BIZOMAT MAKEOS · Mechanics
Cam and Spring-Loaded Follower Design
Will this cam’s follower stay in contact at speed, what spring preload does it need, and is the pressure angle acceptable?
Design check of a radial cam with a translating roller follower held by a spring: follower displacement, velocity and acceleration through the rise for simple harmonic, cycloidal or constant-acceleration motion, the maximum pressure angle, the contact force through the cycle from inertia, spring and external load, and the spring preload needed to keep contact with a margin.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Rise motion | choice | Motion law used for the rise (the return is assumed symmetric). |
| Rise | mm | Total lift. |
| Cam angle for the rise | ° | Cam rotation over which the rise happens. |
| Cam speed | rpm | Cam speed. |
| Base circle radius | mm | Base circle radius of the cam. |
| Roller radius | mm | Radius of the follower roller. |
| Follower and linkage mass | kg | Moving mass reduced to the follower. |
| External load opposing the rise | N | Constant external force the follower works against. |
| Spring rate | N/mm | Return spring rate. |
| Spring preload at the bottom of the rise | N | Spring force with the follower at the bottom of its travel. |
| Contact margin on preload | Factor on the preload needed just to keep contact. | |
| Pressure angle limit | ° | Largest pressure angle you accept (about 30° for translating followers). |
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: Rise motion
- What it is
- The mathematical motion curve the follower follows during the rise. It decides how velocity and acceleration vary, and so the peak acceleration and spring force needed.
- Units and format
- Choose one of 3 options from the list: Simple harmonic; Cycloidal; Constant acceleration (parabolic).
- Example
- The form opens with “Cycloidal” selected as a worked example. Choose the option that matches your case.
- Get it right
- The return is assumed to mirror the rise; dwell periods are not modelled.
What this means: Rise
- What it is
- Total distance the follower travels during the rise, from the lowest to the highest point of its motion.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 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
- Follower velocity and acceleration rise in proportion to the lift.
- Get it right
- Measure lift at the follower; if a lever multiplies the motion, enter the lift at the cam.
What this means: Cam angle for the rise
- What it is
- Angle the cam turns through while the follower completes its rise. A larger angle spreads the same lift over more rotation.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° 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; the pressure angle also falls.
- Get it right
- Use the rise angle only, not the full cycle including dwells and return.
What this means: Cam speed
- What it is
- Rotational speed of the camshaft. With the cam angle it sets how fast the follower moves.
- 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 600 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Follower acceleration and the inertia force rise with the square of speed.
- Get it right
- Use the camshaft speed, not motor speed, if there is a reduction between them.
What this means: Base circle radius
- What it is
- Radius of the smallest circle that touches the cam profile, centred on the camshaft. It is where the follower sits at the bottom of the rise.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger base circle lowers the pressure angle but makes the cam bigger.
- Get it right
- This is a radius from the camshaft centre, not a diameter.
What this means: Roller radius
- What it is
- Radius of the roller on the follower that runs on the cam. It is added to the base circle radius in the pressure angle calculation.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger roller slightly lowers the pressure angle.
- Get it right
- Enter the radius, half the roller diameter; 0 treats the follower as a point contact.
What this means: Follower and linkage mass
- What it is
- Mass of the follower and everything moving with it, referred to the follower’s line of motion: stem, roller, linkage and part of the spring.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 10000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The inertia force rises in proportion, so more preload is needed to keep contact.
- Get it right
- Include the share of the spring mass that moves and any linkage, referred to the follower motion through its lever ratio.
What this means: External load opposing the rise
- What it is
- Steady external force pushing the follower back towards the cam throughout the rise, such as a process or gravity load.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N to 1000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- An opposing load helps keep contact, reducing the preload needed.
- Get it right
- Enter 0 when nothing but the spring holds the follower on the cam.
What this means: Spring rate
- What it is
- Stiffness of the return spring that holds the follower against the cam: the extra force per millimetre of compression as the follower rises.
- Units and format
- Enter a number in N/mm: newtons per millimetre. The form accepts 0 N/mm to 1000000 N/mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 N/mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the rate of the actual spring from its data sheet; 0 means a constant force with no spring rate.
What this means: Spring preload at the bottom of the rise
- What it is
- Force the return spring already exerts when the follower is at the bottom of its rise, before any lift.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More preload raises the minimum contact force; it must exceed the preload needed.
- Get it right
- This is installed spring force, not free length; measure or calculate from the installed compression.
What this means: Contact margin on preload
- What it is
- Multiplier applied to the preload that is only just enough to keep the follower on the cam, to cover spring tolerance and dynamic effects.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The preload needed rises in proportion.
- Get it right
- This multiplies the minimum preload, so 1 gives no margin at all.
What this means: Pressure angle limit
- What it is
- Largest pressure angle you accept between the follower’s line of motion and the normal to the cam surface at contact. Steep angles push the follower sideways and can jam it.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 5° to 60°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take the limit from your design practice for the follower type; it is checked against the maximum during the rise.
Method and formulas
- Follower motion y(θ), y′(θ), y″(θ) for the chosen law; velocity = y′ω, acceleration = y″ω².
- Pressure angle = atan[y′ ÷ (R_b + R_r + y)], maximum found over the rise.
- Contact force N = F₀ + k y + F_ext + m a; the follower jumps where N < 0.
- Preload needed = margin × max(−m a − F_ext − k y) over the rise.
- Example: a 20 mm cycloidal rise over 120° at 600 rpm peaks at 113.1 m/s² and needs 142.44 N of preload.
Limitations
- Rigid follower train; at high speed elasticity adds vibration and needs a dynamic model.
- Symmetric return assumed; dwell periods are not modelled.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size the return spring for a cam follower
- Check a cam for follower jump at a higher speed
- Choose base circle size for the pressure angle
Who it is for
- Machine designers
- Automation engineers
- Design engineers
What you get
- Peak velocity, acceleration and pressure angle
- Minimum contact force through the rise
- Spring preload needed
Interpreting the result
- Cycloidal motion has no jerk spikes and is preferred at speed; a larger base circle lowers the pressure angle.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2284–2310. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Useful alongside · BIZOMAT original book
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