The Cycloidal profile curves may be seen with reference to figure below.  This profile is derived by assuming that the follower acceleration function is a sine curve.


The necessary understanding of this profile can be obtained from the graph of the functions, as seen in the graph.


Cycloidal Properties: 


The acceleration is a maximum at θ/β=0.25

The acceleration is a minimum at θ/β=0.75

The velocity is a maximum at θ/β=0.50

The curves are symmetrical; therefore the displacement at θ/β=0.50 is 1/2 of the total.

The velocity curve has zero slope at θ/β=0, θ/β=0.5, θ/β=1.0.  This means the acceleration is zero at these points.

The displacement has zero slope at θ/β=0 and θ/β=1.  This means the velocity is zero at these points.

Acceleration of the follower is required to increase the velocity from zero and deceleration is required to reduce the velocity from a non-zero value.  This is true whether the resulting velocity is positive or negative.


1.These curves are drawn for a positive displacement of the follower.  A negative displacement will result in a mirror image of the graphs about the x-axis.

2.The X axis is θ/β from 0 to 1

3.The Y axis is based on a displacement of 1.


Figure 1

Cycloidal Profile