[alogo] Roulette

In the most general case Roulettes are curves generated by rolling a curve a, without slipping, along another curve a. The Roulette is generated by a point rigidly attached to the rolling curve b. The system below illustrates [Roulettes] resulting when a circle of radius b rolls inside a circle of radius a > b. Besides N = a/b is here an integer. Given the radii a and b. The shape of the roulette depends on the distance h of the attached point from the center of the rolling b-circle. For h=b we get the hypocycloids with N cusps (see Hypocycloid.html ). For h < b we get the hypotrochoids.

[0_0] [0_1] [0_2] [0_3]
[1_0] [1_1] [1_2] [1_3]
[2_0] [2_1] [2_2] [2_3]

To change the shape of the roulette change N or/and the location of the moving point (red) attached to the rolling disc.

See the file Roulette2.html for the case of a circle rolling ouside the big circle and a point attached to the rolling disc.

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