- #1
Zetor
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So the kinematics of the contact point of a disc rolling without slip in a Cartesian plane if fairly straightforward. The velocity for the contact point is just
v = ω r ev
where r is the wheel radius and ev the current direction vector of the wheel.
However, say that you grab the plate and force a rotation that is not around the axis around where it would roll when rolling freely on the floor. If the plate is vertical, the contact point will not change (if anything you will drill a hole in the table after while perhaps). However, if you lean the plate, this rotation will clearly induce a change of the contact point. The rate of change is largest when the plate is almost flat to the surface. Does that make sense? I could not find any visualization for this, nor did I bother to formulate this formally as I do not think it helps too much, but if you grab a plate you could probably figure out what I mean.
Where can I find a model for this kinematics? I am modeling a unicycle and no papers I have read so far consider this effect. As I could not find any full model for it yet, I guess the topic classifies as advanced. Probably the answer is related to the projection of the disc onto the plane.
v = ω r ev
where r is the wheel radius and ev the current direction vector of the wheel.
However, say that you grab the plate and force a rotation that is not around the axis around where it would roll when rolling freely on the floor. If the plate is vertical, the contact point will not change (if anything you will drill a hole in the table after while perhaps). However, if you lean the plate, this rotation will clearly induce a change of the contact point. The rate of change is largest when the plate is almost flat to the surface. Does that make sense? I could not find any visualization for this, nor did I bother to formulate this formally as I do not think it helps too much, but if you grab a plate you could probably figure out what I mean.
Where can I find a model for this kinematics? I am modeling a unicycle and no papers I have read so far consider this effect. As I could not find any full model for it yet, I guess the topic classifies as advanced. Probably the answer is related to the projection of the disc onto the plane.
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