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A cycloid is a curve generated by a point on the circumference of a circleWhich 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
Draw a circle with given diameter as shown
Diameter
Divide the circle 12 equal parts as shown
0’
0/121
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5 7
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9
1011
6
Name the points as shown
0’
0/121
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5 7
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9
1011
6
πD
Draw a line equal to circumference i.e. πD as shown
0’
0/121
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3
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5 7
8
9
1011
6Divide the line 12 equal parts as shown
1 2 3 4 5 6 7 8 9 10 11 0/12
0’
0/121
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5 7
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9
1011
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1
Draw a centre line as shown
1 2 3 4 5 6 7 8 9 10 11 0/12
0’
0/121
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5 7
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9
1011
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1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a vertical line as shown from point 1
0’
0/121
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5 7
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1011
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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
0’
0/121
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5 7
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9
1011
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
0’
0/121
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3
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5 7
8
9
1011
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw vertical a line as shown from point 2
0’
0/121
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5 7
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9
1011
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
0’
0/121
2
3
4
5 7
8
9
1011
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
0’
0/121
2
3
4
5 7
8
9
1011
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a vertical line as shown from point 3
0’
0/121
2
3
4
5 7
8
9
1011
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
0’
0/121
2
3
4
5 7
8
9
1011
6
1 2 3 4 5 6 7 8 9 10 11 0/121 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
0’
0/121
2
3
4
5 7
8
9
1011
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a vertical line as shown from point 4
0’
0/121
2
3
4
5 7
8
9
1011
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
0’
0/121
2
3
4
5 7
8
9
1011
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
0’
0/121
2
3
4
5 7
8
9
1011
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a vertical line as shown from point 5
0’
0/121
2
3
4
5 7
8
9
1011
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
0’
0/121
2
3
4
5 7
8
9
1011
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
0’
0/121
2
3
4
5 7
8
9
1011
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Draw a vertical line as shown from point 6
0’
0/121
2
3
4
5 7
8
9
1011
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
0’
0/121
2
3
4
5 7
8
9
1011
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
0’
0/121
2
3
4
5 7
8
9
1011
6
1 2 3 4 5 6 7 8 9 10 11 0/12
Join the points with smooth curve as shown
0’
0/121
2
3
4
5 7
8
9
1011
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
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