A cycloid is a curve generated when a circle rolls along a straight line without slipping. The document provides step-by-step instructions to draw a cycloid curve by marking points along the circumference of a rolling circle and connecting those points to form the curve. First, a circle is divided into 12 equal parts and a line is drawn that is the length of the circle's circumference. Corresponding points on the circle and line are then connected to create the curved shape of a cycloid.

2. A cycloid is a curve generated by a point on the circumference of a circle
Which rolls in a plane surface along a straight line without slipping
πD
1 2 3 4 5 6 7 8 9 10 11 12
Principles of cycloid

3. Draw a circle with given diameter as shown
Diameter

4. Divide the circle 12 equal parts as shown

5. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
Name the points as shown

6. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
πD
Draw a line equal to
circumference i.e. πD as shown

7. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
Divide the line 12 equal parts as shown
1 2 3 4 5 6 7 8 9 10 11 0/12

8. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1
Draw a centre line as shown
1 2 3 4 5 6 7 8 9 10 11 0/12

9. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a vertical line as
shown from point 1

10. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a horizontal line
line as shown from
point 1 on the circle

11. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Locate the point as
shown such that the
line drawn is equal to
radius of circle and
locate point as shown

12. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw vertical a line as
shown from point 2

13. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a horizontal line
line as shown from
point 2 on the circle

14. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Locate the point as
shown such that the
line drawn is equal to
radius of circle and
locate point as shown

15. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a vertical line as
shown from point 3

16. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a horizontal line
line as shown from
point 3 on the circle

17. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
1 2 3 4 5 6 7 8 9 10 11 0/1
Locate the point as
shown such that the
line drawn is equal to
radius of circle and
locate point as shown

18. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a vertical line as
shown from point 4

19. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a horizontal line
line as shown from
point 4 on the circle

20. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Locate the point as
shown such that the
line drawn is equal to
radius of circle and
locate point as shown

21. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a vertical line as
shown from point 5

22. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a horizontal line
line as shown from
point 5 on the circle

23. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Locate the point as
shown such that the
line drawn is equal to
radius of circle and
locate point as shown

24. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a vertical line as
shown from point 6

25. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a horizontal line
line as shown from
point 6 on the circle

26. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Locate the point as
shown such that the
line drawn is equal to
radius of circle and
locate point as shown

27. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Join the points with smooth curve as shown

28. 0’
0/12
1
2
3
4
5 7
8
9
10
11
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Complete the curve as
shown with mirror
image already drawn
and is the required
cycloid