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My father is a software engineer and yesterday he asked me a question to test me, that I cannot, for the life of me, seem to figure out. He told me that I need to make a tissue paper dispenser that, upon activation, would dispense tissue paper of only length 15cm. Now suppose I have a tissue roll of 7.5 cm with a hole in the center of the roll with a radius of 3 cm, height 15 cm and the thickness of one sheet of tissue being 0.1mm. The tissue paper roll would go onto a stand and that stand is controlled by the rotations of a motor fixed to it. Now you tell me, how would this machine of yours work. Would the rotation of the motor in order to dispense be angle of rotation dependent or would it be time dependent? How would you account for the continuously changing radius of the toilet paper? What would be the formula, rather, algorithm you would use for this rotation of the motor and the continual change of radius, considering you need some buffer length of tissue from the roll to the cutter?

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  • $\begingroup$ I'd be more concerned about how to stop the paper tearing then the loose end sticking to the roll messing with the feed. When I need toilet paper and none comes out, that is much worse than if 20cm comes out when it should be 15cm. $\endgroup$
    – DKNguyen
    Nov 25 '21 at 16:35
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Use two drive rollers with the paper gripped between, then drive the rollers with a stepper motor or even a cam and switch to control the length.

That way the diameter of the supply roller is moot.

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  • $\begingroup$ What about those crappy rolls where it is so tight or mashed it tears when you pull on it? Though I suppose the paper tearing at any point by mistake or the user could leave the loose end stuck to the roll even if it was on a spindle and not pull rollers. $\endgroup$
    – DKNguyen
    Nov 25 '21 at 16:34
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A partially non-contact method would be to use the components and circuit of an optical mouse. A roller on the surface roll would keep the mouse circuit a uniform distance from the material on the roll, while the circuit provides a measurement reference. When one considers that some optical devices advertise four hundred dots per inch, one could expect excessive accuracy in the dispensing.

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If you want to use an angle sensor you could use a second distance sensor to measure roll diameter before you start dispensing and just assume the diameter is constant as you roll out one sheet rather than doing a spiral calculation. Because accuracy isn't that important, the sheet is short, and the paper is very thin relative to the diameter of an empty roll, let alone a full roll.

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Use a surface drive; the radius wouldn't matter.

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