Textbook of Engineering Drawing, Second Edition

4.28 Textbook of Enginnering Drawing------------------

4.3.1 Cycloid

A cycloid is a curve generated by a fixed point on the circumference of a circle, when it rolls
without slipping along a straight line.

To draw a cycloid, given the radius R of the generating circle.

Construction (Fig. 4.41)

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9

Directing line

2nR

Fig. 4.41 Construction ofa Cycloid

1. With centre ° and radius R, draw the given generating circle.

B

2. Assuming point P to be the initial position of the generating point, draw a line PA, tangential

and equal to the circumferance of the circle.

3. Divide the line PA and the circle into the same number of equal parts and nuber the points.


4. Draw th~ line OB, parallel and equal to PA. OB is the locus of the centre of the generating
   circle.


5. Errect perpendiculars at 1 I,2I,3I, etc., meeting OB at ° 1 , 0z' 03' etc.


6. Through the points 1,2,3 etc., draw lines parallel to PA.

7. With centre 0, and radius R, draw an arc intersecting the line through 1 at PI' PI is the

position of the generating point, when the centre of the generating circle moves to ° 1 ,

S. Similarly locate the points Pz, P 3 etc.

9. A sIIlooth curve passing through the points P,P I' P z,P 3 etc., is the required cycloid.
   Note: T-T is the tangent and NM is the normal to the curve at point M.