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The speed is not a factor but the acceleration of the person is. The equations are m= mass of the person $\mu=friction\ index$ $\alpha= acceleration$ g=9.8ms^2 $\theta= angle\ of\ the\ ramp$ $$F_{net}=mgsin \theta-\mu mcos\theta=ma$$ Dividing both sides by m we get $$a= g sin\theta-\mu cos\theta$$ This is the acceleration downslope if the person is ...

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Contact motor vendors. They will be happy to recommend options. Their goal is to help you ultimately buy their offering for your product. I've seen where they recommend one option, and if it doesn't perform well enough, provide others at no (or reasonable) cost to help you get the right combination. This at least is my experience in big industry.

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From the solutions you are suggesting: increasing the gear ratio: the gear ratio is already too high. And even if you add another gearbox, in series, you would still get a respective drop in rpm ordering a custom DC motor: to me that is the viable solution, although expensive. Edit: after comment that might improve this answer. As you noted you can't go ...

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I think it's the effect of "tightening the screw", a lot of friction distributed over a large area. Even if the plate doesn't bend, it will still accumulate a bunch of tension, and as a result, friction. You need to stop the motor before that happens. I think a mechanical stop could work: put a small "blade" of sheet metal on the shaft (...

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What's causing the plate to become stuck is a binding action. As the plate hits the hook stop, it will start to tilt. As it tilts further and further the friction between the disk and screw will increase until the motor stalls. As you've noticed this friction is basically omnidirectional, so once the motor is stalled you generally cannot retract it. This ...

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I'd make both stops as big as the moving plate itself, so you're not putting a moment on that plate. I imagine that's mostly what's causing the problem. You could also use springs or rubber bumpers at the ends so it's not so much of a hard stop, but it will compress until it just reaches stall torque. That might help prevent it from really getting stuck from ...

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This is probably either motor backlash or residual magnetisim in the motor poles, or both. You'll need to measure out how much is actually there. There are many ways to model this. The basic idea is to have a piston that fills up and doesn't allow anything to pass unless the piston is either fully extended or fully retracted.

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