Christmas STEM Challenge: Stepper Dice and Wheel-of-Fortune
Image credit: Neil Downie
Our STEM Challenge series is back, just in time for the festive season! This week, Neil Downie shows how to guarantee fair play in your board games with a motorised Wheel-of-Fortune and Stepper Dice made from your old printer.
Stepper motors are those neat little motors that don’t just go round and round when you connect them, but go round in jerks, 7.5°, 10° or 15° at a time. This is technically called ‘cogging’. Inside, they have two sets of electromagnet coils that pull the magnetic rotor around by a small angle each time they are pulsed.
You can buy a stepper motor for less than $10 (£8), but don’t buy one straight away. You may find you can use one from an unused or broken printer or scanner. The printer in the picture below has three stepper motors. If you have a choice, choose the stepper motor that feels the most ‘notchy’, the one that clicks most positively into place as you rotate the shaft. (Cleaning and light oil may be needed for a stepper that has paper dust and ink toner on its bearings.)
Stepper motors mostly have four wires, two coils with wires to both ends of both coils. They are normally driven in sequence by computer-driven electronics with current to coil 1 positive, then coil 2 positives, then coil 1 negative, then coil 2 negatives. But with an AC sine wave on coil 1 and ~90° phase-shifted AC on coil 2, you’ve got an equivalent to the digital drive sequence. (With 5-wire steppers, the coils have centre taps wired to the 5th wire.)
You’ll also need a mains transformer supplying 2 to 12V AC output, but again you will often find one you can reuse. Some plug-in PSUs are AC, and inside battery chargers you’ll find 12V AC. You’ll need a capacitor to go in series with one coil and a resistor to go in series with the other. The resistor reduces the current to the motor, as does the capacitor. The capacitor has an additional effect: it phase shifts the AC waveform, delaying it by about 90°. No transistor, microprocessor or computer program is required!
Now add a wheel on the shaft and a pointer, or a pointer on the shaft and a circle of numbers. Add the on-off switch, and you have your very own Wheel-of-Fortune. Put the numbers in random order to stop cheating by blipping the wheel on briefly. When you switch it on, it’ll whizz around too fast to see and when it stops, it will use its natural ‘steppiness’ to point precisely to a number.
The stepper in the pic above has 24 steps, with 12V AC from a plug-in PSU, a 100uF capacitor in one coil circuit, and 440 Ohms resistance in the other. You will need to play around resistor/capacitor values, as your stepper and AC supply won’t be the same, but keep the current down to mA levels.
Stepper motors are commonly 24-step, so you can mark it with four sets of 1 to 6 to use as dice. Or you can mark up the wheel to simulate polyhedral dice of a game like Dungeons & Dragons. For double-dice scores, you can just use the 1-to-6 labelling on the pic, and whizz the wheel twice. Or put two pointers on the wheel and add up the score from each. But can you save your brain the mental effort of adding up by numbering the wheel with numbers from 2 (double-one) to 12 (double-six)? Yes, you can... but it turns out that numbering with random numbers from 2 to 12 for the double dice isn’t straightforward.
The problem is the scores don’t all have the same probability. The probability of a 2 (double one) is small. You’re more likely to get 3 (two-and-one or one-and-two). And even more likely to get 4 (one-and-three or three-and-one or two-and-two)... and so on. The graph shows the double-dice scores from 100 double runs of the Stepper Dice.
In fact, to get the probabilities right you have to put different numbers of each score in: one 2, two 3s, three 4s, four 5s, five 6s, six 7s, five 8s, four 9s, three 10s, two 11s and one 12. That adds up to 36. So a 36-step stepper will work nicely, with the wheel giving the double-dice throw scores many games require.
However, if your stepper has 24 steps, then you could get the probabilities roughly right by marking up your motorised Wheel-of-Fortune with one 2, two 3s, two 4s, two 5s, three 6s, four 7s, three 8s, two 9s, two 10s, two 11s and one 12. Now get out your Christmas Monopoly, Dungeons & Dragons or Carcassonne, and have fun!
If you liked this, you will find lots more fun science stuff in Neil Downie’s books, like ‘The Ultimate Book of Saturday Science’ from Princeton University, and for lots of other things (and a free copy of the ‘Exploding Disk Cannons’ book), visit www.saturdayscience.org. In line with this experiment, Neil’s current work includes developing a new ventilator system to support people with breathing difficulties – get more information on this great project here: Exovent.org.
There is a back catalogue of STEM-related challenges from the past year to choose from if you are looking for more options. The IET also has a host of resources that adults can use to engage children with the world of STEM.
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