CYCLOIDS,EPICYCLOIDS ,HYPOCYCLOIDS

What is a Cycloid?

• A cycloid is a curve generated by a point on the circumference of the circle as the circle rolls along a straight line with out slipping..
• The moving circle is called the "Generating circle" and the straight line is called the "Directing line" or the "Base line".
• The point on the Generating circle which generates the curve is called the "Generating point"

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Construction of a Cycloid

EPICYCLOIDS

What is Epicycloid?

• The cycloid is called the epicycloid when the generating circle rolls along another circle outside(directing circle)

• The curve traced by a point on a circle which rolls on the out side of a circular base surface

CONSTRUCTION OF EPICYCLOID

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HYPOCYCLOIDS

construction of hypocycloid

• The curve traced by a point on a circle which rolls on the inside of a circular base surface.

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Applications of the cycloids

• cycloid curves are used in the design of the gear tooth profiles
• It is also used in the conveyor of mould boxes in the foundry shops.
• cycloidal curves are mainly used in Kinematics.