mitsumi M38E-3SC) for which I’ve been unable to find any specifications, other than the 2400RPM and 12V on the label. I did find bunch of specs for other motors on Mitsumi’s web site, but this motor has apparently been discontinued, and the manufacturer has no interest in keeping historical specs on their website.  (I wish more manufacturers would, since it makes it easier to find out the specs for surplus and recycled parts, which in turn allows finding the closest currently manufactured model.)

They mounted the motor with the pulley on the shaft rubbing against a caster wheel, which spun nicely with no load.  Unfortunately, even the weight of the motor pressing the caster wheel against the floor was enough to stall the motor.  (Based on the other Mitsumi motors, I’m guessing that the motor has under 80 mNm of torque.)  We need to get a more powerful motor, but how powerful and how fast a motor?  Today we looked at the design from first principles and started trying to spec the motor and wheel.

They decided that they wanted a panning speed of about 180°/sec.  They’re panning to do this by mounting a wheel at the end of a 60cm arm, so the wheel needs to move at about 190 cm/sec (75 in/sec).  With a 3″ diameter wheel, that  would require a shaft turning at about 470 RPM (a 1″ wheel would need about 1420RPM). If you have any trouble with this easy calculator computation, you could use Lynxmotion’s wheel-speed calculator. They could either get a faster motor and gear it down, or buy a gear motor that has about the right speed and is already geared down.  There are a lot of hobbyist motors and gear motors on the market, but a lot of them are made for RC vehicles, and so run at 6v or 7.2v instead of 12v, or for kid’s toys and run off 3v.  The 12V motors tend to be marketed for the automotive and marine market and are heftier and pricier (except for oddities, like the surplus Mitsumi motors).

How much torque do we need?  We tried pulling on the arm with a force gauge to see what it took to move it, but we couldn’t measure forces that low (under 0.1 N).  Of course, moving it at speed will require more torque—I should probably set my son the task of estimating the moment of inertia and determining how much torque would be needed to swing the mechanism from motionless in one position to motionless 180° away in a second.

Obviously we need more torque than we can get from the Mitsumi M38E-3SC, but how much is that?  We measured the stalling torque by taping a string to the caster wheel and measuring the force with the motor stalled but pulling on the string.  We measured about 0.7N and the wheel had a 5cm diameter, so the stalling torque was about 0.0175±0.003 Nm.  Unfortunately, very few motors have their torques reported in SI units.  Instead, weird units like in-lb, oz-in, and kg-cm are used.  Translating, the stalling torque for the motor is about 0.15 in-lb, 2.5 oz-in, or 180 g cm. (Rather than remember or look up all the conversion factors, I used an online calculator for the unit conversion.)

Any motor with less than 5 times that much torque (0.88 Nm, 0.75 in-lb, 12 oz-in, 900 g cm) is probably unusable, and we may need a much higher torque.  Keep in mind that the torque when the motor is stalled is usually much higher than torque at the rated load (which is typically at the maximum efficiency point for the motor).

I looked for wheels, gears, and motors for several hours today, in order to give the students in the robotics club some reasonable choices to consider.  In this post I’ll just discuss the wheels, not gears or motors.

Motors

I said I wouldn’t discuss motors, but I’ve already made one exception for the Mitsumi motor that stalled.  We also currently have a spare 12v bilge-pump motor with a 1/8″ (3.2mm) shaft which is intended for a 500 GPH bilge pump.  I have no idea what torque it is capable of nor what speed it runs at.

We should be able to measure the speed with a light and a photodiode—this might be a good time to use a Fairchild QRE1113 reflectance sensor (I bought a couple for an idea I had for the circuits course, but that idea is not currently looking too promising).  I think that the flat on the shaft of the motor should change the reflectance enough that we should be able to get a good pulse out of holding the reflectance sensor a couple of millimeters from the rotating shaft.

Measuring the torque is harder (says the ex-computer engineer—electronics is always easier than anything mechanical!).  We’ve got some 3.2mm collet adapters which could give us a 5mm shaft to tape a string to and the outside collar of the collet has a 1.2 cm diameter.   I suppose if we need a longer lever arm to reduce the force, we could drill a 5mm hole in something and clamp it on with the adapter.  We certainly have plenty of spring force gauges, so we should be able to find one that has a reasonable range.

Wheels

There are a lot of pre-made wheels on the market, and there are some wheel systems that allow robot designers to match their needs for shaft size and wheel size with a standard hub in the middle.

BaneBots wheel system

The BaneBots wheel system has wheels that are 0.4″ or 0.8″ wide with hexagonal hubs that are 0.5″ or 0.75″. For example to drive a 2 7/8″ (73mm?) wheel from a 4mm motor shaft could be done with a 0.4″-wide 1/2″ hex hub for a 4mm shaft  ($4), then a 2.875″D 0.4″ wide wheel ($3).  To hold the wheels on the hubs requires a snap ring (included with the hubs), which means buying some snap-ring pliers ($5) as well.

Here is the description from the RobotShop web pages (Trossen Robotics has a nice summary of the BaneBots system with pictures, but their prices are not as good as Robot Shop):

The BaneBots Wheels were conceived for absolute versatility. They are constructed with a thermoplastic rubber tread bonded to a black polypropylene core making them light weight and durable while providing excellent traction. The variety of sizes and mounting options make it easy to find the wheel (or combination of wheels) that meets your needs. These wheels offer a low cost solution that is durable enough for a combat robot yet still light enough to be practical. These wheels can be used both indoors and outdoors and are maintenance free.

Wheels are available in various tread durometers (hardness):

Green Rubber tread:	30 Shore A	(soft and “semi flexible”)
Orange Rubber tread:	40 Shore A	(medium)
Blue Rubber tread:	50 Shore A	(hard and “stiff”)

Standard low profile hubs and bushings are available supporting shaft sizes from 2mm up to 1/2″ in both drive wheel and caster applications. Wheels can be mounted one, two, or even three wide. Mounting two or three wheels to the same hub gives the flexibility of creating wider tread or mixing different durometers. The hubs and bushings offer even more versatility, allowing you to connect to metric (2mm, 3mm, 4mm, 6mm) and imperial (1/8”, ¼”, 3/8”, ½”) shaft sizes.

0.4″ Wide x Diameter:

Diameter:	1-3/8″	1-5/8″	1-7/8″	2-3/8″	2-7/8″
Green	½” Hex	½” Hex	½” Hex	½” Hex	½” Hex
Orange	½” Hex	½” Hex	½” Hex	½” Hex	½” Hex
Blue	½” Hex	½” Hex	½” Hex	½” Hex	½” Hex

2-7/8″ Diameter x 0.8″ Wide:

Green	½” Hex	¾” Hex	3/8” Key	½” Key	3/4” Bushing	Unfinished
Orange	½” Hex	¾” Hex	3/8” Key	½” Key	3/4” Bushing	Unfinished
Blue	½” Hex	¾” Hex	3/8” Key	½” Key	3/4” Bushing	Unfinished

3-7/8″ Diameter x 0.8″ Wide:

Green	½” Hex	¾” Hex	3/8” Key	½” Key	3/4” Bushing	Unfinished
Orange	½” Hex	¾” Hex	3/8” Key	½” Key	3/4” Bushing	Unfinished
Blue	½” Hex	¾” Hex	3/8” Key	½” Key	3/4” Bushing	Unfinished

4-7/8″ Diameter x 0.8″ Wide:

Green	½” Hex	¾” Hex	3/8” Key	½” Key	3/4” Bushing	Unfinished
Orange	½” Hex	¾” Hex	3/8” Key	½” Key	3/4” Bushing	Unfinished
Blue	½” Hex	¾” Hex	3/8” Key	½” Key	3/4” Bushing	Unfinished

Lynxmotion wheels

The Lynxmotion wheel system also consists of hubs and wheels, but in a smaller variety than the BaneBots system. They also sell all their hubs and tires in pairs, so we’d be buying 2 hubs and 2 tires. Lynxmotion has 3 hub styles: universal hub (for 4 of their wheel types), 12mm hex hub (for one truck wheel), and mounting hub (for 7 of their wheel types). All the hubs are $8 for a pair of hubs.

I believe that we would be most interested in the cheapest and most versatile of their systems: the mounting hubs (which are for 3mm, 4mm, or 6mm shafts) and NFT-01 through NFT-07 neoprene foam tires.  The tire diameters are 1.5″ ($3.87/pair), 1.75″ ($4.10/pair), 2.25″ ($4.64/pair),  2.5″ ($4.86/pair), 2.75″ ($5.13/pair), 3″ ($5.36/pair).  Both the BaneBots and the Lynxmotion systems come to about $7 a wheel for the larger sizes (around 3″), but Lynxmotion requires buying in pairs.

The universal hubs (which are used with their more expensive wheels) are interesting in their own right, since they provide 4 tapped screw holes in the aluminum hub, to which anything could be mounted with the 2–4  4-40 screws.  They even include 2 5/8″×4-40 screws for each hub and an Allen wrench that fits them. The universal hubs come in 3 shaft sizes: 4mm, 6mm, and 1/4″.

If the robotics club decided that they wanted a 6″ diameter wheel, they could turn one on the lathe and mount it with universal hub.  Better, they could mount the hub to the rough blank then turn that on the lathe, to make sure that the wheel is properly centered.  Of course, to do any of this we’d first have to clear all the clutter around the lathe (which I haven’t used for 20 years), and I’d have to get a headstock mount drill chuck ($30) and an adapter ($15), since my lathe has a 3/4″ × 10tpi headstock and most lathe accessories now expect 1″ × 8 tpi.

Solarbotics wheels

Solarbotics makes 2-5/8″ diameter wheels for $4 that fit on 3 mm D-shaped shaft and on their double-flat 3mm shaft that is the output of their gearboxes.  It seems to be cheaper to get the wheels from Pololu ($3.50).  Pololu also makes gearboxes that can drive the wheels that are a bit cheaper than the Solarbotics gearboxes.  Unfortunately, neither Pololu nor Solarbotics goes in for 12v motors, and their little 3V motors and gearboxes may not be suitable for this application.  I’ve not seen any adapters for mounting the Solarbotics wheels on larger shafts.

Tamiya wheels

Tamiya, best known for their wide selection of toy gearbox kits, also makes wheels.  The wheels are cheap, but only fit on the Tamiya 3mm hex shafts.

Pololu wheels

Pololu sells wheels that fit their 3mm D shafts and onto the outputs of Solarbotics gear motors.  The wheels come in 3.2cm ($7/2), 6cm ($8/2), 7cm ($8.50/2), 8cm ($9.25/2), and 9cm ($10/2) diameters.

Pololu also makes universal hubs with 4-40 tapped holes, for 3mm ($6/2), 4mm ($7/2), 5mm ($7.50/2), and 6mm ($8/2) shafts.  This looks like a slightly cheaper way to get a universal hub than the Lynxmotion ones. The 6cm and larger wheels have 2 holes that can be mated with the holes in these universal hubs, so the Pololu wheels can be put on other shaft sizes for $7–9 a wheel, depending on wheel and shaft size (similar to the prices for BaneBots and Lynxmotion wheel systems).

Bottom line

It looks like we can get wheels for 3mm, 4mm, 5mm, and 6mm shafts with diameters from 3.5cm to 90cm for $7–9 a wheel.  We can also use universal hubs to mount home-made wheels onto those shaft sizes.

Systemizing

In Out In Left Field: Systematizing in different dimensions: the linear, left-brained thinker, Katherine Beals posted a link to Simon Baron-Cohen’s Systemizing Quotient test, which purports to measure how systematic people’s thinking is.  The test scores show a distinct difference between male and female responses, but Ms. Beals points out that this bias may be built into the test in the choice of topics asked about, rather than in the people being tested.  Note: the test appears to be the real instrument taken from Simon Baron-Cohen’s recent book The Essential Difference: Men, Women and the Extreme Male Brain, not an amateur rewrite.  Other tests from the book are also available on-line.

I took the on-line test, and as always with psych tests, I found that the statements to agree or disagree with were poorly worded, and I was torn between replying to the prompt as written or as the author of the test intended.

For example, “If I were buying a car, I would want to obtain specific information about the engine capacity.” Well, I don’t drive, so if I were buying a car, it would be for the scrap metal most likely, and so the engine capacity would be irrelevant, but the author clearly meant the question to mean “If I were buying something expensive and complicated that I was going to use a lot, I would pay attention to technical specifications.”  (Several of the statements were in this form, with different expensive things and different technical specs—one of Ms. Beal’s complaints was that they were stereotypically male purchases.)

Another example of a difficult statement to agree or disagree with: “When I’m in a plane, I do not think about the aerodynamics.”  Well, the first few times I flew I did think about aerodynamics, but there’s not much new for me to think about there now, unless I got into designing new aircraft, which doesn’t interest me much. On the other hand, if I were to take an unfamiliar mode of transportation (hovercrafts, for example, or helicopters), I would be thinking about the technology involved.  So is this question about my thinking in familiar or unfamiliar environments?  Should a test like this make social-class assumptions about how commonly the test subject flies?

A lot of the statements require close reading, because they are awkwardly formed negations: “When I learn about historical events, I do not focus on exact dates.”  Others pair dissimilar activities into a single category: “I do not tend to watch science documentaries on television or read articles about science and nature.”  (I read articles, but I don’t watch TV—and figuring out exactly what is meant by “do not tend to” is tricky also.)

The sloppiness and fuzziness of the wording of psych surveys always irritates me profoundly, which probably tells you more about my “systemizing quotient” than the test itself is capable of.

Incidentally, the scores I get on the on-line Systemizing Quotient and Empathy Quotient surveys are typical for people with Asperger’s Syndrome, but the Autism Quotient, while above average, was below the level usually seen with Asperger’s Syndrome.  I don’t know whether or not I have Asperger’s Syndrome, never having been professionally diagnosed, but some of the informal descriptions I’ve seen do fit my personality. I have read Tony Attwood‘s The Complete Guide to Asperger’s Syndrome, which was loaned to me by a student who did have that diagnosis, saying that the book had the best description of the syndrome he’d found—some of the description there fits me, but not perfectly.  I suspect that different psychologists would differ about whether to give me the label or not.

 

Instrumentation amp protoboard rev2.1

Revision 2.1 of the instrumentation amp protoboard. This version allows the screw terminals for Gnd input to be disconnected from the board Gnd when a barrel connector is plugged in, or not, depending on jumper wires.

In Instrumentation amp protoboard, I showed an earlier draft design for the instrumentation amp protoboard. After tweaking the design a bit, I think I’m ready to try fabricating it.

I’m planning to try fabricating through iteadstudio this time, since they have the cheapest rates I’ve found yet: 10 boards for $9.90 + $3.90 shipping, for only $13.80.  Of course, the shipping is from China, so even air mail may take a while, and I don’t know what their turnaround time is for orders.  They also have small-batch orders that are even cheaper: $45 for 50 boards, $75 for 100 boards, making this very attractive for classroom use.  Of course, if the board gets just a tiny bit bigger, the price doubles or quadruples, since they have a 5cm×5cm bounding box for this price.

This will be the 4th different PCB prototype service I’ve tried. The others are 4pcb.com (good service, USA made, but a bit pricey), batchPCB (a little slower, but cheaper, probably from China), and OSH Park (USA made, cheap if boards are tiny or you need 3 copies , accepts Eagle brd file, don’t know how fast yet).

I think that someone using Eagle for design might do best with OSH Park, since learning how to use Eagle to produce the Gerber files needed by the other fab houses was a bit of a pain.

iteadstudio does provide Eagle design-rule check and CAM files, but they seem to be pretty much the same as the default Eagle ones—I’ve not gone through them carefully to see if there are any subtle changes.  They do have the most awkward way for delivering the Gerber files, requiring that they be e-mailed as a zip file, rather than accepting upload over the web like the other services.

Worksheet for designing layout. This PNG image is a little small, but Eagle can make a PDF output that is big enough for easy layout.

I improved the top documentation layer, so that the combination of the documentation and top silkscreen make a useful worksheet for students to design their layout on. If printed at 3.5× real size, the worksheet fits nicely on a page and leaves room in each resistor for adding a value.

I tried a couple of slightly different layouts for the EKG blinky circuit with optional Arduino output, and it seems to be fairly easy to lay out.  The hard parts for students will be coming up with the circuit design and soldering it up without shorting adjacent pads.

I’ll have to write up some documentation for the board, to explain the options for power (from an Arduino, from a DC power barrel, or from screw terminals; whether an RC filter is added to the power input or not; where the power and Gnd connections are available on the board, …).  I’ll probably also have to write some assembly/soldering instructions for the parts of the board that aren’t student customized.

Opening night for Twelfth Night

Last night my family went to opening night for Twelfth Night at Shakespeare Santa Cruz.  I’ve seen a number of different productions of the play over the past 40 years, and this was neither the best nor the worst of them.

What worked:

• Paul Vincent O’Connor was probably the best Sir Toby Belch I’ve seen. He was appropriately coarse and rowdy, but tender with Maria (a facet of the character often missed).
• Jerry Lloyd did an excellent job as Malvolio.  Malvolio’s monologue on finding Maria’s forged letter is one of Shakespeare’s best comic monologues, and Mr.Lloyd played Malvolio’s overweening self-importance well throughout the play.
• William Elsman as Sir Andrew Aguecheek had the upper-class twit part perfected.  His comedic timing was excellent.
• Jason Marr did a good job in the rather thankless role of Fabian.  I hope we see him in a meatier role in future.
• The twins looked at least vaguely similar to each other (though not so close that they were hard to tell apart).  Too many productions rely entirely on costuming to make twins of an actor and actress who look nothing like each other.
• Shannon Warrick as Maria seemed to take real delight in her jokes and made the Maria’s affection for Sir Toby seem real (rather than a rather crude play for money or social standing that is often done).  She should have been made up to look a little older, though.
• Good voice projection.  A few years ago there were some SSC productions with actors who couldn’t make themselves heard.  Although I’ve gotten deafer in the intervening years, I had no problems at all hearing these performers even at their quietest.

What failed:

• The costuming.  There were some good touches (like Malvolio’s chain of office with his bathrobe and Sir Toby Belch’s foot brace), but for the most part the costuming seemed irrelevant and distracting—ideas thrown together without much attention to whether they worked well with each other.  Olivia’s slit skirts were unflattering and made her look more like a strumpet than a countess.  Feste’s drab costume seemed inappropriate for a fool (and Mark Christine’s rather flat performance of Feste didn’t help).  Some costume choices just seemed bizarre and pointless, like the horsetails on an umbrella frame for Olivia.
• The music. Feste had a nice enough voice, but not one to write home about. The addition of a parody of the twelve nights of Christmas to the catch scene was gratuitous, adding nothing to the play, and the arrangements of the music were mostly lame.  Of course, I’ve been spoiled because at one of the first productions I saw of  Twelfth Night (over 30 years ago in Berkeley) Oak, Ash, and Thorn sang all the songs alluded to in the play before the play and during the intermission. (I don’t know if the current Oak, Ash, and Thorn group has the same singers, but they’re about the right ages.)  There are a lot of references to popular songs of the day in the play. I would have also liked to see a little dancing: Sir Toby attempting a cinque pas for the line “I would not so much as make water but in a sink-a-pace” (for that matter, doing a few seconds of each dance mentioned in that speech).  Again—I’m spoiled by that Berkeley production.
• The mixed concept.  The director tried to mix a set based on Tim Burton’s art, costumes sort of from Cirque du Soleil, and a few steampunk props. Any of these ideas could have worked if followed through, but the half-hearted mixture of them was not successful. I think that a fully steampunk version would have worked best, but perhaps their costumers and prop makers were not up to the task—Orsino’s steampunk bow was amusing, but the single bicycle sprocket on Andrew Aguecheek’s carpetbag was just pathetic.
• The makeup.  The clown makeup was distracting and added nothing to the performance—they would have been better off with ordinary stage makeup (except for Feste, of course).  I thought that the Shakes to Go performance that I saw on June 8th (the final performance of their 27 performances this year) used the clown makeup more effectively.  Perhaps the minimal set necessitated by the Shakes to Go traveling show lends itself more to the clown approach.  Or maybe Patty Gallagher is just a better director than Marco Barricelli.

Overall, the production was a good, crowd-pleasing one, well worth seeing, even if not the finest work Shakespeare Santa Cruz has ever done.

GPA or SAT?

I was just reading the College Board report today that looked at whether high school GPA, SAT score, or both was the best predictor of first-year college GPA: Students with Discrepant High School GPA and SAT Scores.

The interesting thing about this particular study was that they separated the students into 3 groups: those for which the SAT and HS GPA said the same thing, those for which the SAT was much higher than expected from GPA (smart but lazy? rebellious?), and those for whom the SAT was much lower than expected (slow but teacher pleasers? bad test takers?).

The correlation with first-year GPA was not good for any of the predictions (highest R² value was 0.232 for regression using both HS GPA and SAT scores with the group for which the two predictors were in close agreement). The worst predictions were for using the high-school GPA when it it was much higher than the SAT (rampant grade inflation?)—only R² 0.127.

What interested me was that for both the “discrepant” groups, the lower of the two measures was the better predictor of future performance.  That raised an immediate question for me, which unfortunately the unimaginative researchers at College Board did not consider: how good a predictor would the minimum of the HS GPA and SAT score (both converted to Z-scores) be?  My guess is that it would be a better predictor than either alone, and probably better than the standard linear regression of both.  But I have no access to any data to confirm or refute that conjecture.

I suspect that success in college is best achieved by those who have both brains well tuned for test taking and a willingness to work within the system, so that a low SAT or HS GPA limits performance in college.  The minimum function serves as an “AND” operator, in a way that linear regression can’t really mimic.