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How to pull on a fishing line

I'm making some simple motorized (but small) clothing accessories, and part of it is actuated by pulling on a length of fishing line. I'm trying to figure out the best way to do that. I was thinking a little spool, but there are some problems. The fishing line could go slack if the part is pushed on, and I need the line to not unspool. Second is that it needs to be really small... the closer to about a half centimeter (from flange to flange), or less, the better. I'm having a hard time finding something that small. Is there some better way than a spool? I was thinking about just wrapping it on the drive shaft of the motor, but I don't know if the RPMs will be adequate at such a small diameter (it's a geared motor). I only need to pull about a couple inches in say... 500 to 750 ms... with something like https://solarbotics.com/product/gm24/ Any advice? Thanks.

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I think you may be looking for a regular ol' servo with an extended arm on it (to give you the couple inches throw you need). The only issue would be the room needed for the swing of the arm.

You might be looking for one of these https://solarbotics.com/product/gm11a/  or something similar. I have used these little gear motors for years and they are great little motors. I think your spool thing would work, you just have to do the math on the dia of the spool vs. the RPM of the motor to figure your pull speed.