Spherical Cycloid

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One can construct rolling curves on the sphere in the same way as in the plane. A drawing stick is attached to the rolling circle and draws the curve. The point where the rolling circle touches the fixed circle (or: where the rolling wheel touches the street) is a momentary fixed point of the rolling motion of the sphere. This implies a tangent construction for the rolling curve: The tangent is orthogonal to the segment between the current curve point and the current fixed point ( or: orthogonal to the current “radius”)
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Rolling curves drawn with sticks of varying length.
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Rolling curves from varying stick length rendered as tubes.



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Rolling curve with osculating circles. Note that these best approximating circles lie on the sphere. Their midpoints trace out a curve called evolute.
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The normals of the rolling curves are drawn until they meet the evolute.