BIZOMAT MAKEOS · Gears
Cam Follower Peak Velocity and Acceleration
What peak velocity, acceleration and inertia force does this cam rise produce?
Peak follower velocity and acceleration for simple harmonic, cycloidal, constant-acceleration and 3-4-5 polynomial rise motions at a given cam speed, with the follower inertia force.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Motion law | choice | Motion law of the rise segment. |
| Rise (lift) | mm | Total follower rise. |
| Cam angle for the rise | ° | Cam rotation angle over which the rise happens. |
| Cam speed | rpm | Cam shaft speed. |
| Follower moving mass | kg | Mass of the follower and parts moving with it. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Motion law
- What it is
- The mathematical shape of the follower motion during the rise, which sets the peak velocity and acceleration coefficients.
- Units and format
- Choose one of 4 options from the list: Simple harmonic; Cycloidal; Constant acceleration (parabolic); 3-4-5 polynomial.
- Example
- The form opens with “Cycloidal” selected as a worked example. Choose the option that matches your case.
- Get it right
- Simple harmonic and constant acceleration have acceleration jumps at the ends of the rise; cycloidal and 3-4-5 polynomial do not.
What this means: Rise (lift)
- What it is
- The total distance the follower moves during the rise, from its lowest to its highest position.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Peak velocity, acceleration and inertia force rise in proportion.
- Get it right
- Use the follower lift, not the cam radius difference if a rocker arm changes the ratio.
What this means: Cam angle for the rise
- What it is
- The angle the cam turns through while the follower completes the rise.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 1° to 360°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Acceleration falls with the square of this angle, so a longer rise angle greatly lowers it.
- Get it right
- Enter the rise angle only, not the whole rise, dwell and return cycle.
What this means: Cam speed
- What it is
- The rotational speed of the camshaft.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Acceleration and inertia force rise with the square of speed.
- Get it right
- Use the camshaft speed, which may differ from the motor or crankshaft speed.
What this means: Follower moving mass
- What it is
- The mass of the follower and every part that moves with it during the rise, such as push rods, tappets and tooling.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 100000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Peak inertia force rises in proportion; velocity and acceleration do not change.
- Get it right
- Include a share of the return spring mass if your method calls for it.
Method and formulas
- ω = 2πn ÷ 60; β in radians.
- Simple harmonic: v = πhω ÷ 2β, a = π²hω² ÷ 2β². Cycloidal: v = 2hω ÷ β, a = 2πhω² ÷ β².
- Constant acceleration: v = 2hω ÷ β, a = 4hω² ÷ β². 3-4-5 polynomial: v = 1.875hω ÷ β, a = 5.7735hω² ÷ β².
- Inertia force = m × a.
- Example: a 20 mm cycloidal rise over 120° at 300 rpm peaks at 28.274 m/s².
Limitations
- Rise segment only; dwell transitions with simple harmonic and parabolic laws have acceleration jumps that cause vibration.
- Follower and frame flexibility are not modelled.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose a cam motion law for a mechanism
- Check follower spring force needed to keep contact
- Compare peak accelerations of motion laws
Who it is for
- Machine designers
- Automation engineers
What you get
- Rise time
- Peak velocity
- Peak acceleration
- Peak inertia force
Interpreting the result
- Cycloidal and 3-4-5 laws have no acceleration jumps and suit higher speeds.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2284–2309. Topic reference; no source tables or recommended settings are reproduced.
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Open the Cam Follower Peak Velocity and Acceleration calculator