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A circle rolls without slipping on a flat surface. The path traced by a point, lying on circle’s periphery during its rolling is:

A circle rolls without slipping on a flat surface. The path traced by a point, lying on circle’s periphery during its rolling is: Correct Answer Cycloid

There are different Engineering Curves:

Cone is a surface generated by making a straight line keeping one of its end fixed and other end making a closed curve.

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Conics: The locus of point moves in a plane in such a way that the ratio of its distance from a fixed point (focus) to a fixed straight line (Directrix) is always constant. PF/PM = Const

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Ellipse is the locus of a point which moves in a plane so that the ratio of its distance from a fixed point (focus) and a fixed straight line (Directrix) is a constant and less than 1. PF/PM < 1

 

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Parabola is the locus of a point, which moves in a plane so that its distance from a fixed point (focus) and a fixed straight line (directrix) are always equal. PF/PM = 1

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Hyperbola is the locus of a point which moves in a plane so that the ratio of its distances from a fixed point (focus) and a fixed straight line (directrix) is constant and greater than one.

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Cycloidal group of curves:

When one curve rolls over another curve without slipping or sliding, the path of any point of the rolling curve is called Roulette.

When the rolling curve is a circle and the curve on which it rolls is a straight line or a circle, we get cycloidal groups of a curve.

A cycloid is a locus of a point on the circumference of a rolling circle (generator), which rolls without slipping or sliding along a fixed straight line or a directing line.

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Epicycloid is a locus of a point on the circumference of a rolling circle (generator), which rolls without slipping or sliding outside another circle called directing circle.

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Hypocycloid is a locus of a point (P) on the circumference of a rolling circle (generator), which rolls without slipping or sliding inside another circle called directing circle.

 

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A trochoid is a locus of a point inside/outside the circumference of a rolling circle, which rolls without slipping or sliding along a fixed straight line or a fixed circle.

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