Mathics: How To Do Hard Math When You’re Not An MIT Janitor

Algebra is the bane of many a student, but it is surprisingly useful when it comes to electronics. Sure, you can just memorize all the permutations of things like Ohm’s law. But it is better if you can remember one form and deduce the others on the fly.

There are many occasions where you — as our old Algebra teacher used to say — need to use what you know to get what you don’t know. The gold standard, of course, is a computer program called Mathematica. For home and student use, the software is “only” about $160-$600, but commercial versions range from about $1,000 to nearly $8,000. Of course, there are free alternatives, and the one we’re looking at today is Mathics. It will run in your browser or as a desktop application powered by Python, and it’s available for free.

The program does a nice job of displaying mathematical formulae and you can get an idea of its power by visit the online version. which has examples if you click the question-mark in the upper right and look for the fourth item down. There’s also a standalone version of the online help.

We did have a little trouble with some of the gallery examples timing out, as well as the site certificate being expired. We also had a bit of difficulty remembering the linear algebra classes we took a long time ago! If you want something easy to play with try this:


Don’t forget to press Shift+Enter in the browser to get the solution.

Under the hood, MathJax and SymPy do a lot of the heavy lifting. In fact, we imagine a lot of the program’s intended audience would wind up using Jupyter notebooks with Python underneath. Of course, there are copies of Wolfram software on stock Raspberry Pi’s, too.

3D-Printed Mobius Strip Of Gears

Exploring the mathematics behind everyone’s favourite unorientable single-sided surface can be quite the mind-bending exercise, so it’s nice that it’s so easy to make a Mobius strip out of paper and a single piece of tape. That demonstration was far from enough for [elmins]. who printed this Mobius strip of gears. The teeth fit together, and all the gears move, but there is still only one side and one edge (we think).

This animation helped spawn the project.

The idea to tackle the project came from seeing an animation of Mobius gears. Wondering if it would be possible to actually create such a thing, [elmins] got to work. The design is printed in 60 pieces, 30 each for the inner and outer parts. The entire assembly is printed in PETG, an unconventional choice but by no means unsuitable. 285 ball bearings help the rings rotate.

The gears use a standard involute bevel profile, though [elmins] suspects this could be an area of further optimisation. The parts were printed in an orientation to ensure the print lines run around the races, allowing for minimal finishing and smooth rolling of the bearings. This is a good study of just what can be achieved with some smart modelling and perseverance.

If you’re thirsty for more madcap machining, consider exploring the concept of the Reuleaux triangle bearing.

Battle Tested Current Limiter For Cheap DC Motor Controllers

Running a brushed motor in muddy or dusty environments takes a toll on controllers, with both heavy back EMF and high stall currents. This explains one of the challenge in Europe’s Hacky Racer series, which is decidedly more off-road than America’s Power Racing Series.

In pushing these little electric vehicles to the limits, many builders use brushless Chinese scooter motors since they’re both available and inexpensive. Others take the brushed DC route if they’re lucky enough to score a motor — and then the challenge becomes getting the most performance without burning up your controller. To fix this, [MechanicalCat] has come up with a current limiter for cheap DC motor controllers.

Circuit protection added to motor controller

The full write-up is in the included PDF file, and describes the set-up of an Arduino Nano sitting between throttle and controller, and taking feedback from a current sensor. The controller in question is a 4QD Porter 10 so an extra component is a DC-to-DC converter to provide a floating ground for the Arduino. However, there is also the intriguing possibility of the same set-up being used with absurdly cheap Chinese motor controllers. There is also advice on fitting flyback diodes, something which might have saved one controller in the Hackaday pits last year.

It’s yet to be seen what effect this will have on Hacky Racer competitiveness, however its applications go far beyond that field into anywhere a reliable small DC motor drive on the cheap is required. Meanwhile, if you’re unsure where this Hacky Racer stuff came from, you could start here.

What’s More Accurate Than A GPS Clock? The OpenPPS GPS Clock

Making a GPS clock is a relatively straightforward process on the face of it. Buy a GPS module for a few dollars, hook it up to a microcontroller board of your choice, pick the appropriate library and write a bit of code, et voila! A clock with time-wonk bragging rights!

Of course, your GPS clock will always tell the right time, but it won’t be really right. Your microcontroller will introduce all sorts of timing errors and jitter, so at best it’ll only be nearly right. [Rick MacDonald] has been striving to quantify and minimise these errors in his OpenPPS project, which aims to be as accurate a GPS time and frequency reference as possible.

In a very comprehensive multi-page write-up, he details his progression, through the GPS modules he used, his experience with timing jitter when he used an ESP32 alone to process their output, and then his experiments with an FPGA and then temperature-compensated oscillators. It moves from being a mere description of a GPS clock into a fascinating run-down of both GPS timing itself and the development pitfalls he encountered along the way. At the end of it all he has a GPS clock in a smart 3D-printed enclosure which he admits as yet doesn’t do anything more than tell the time, but as he points out it’s a clock with minimised jitter, delay, and drift, and it remains an ongoing project that will evolve into a full-blown time and frequency standard.

If your taste in GPS clocks is far more simple, there are plenty of projects showing how a more basic one can be produced.

Bluetoothing Beautiful Phones

You’ve seen a landline phone converted into a Bluetooth headset. There’s nothing new there. It’s great for confusing kids when asking them to dial a rotary phone, but that’s about it. It’s the same phone, built by Ma Bell for fifty years, converted with a little Bluetooth breakout board.

You’ve never seen a landline conversion like this. This is [Alessandro]’s Bluetooth-converted Beocom 600, complete with a drop-in replacement circuit board that turns this beautiful Bang & Olufsen design into a useful device for the smartphone era.

This phone was designed as Bang & Olufsen’s entry into phone design, and we’re shocked, simply shocked, that Apple hasn’t tried to lift this design yet. Unfortunately, it’s designed for landlines, making it horrifically inconvenient to take to Starbucks. That’s where the Bluetooth comes in, and [Alessandro]’s custom board that is meant to replace the guts of this vintage phone. Honestly, with Bluetooth modules it’s probably easier to deal with that instead of a telephone line.

Right now, the work is concentrated on the user interface, which means taking apart and mapping the pinout of the buttons. This keypad is plastic over rubber domes contacting a polyester sheet with contacts, feeding out to a ribbon cable. It’s fantastic work and finally some of the best design out there will be brought into the modern era.

Build A Sprint Race Timer To Help Your Training

Any exercise is a positive thing, but if you’re looking to improve over time, you’ve got to measure your performance. [Nikodem Bartnik] is a runner and is looking to improve his sprinting abilities. Naturally, an Arduino is the perfect companion to help in this quest (YouTube link, embedded below).

The Arduino is built into a 3D printed enclosure, with several buttons for input. Rather unconventionally, a small e-paper display was chosen for the interface. This has the benefits of being easily readable outdoors during the day, as well as using very little power.

The device is simple to use, and makes training alone a breeze. The distance to be run can be selected, and the unit emits a series of beeps to indicate to the runner when to begin. The timer is placed at the finish line, and detects the runner passing by with an ultrasonic sensor.

It’s a useful build for sprint timing, and could be made even more versatile with a remote start function. If you need to time Hot Wheels instead of sprinters, don’t worry – there’s a build for you too. Video after the break.

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Volkswagen EGon Is A Rolling Electric Car Circuit Sculpture

Over the past few decades of evolution, cars have grown to incorporate a mind-boggling number of electric components. From parking distance sensors, to the convenience of power locks and windows, to in-car entertainment systems rivaling home theaters. Normally this interconnected system’s complexity is hidden between exterior sheet metal and interior plastic trim, but a group of students of Volkswagen’s vocational training program decided to show off their internal beauty by building the Volkswagen eGon exhibit.

Seeing a super minimalist Volkswagen electric Golf on the move (short Twitter video embedded below) we are immediately reminded of circuit sculptures. We saw some great projects in our circuit sculpture contest, but the eGon shows what can be done with the resources of a Volkswagen training center. Parts are bolted to the car’s original structure where possible, the rest were held in their representative positions by thin metal tube frames. At this scale, they look just like the brass rods used in small circuit sculptures! Certain component enclosures were replaced with transparent pieces, or had a window cut into them for visibility.

This exhibit was built for IdeenExpo, an event to expose students to science and technology. Showing them what’s under the cover in this “see-through car” with internal components tagged with QR codes pointing them to additional information. The number of electronic modules inside a car is only going to continue rising with the coming wave of electric and/or self-driving cars. Even if the timing of their arrival is debatable, we know we’ll need brain power helping to answer questions we don’t even know to ask yet. The eGon is doing a great job attracting attention and inviting bright young minds to participate.

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