This curve (of the trigonometric family), as the name implies, is basically generated from a cycloid. A cycloid is the locus of a point on a circle which is rolled on a straight line. Applied to cam contours, this line is the y axis, the circumference of the circle is made equal to rise h, and the radius is equal to h/2π .for high speeds, the cycloidal curve is the best of all contours if the accuracy of machining can be maintained at the beginning and at the end of the stroke where other curves exhibit their difficulty.
It has the lowest vibration, wear, stress, noise and shock. The reason for its excellent performance is that there is no change in sudden acceleration at the intersection of the dwell period and the rise curve .It is easy starting , the spring needed to keep the follower on the cam is small , and the side thrust of the translating follower is low.
Characteristics:
The equation for the displacement is
y=h/π (φ-1/2sin2φ)
= h/π (πθ/β-1/2sin2πθ/β).
Differentiating to find the velocity and acceleration yields
v=dy/dt= hω/β (1-cos2πθ/β)
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