I must be missing something. Let P be the original plane, and Q be the plane containing the axis that is perpendicular to P. Can't you just move the axis in the direction perpendicular to Q, rolling the circle as you go, so that the circle-plane contact describes a straight line? More generally, move the axis any way you like, keep the circle in a plane parallel to its original position. Have the circle rotate so that the speed of rotation matches the speed at which the circle/plane intersection moves. Isn't this "rolling without slipping"? Andy On Sun, Sep 9, 2012 at 12:01 PM, David Wilson <davidwwilson@comcast.net> wrote:
Consider a circle whose diameter lies on a fixed axis line passing obliquely through a plane (not perpendicular to the plane)
Now rotate the circle about the axis line subject to the following conditions:
- The plane position is fixed. - The circle radius is fixed. - The axis is parallel to its initial position. - The circle is tangent to the plane, on the same side of the plane as its initial position.
Can the circle be made to move without slippage along the plane? What is the locus of the point of circle-plane contact?
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