Roulette

The name of a planar curve considered as the trajectory of a point which is rigidly connected with some curve rolling upon another fixed curve. In case a circle rolls upon a straight line, the roulette is a cycloid; if a circle rolls upon another circle it is a cycloidal curve; if a hyperbola, an ellipse or a parabola rolls upon a straight line it is a Sturm curve (cf. Sturm curves). The trajectory of an ellipse rolling upon another ellipse is called an epi-ellipse. Each planar curve can be considered as a roulette in many ways; for example, any curve can be formed by rolling a straight line upon its evolute.

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