This is the universal coil I use for everything: both sensing of magnetic flux and generating forces on magnets for motors of all kinds. It is made from 30 AWG copper magnet wire with something like polyamide insulation, which can in theory be found in the trash or unspooled from salvaged electronics and motors, a HDPE milk or water bottle and some duct tape. It also requires a candle and lighter, a pair of flat bladed tweezers, scissors, marker, something to score with like a fork, and a razor blade.
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Step 1: Go Get HDPE Plastic
HDPE is what most milk containers are made of. I use generic brand milk bottles from the local supermarket. Be sure to wash the bottle as soon as it's done being used, and immediately cut it up, rather than leaving the uncut bottle around for weeks to get stinky. Make as large an area sheets as you can.
Step 2: Cut Out Patterns
Use 1/4 inch graph paper to do this the easy way. See images for guide on how to lay the pattern out on the graph paper, cut it out, trace it only the plastic, and cut the plastic out in the right shape with the marker lines along the fold and cut lines. Note solid lines are cuts, and you have to cut in from the sides as shown, but not cut all the way through.
Step 3: Score the Folds
Dotted lines of two different kinds in diagram show which way folds go. Crease each fold with a fork or other pointy object like a skewer, the end of a pair of scissors, or anything else a bit sharp but not too sharp, using a ruler to guide the sharp thing along the dotted lines. Flip over and score as needed to all folds are on the correct side.
Score and bend, form into approximate coil core shape as shown.
Step 4: Weld the End Tab and Fold It Over
I'll put up another Instructable about how to do HDPE welding with a candle. It's really just trial and error, though. You want it to never catch fire, or blacken, but go through the so-called "glass transition" where the milky plastic becomes clear like glass and can be formed like putty and welded by smashing it with tweezers or pliers. It takes trial and error not just to learn how to do this but to figure out the flame character each time, as the candle burns lower. So just get a candle and lighter and try it.
Step 5: Wind Coil
Again, this is some trial and error to do by hand, and I'd like to automate it in the future using this motor technology to make it more self-assembling, but for now just put the spool on a pencil stabbed into a box and wind it by hand. 350 turns is a good target, if it's a couple dozen more or less it doesn't matter, there is a ton of leeway built into this.
Step 6: Use Duct Tape to Fold and Seal All 6 of the Wings
As seen in the images, just bend the plastic and wrap the tape, which you want to cut into thinner strips as shown so the width matches the 6 wings.
Step 7: Finish, Measure, Document
Use the razor blade to carefully remove insulation along all sides from the end of each wire down a few mm. Trial and error learning are required to learn to not cut the wire, while scraping the insulation off reliably. This is a very useful skill for bringing trash back from the dead in electronics, so it's worth practicing. Be sure to remove from ALL angles, not just a couple sides. Magnifying lenses of some kind and a very bright light make this easier.
When ends are stripped, use more strips of duct tape to strain relieve the whole thing and wrap it around under tape so that the stripped ends just barely protrude, but enough for a very easy solder joint, one hex wing away from each other. Measure with an Ohm meter on the lowest possible range setting, and you should see something in the range of 9-15 Ohms. That means that for 5 V from a USB battery or wall power supply should be not more than about 500 mA, meaning the whole world of cheap modular commercial mass market LiPo USB batteries are available as a power source.
This should go along with some other instructions, for HDPE welding as a skill unto itself, fabricating the drive and amplifier circuits, and the whole set of lab tools and robotics components I'm planning to build here, but I had to start somewhere, so here's my basic coil. 350 turns of 30 AWG magnet wire, 500 mA 5V drive coil.