The speed of the curve is the length of the first derivative. For a non-zero number of rotations within the Frenet frame, the amount of rotation is proportional to the speed. It can be observed from the difference between the twisting to the same knot with zero rotations. The models in the first and the last rows wind once around the meridian. If for these models we have R = 2r, then the motion of the Frenet frame has a discontinuity at cost = 0 and sint = 1. This is the reason for the rapid twisting in the neighborhood of the point where the curve passes through the narrow neck of the torus.


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(1, 1, -24/6)

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(1, 1, -12/6)

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(1, 1, 0)

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(1, 2, -24/6)

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(1, 2, -12/6)

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(1, 2, 0)

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(1, 3, -24/6)

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(1, 3, -12/6)

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(1, 3, 0)

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(2, 2/2, -24/6)

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(2, 2/2, -12/6)

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(2, 2/2, 0)

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