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To show you how to use the regular LED bulb, I've thrown together a quick fabric flower project, but there is no end to the ways you can use this technique. Here are the sewing supplies I used:
Pictured above: One pre-made fabric flower (you can make one or use whatever else you'd like), 4-ply conductive thread, needle, and two disks of fabric. One pretty, in case it peeps through the flower, one thick, to support the weight of the battery holder. If you have a thick fabric that will look nice peeking through, feel free to use only one disk!
You will also need a few small electronics pieces, of course.
First, you'll want to place the flower or object between the legs of the LED. This is also a good time to mark one leg, if you're not sure you'll remember which is positive and which is negative. If you look at the bottom of the LED, you should see that one side is flat - the leg on that side is negative. Feel free to mark it for reference later. If you're using a flower, or a similar piece, you'll want the positive leg on one side and the negative leg on the other. The fabric will insulate the legs from touching each other and shorting the circuit.
Next, place the disk of fabric that will go against the back of the flower- this will be the more decorative disk, as it will sometimes be partially visible. Press the center of the disk against the tips of the LED legs, then push them through the fabric. Push the fabric down until it is against the back of the flower.
Repeat this process with the second disk of fabric. If the disks line up poorly, you can trim them to match provided you have enough room left to accommodate the battery pack, resistor, and the light where it is without overlap.
Grasp one leg of the LED with a small pair of pliers. You'll want to be very gentle - the legs are delicate and can be snapped off by this process if you aren't careful. Holding the LED steady in your other hand, twist the pliers so that the leg wraps around them into a small loop. Keep twisting until the entire leg is part of this loop, and flush with your disk, then gently wiggle the pliers out of the loop.
Repeat this process with the second leg. When you have finished, both loops should lay flush against the back of the disks, and the top of the LED should still be pressed up against the flower. The LED will be holding everything together, so make sure things are secure now, and tighten if necessary.
Each LilyPad board has a tiny resistor built in. When using regular LEDs, you'll have to add your own resistors to the circuit, which means adapting them for sewing in the same manner you've adapted the LED. Grasp one end of your resistor in the pliers, and twist it, similar to the way you twisted the legs of the LED. This wire is thinner and easier to bend than the LED legs are, but are still delicate, so be careful.
Bend the second leg in the same manner, and make sure that both loops of wire are flat on the same side, so that it can be sewn down flush to the fabric.
The first thing you'll need to sew down is the battery pack. Sew both holes on the positive side down to the fabric, several stitches in each hole.
Place the resistor between the positive side of the battery pack and the positive end of the LED. When you're happy with the location, stitch from the positive side of the battery pack that you've just sewn down to the nearest end of the resistor. Knot your thread off and cut it, then restart stitching on the other side of the resistor. Connect this side to the positive leg of the LED.
Sew down the negative side of the battery pack the same way you did the positive side. Be careful - if the thread touches the tab between the two holes, it will short your circuit. Continue sewing from the battery pack to the negative side of the LED.
Your circuit should be completed. Insert your battery into the holder, and the LED should light up. If it doesn't, check your stitches to make sure that there's no point where the positive side and the negative side come into contact.
Congratulations! You can use this technique for any number of crafts that are better suited to a bulb shaped LED than a flat LilyPad LED. If you don't need to keep the LED legs out of view, you can always twist them up first, and then secure them to the fabric the way you did with the resistor.