Technical Drawing - Cycloids - Basic Cycloid
What is a Cycloid ?
A Cycloid is the path or Locus followed by a point on a circle when it moves a long a straight line without slipping.
Construction of a Cycloid
Below is a discription of how to construct a Cycloid for a point Pon a circle as it rotates along a straight
line without slipping.
Now divide the circle into an equal number of parts. Here we have used the 60°-30° set square to give us 12 equal divisions. Lable these sections 0 to 12.
Taking the distance between any two of these points with your compass mark 12 off these distances along the base line along which the circle will rotate. Lable these points 0 to 12 as shown. When taking the distance between any two of the divisions of the circle you should add a little bit to the distance on your compass to account for the curve of the circle.
Project the new points onto a line from the centre of the circle and label then C1 to C12.
As the circle rotates along the line, point 1 on the circle will move to point 1 on the line, and therefore the center of the circle will now be at point C1.
Next project lines from the equal divisions of the circle parallel to the straight line. These are the height lines.
With your compass set to the radius of the circle, place the point of the compass on the point C1 and cut the height line coming from point 1 on the circle. Then repeat this for point C2 and height line 2, etc. until you reach point C12 and line 12.
By joining these new points you will have created the locas of the point P for the circle as it rotates along the straight line without slipping. In other words, you have created a Cycloid.
Essentially what you have done is break up the continuous movement of the circle along the straight line into 12 sections and found the position of point P for each movement.
It would get very cluttered if you drew in every circle along the way.
And your final result is a Cycloid.
Construction of a Tangent and a Normal to a point on a Cycloid
You can construct a Tangent and a Normal to
any point on the Cycloid by using this method.
How to find the Centre of Curvature to a point on a Cycloid
You can find the Centre of Curvature to any point on
the Cycloid by using this method.