Cam Follower Motion Calculator: Displacement, Velocity and Acceleration (SHM, Cycloidal and Parabolic)
Follower motion for a cam rise.
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How this calculator works
Choose the type of follower motion.
Enter the rise, the rise angle and the cam speed.
Enter the cam angle to calculate at.
Formulas used
- s = \frac{h}{2}\left(1 - \cos\frac{\pi\theta}{\beta}\right)
- v = \frac{\pi h\omega}{2\beta}\sin\frac{\pi\theta}{\beta}
- a = \frac{\pi^2h\omega^2}{2\beta^2}\cos\frac{\pi\theta}{\beta}
Worked example
With the default numbers in the calculator above:
- Displacement of the follower: 10 mm
- Velocity of the follower: 0.62832 m/s
- Acceleration of the follower: 0 m/s2
- Largest velocity during the rise: 0.62832 m/s
- Largest acceleration during the rise: 39.478 m/s2 (4.026 g)
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: Follower motion Cycloidal motion.
- Displacement of the follower: 10 mm
- Velocity of the follower: 0.8 m/s
- Acceleration of the follower: 0 m/s2
- Largest velocity during the rise: 0.8 m/s
- Largest acceleration during the rise: 50.265 m/s2 (5.126 g)
Common questions
Which follower motion is the smoothest?
Cycloidal motion, because the acceleration is zero at the start and end of the rise, so there is no jump.
Which has the lowest peak acceleration?
Constant acceleration (parabolic) motion, but the acceleration jumps suddenly at the start, middle and end.
Why does acceleration matter?
The force on the follower and the cam is the mass times the acceleration, so a high peak acceleration means high forces, noise and wear.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any theory of machines text (cam and follower motion).
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