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A string is wound over a circular disc. It is now unwound with its “free end” letting it remain tight and tangent to the disc. The curve traced by the “free end” is

A string is wound over a circular disc. It is now unwound with its “free end” letting it remain tight and tangent to the disc. The curve traced by the “free end” is Correct Answer Involute

Involute

  • Involute is the curve traced by a point on a chord as it unwinds (but remains tight) around a circle
  • Alternatively, an involute may be defined as the curve traced by a point on a straight line which rolls around a circle or polygon without slip

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  • Depending on the plane shape around which the line rolls, the involutes are named as involute of a triangle, involute of a square, involute of a polygon, involute of a circle etc

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  • Application: The most common application of involute is seen in the manufacture of gears. The profile of a gear tooth is the shape of an involute

Cycloid: When the generating circle rolls on a straight line, the path of the point is a cycloid.

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Epicycloid: When the generating circle rolls on the outside (convex side) of a larger circle, the path of the point is an epicycloid. ​

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Hypocycloid: When the generating circle rolls on the inside (concave side) of a larger circle, the path of the point is a hypocycloid. 

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