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Originally Posted by kamocat
Yes, you need overlap between your rollers.
I'll use the term "tread width" here to mean the distance (perpendicular to the wheel axis) that the rollers contact the ground when the 'bot is moving forward. On many two-plate designs, this is also the distance between the plates.
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I think you meant "parallel".
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I believe determining what angle of the wheel that will cover is an inverse sine function of (tread width)/(wheel radius).
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Yes, you can get a good-enough answer just by dividing the tread_width by the wheel_radius and that gives you the angle in radians that is subtended by each roller. Pedantically, the calculation should be 2*asin(tread_width/2/wheel_radius)
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So take 360 divided by that angle, and round up. That's how many rollers you need on your wheel.
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If there is overlap, that has to be subtract from the angle before dividing.