I need to attach a rotary encoder to an arduino. The rotary encoder has 3 metal prongs that I need to attach wires to.
This picture explains exactly what I need:
What type of wire attachment is that? What should I search for to buy?
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Those wires have been soldered to the pins of the encoder. Then each solder joint has been protected by a short length of heat-shrink tubing.
So you want to search for a soldering iron, solder, and heat-shrink tubing. The heat-shrink can be activated by placing it against the tip of the soldering iron, but much better results are produced by getting a heat gun, which produces a stream of hot air.
I'm dealing with this right now. The other answers are correct; the wires are soldered to the rotary encoder pins.
With a steady hand, you can strip a wire and solder it directly to the pins. However, it is easier if you have a wire with a female connector terminal.
This is the YouTube video that helped me out.
These wires (female to male) will be what you would need for the connection depicted in your image.
You cut off three suitable lengths of heat shrink tubing, thread each wire through it, and move the tubing back a cm or two from the wire end, then solder each wire to each pin, taking care not to leave any spikey bits that might puncture the tubing.
Then you slide the tubing up to cover the joint and then shrink the tubing. A heat gun with controlled temperature works best, but the barrel of soldering iron will work (slowly) or some folks apparently use an open flame. Don't use a sooty flame, as soot is electrically conductive.