Calculating Distance Traveled by a Point on a Rotating Wheel

[willworkforfood]

If I know a distance the center of a wheel travels and what the radius of that wheel is, in what manner can I figure out how far some point on the rim of the wheel travels?

 

[andrevdh]

Try rolling a round object along a ruler.

 

[arildno]

You can't, really, unless you know the angular velocity.
A common case will be that the angular velocity is given implicitly by assuming that the wheel ROLLS on the surface, in which case a point on the rim will have moved a distance equal to the distance the contact point on the surface has travelled.
In the simplest case of that again, when the surface is flat, the distance the contact point on the ground has traveled equals the distance the center of the wheel has travelled, in which case a point on the rim has traveled the same distance as the center of the wheel.

 

[BobG]

If I know a distance the center of a wheel travels and what the radius of that wheel is, in what manner can I figure out how far some point on the rim of the wheel travels?

Relative to what? Technically, a point on the rim moves the same distance the wheel travels. That doesn't mean it will always be the same distance from the starting point as the center.

Relative to the starting point, the point on the rim doesn't trace out a straight line - it traces out a sine wave. Sometimes the point is below the center of the wheel, sometimes behind, sometimes ahead, etc.

The key is to figure out how the distance traveled by the center of wheel changes the 'phase' of the point on the rim. You then have to adjust the distance traveled by the radius times the cosine of the phase. Look at the 'easy' points and you should start to get the idea. Then you have to come up with an equation that expresses what's happening (relate the distance traveled to the phase).

If you need the distance from the starting 'point' rather than just the horizontal distance, it will get more complicated (the point is moving up and down relative to the center in addition to back and forth relative to the center).

 

[andrevdh]

willworkforfood,
the distance traveled by a point (on the rim of a wheel) is the sum of it's rotational distance (around the axis of the wheel) and it's translational distance traveled (the distance the axis has travelled) - does this make sense to you?