BIZOMAT MAKEOS · Gears
Cam Pressure Angle
What is the maximum pressure angle for this cam rise, base circle and roller follower?
Maximum pressure angle and its position for a radial (in-line) roller follower on a disc cam, from the base circle, roller radius, rise, cam angle and motion law, against a limit.
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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. |
| Rise | mm | Total follower rise. |
| Cam angle for the rise | ° | Cam rotation over which the rise occurs. |
| Base circle radius | mm | Radius of the base circle (smallest cam radius). |
| Roller radius | mm | Radius of the follower roller. |
| Maximum pressure angle allowed | ° | Largest pressure angle your design allows (about 30° for translating followers is a common guide). |
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’s rise against cam rotation. It sets how steep the displacement curve gets and so how high the pressure angle peaks.
- Units and format
- Choose one of 4 options from the list: Cycloidal; Simple harmonic; 3-4-5 polynomial; Constant acceleration (parabolic).
- Example
- The form opens with “Cycloidal” selected as a worked example. Choose the option that matches your case.
What this means: Rise
- What it is
- The total distance the follower moves outward 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
- A larger rise makes the profile steeper and raises the pressure angle.
What this means: Cam angle for the rise
- What it is
- How many degrees the cam turns 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 90° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Spreading the rise over a larger angle lowers the pressure angle.
- Get it right
- Use the angle for the rise only, not the whole rise, dwell and return cycle.
What this means: Base circle radius
- What it is
- The radius of the smallest circle that touches the cam profile, centred on the cam shaft: the cam surface at the follower’s lowest position.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 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 the cam surface radius; the tool adds the roller radius to get the prime circle.
What this means: Roller radius
- What it is
- The radius of the roller on the end of the follower that runs on the cam surface.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000 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 increases the prime circle radius and lowers the pressure angle.
- Get it right
- Enter the radius, not the roller diameter.
What this means: Maximum pressure angle allowed
- What it is
- The largest pressure angle your design accepts for this follower, set by your design practice or the follower guide’s capacity to resist side load.
- 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 standard or follower supplier; it depends on follower guidance and overhang.
Method and formulas
- Prime circle radius Rp = Rb + Rr.
- Follower displacement y(θ) and slope dy/dθ from the motion law.
- Pressure angle φ = atan((dy/dθ) ÷ (Rp + y)); the maximum is found by sampling the rise.
- Example: a 20 mm cycloidal rise over 90° on a 40 mm base circle peaks at 23.233°.
Limitations
- Radial (in-line) translating roller follower; offset and oscillating followers need different relations.
- Undercutting (radius of curvature) is a separate check.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose the smallest base circle that keeps the pressure angle acceptable
- Check a cam design for jamming
- Compare motion laws
Who it is for
- Machine designers
- Automation engineers
What you get
- Maximum pressure angle and where it occurs
- Prime circle radius
Interpreting the result
- If the pressure angle is too high, enlarge the base circle or spread the rise over a larger cam angle.
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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