Cams | KEVOS

§1Cam and follower

A cam rotates (or slides) and, through its profile, drives a follower in a precisely timed motion — a valve opening, a tool advancing, a mechanism indexing. It turns steady rotation into any motion you can draw.

The pairing is simple: the cam is the driver with the worked profile; the follower is held against it by a spring or gravity and traces that profile as motion. A full cam cycle is built from segments — a rise (follower moves out), a dwell (follower held stationary while the cam turns), a return (follower moves back), and often another dwell. The designer specifies what motion is wanted in each segment, and the cam profile is then whatever shape delivers it. Everything therefore starts with the graph of that motion.

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§2The displacement diagram

The displacement diagram plots follower lift s against cam angle θ over one revolution. It is the specification of the cam, drawn before any profile is laid out.

Reading it is a chain of derivatives against angle: the slope of the displacement curve is the follower velocity, the slope of that is the acceleration, and the slope of the acceleration is the jerk. Each matters for a different reason — velocity for the follower’s speed, acceleration because it sets the inertia force (F = m·a) the spring must overcome and the contact stress it drives, and jerk because sudden changes in acceleration cause vibration, noise and wear. A good cam law keeps acceleration finite and, ideally, continuous. The hero shows the four standard laws for one rise, and their acceleration is where they differ most.

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§3The motion laws

Four displacement laws cover most cam design, each a different compromise between simplicity and smoothness. All raise the follower by the same lift h over the same rise angle β; they differ in how.

The four rise laws and their peak acceleration (as a multiple of h ω²/β²)
Law	Character	Peak accel factor
Uniform velocity	Constant speed; a straight ramp	∞ (at ends)
Parabolic (constant accel)	Accelerate then decelerate; lowest peak	4.00
Simple harmonic (SHM)	Cosine rise; smooth interior	4.93
Cycloidal	Accel zero at both ends; no shock	6.28
The factor is the multiplier on h ω²/β² that gives the maximum follower acceleration, where ω is the cam’s angular velocity (the Velocity, Acceleration, Work and Energy page) and β the rise angle in radians.

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§4Comparing the laws

The counter-intuitive result: the law with the highest peak acceleration is the best for high-speed cams. Peak value is not the whole story — continuity is.

Uniform velocity looks ideal until the ends: to start and stop the follower instantly demands infinite acceleration, an impossible shock that hammers the mechanism, so it is used only with rounded corners or for slow, lightly-loaded motion. Parabolic motion gives the lowest finite peak acceleration (factor 4.0), attractive for the inertia force alone, but its acceleration jumps abruptly at the start, middle and end — steps that produce finite jerk spikes and vibration. Simple harmonic motion is smooth through the middle but still steps its acceleration at the two ends. Cycloidal motion has the highest peak (factor 6.28), yet its acceleration rises from zero and returns to zero at each end and is continuous throughout — so there is no sudden jerk anywhere. That smoothness makes cycloidal the standard choice for high-speed cams, where vibration and noise, not peak force, are the limiting problem. The rule of thumb: choose parabolic to minimise force at modest speed, cycloidal to minimise vibration at high speed, SHM as an easy middle ground.

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§5Base circle and pressure angle

Two further choices decide whether the cam actually works smoothly: how big to make it, and how steeply the profile pushes the follower sideways.

tan α = ds/dθr_p + s — larger base circle (r_p) → smaller pressure angle α

The base circle is the smallest circle of the cam profile; every dimension grows from it. The pressure angle α is the angle between the direction the follower moves and the line along which the cam actually pushes it — the cam analogue of the gear pressure angle. A large pressure angle throws much of the force sideways across the follower stem, jamming it in its guide; keeping α below about 30° for a translating follower is the usual limit. The cure is a larger base circle: it flattens the profile’s slope for the same lift, dropping the pressure angle — so a jamming cam is very often simply too small, and enlarging it fixes the motion at the cost of size.

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§6Worked rise

A single rise puts numbers on the three finite laws.

Example 1 — a 20 mm rise over 120° at 300 rev/min

Lift h = 20 mm, rise angle β = 120° (2.094 rad), cam speed 300 rev/min so ω = 31.42 rad/s. The base term h ω²/β² = 0.020 × 31.42²/2.094² = 4.500 m/s². The peak follower accelerations are then: parabolic 4.00 × 4.500 = 18.0 m/s²; simple harmonic 4.93 × 4.500 = 22.2 m/s²; cycloidal 6.28 × 4.500 = 28.3 m/s². The SHM peak follower velocity is π h ω/(2β) = 0.471 m/s, reached at mid-rise. So the cycloidal cam accelerates its follower half again as hard as the parabolic at the peak — but does so without the jerk that would make the parabolic cam rattle at this speed.

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§7Quick reference

The working core of the page on one card rack.

Segments

rise · dwell · return · dwell

Diagram

s → v → a → jerk

(slopes against angle)

Peak accel

parab 4.0 · SHM 4.93

cycloidal 6.28 × hω²/β²

Choose

parabolic → least force

cycloidal → least shock

Pressure angle

keep α < 30°

bigger base circle → smaller α

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Handbook application: from concept to controlled practice

Purpose. This expanded section turns the original page into a practical handbook. It preserves the supplied material and adds a repeatable way to apply, check and review Cams. It does not replace a contract, legislation, a controlled standard, competent engineering judgement or specialist advice.

The operating aim is to carry the subject from function and assumptions through design evidence, verification and controlled release. Read the original explanation first, then use the workflow and checks below to convert knowledge into evidence.

Apply Cams by beginning with the duty, not the component or software command. Convert the key ideas—laws, cams, displacement, diagram, motion—into measurable requirements and interfaces. Record operating and non-operating environments, duty cycle, expected life, loads, energy sources, human interaction and reasonably foreseeable abnormal conditions. When a value is not a project requirement or verified supplier datum, identify it as an assumption or illustrative value.

Create a calculation and evidence trail that another competent person can audit. Every input should carry a source, unit, revision and uncertainty or tolerance where relevant. Every model should state its boundary conditions and limitations. Keep nominal capacity separate from design capacity, and keep verification margin separate from an arbitrary safety factor. If a code or standard governs the work, confirm the applicable edition and contractual status rather than copying a number from a secondary summary.

Design for manufacture, assembly, inspection, operation and maintenance at the same time. A technically valid geometry can still fail because it cannot be fixtured, measured, cleaned, guarded, reached or replaced. Review process capability, datum or reference strategy, tolerance accumulation, access, error-proofing and changeover. Where people interact with plant, apply the hierarchy of controls and consult those who will operate, clean, maintain and recover the equipment.

Plan verification before release. Define the characteristic, method, equipment, sample or test condition, acceptance criterion, record and responsible person. Validation then asks a different question: whether the resulting system is effective and suitable in the intended use context. A passed drawing check or analysis does not by itself validate usability, maintainability or production performance.

Step-by-step operating method

Define the duty. Capture the required function, interfaces, operating environment, life, loads and unacceptable outcomes.
Establish the model. Identify governing principles, units, material or process data, assumptions and uncertainty.
Develop alternatives. Compare feasible concepts against performance, manufacturability, safety, maintainability and cost.
Verify the design. Use analysis, test, inspection or demonstration with acceptance criteria defined before execution.
Release and learn. Baseline the design, control changes, retain evidence and feed operating results into the next revision.

Illustrative design review record

Illustrative values only. Build a one-page record with the required function, input sources, assumptions, governing load or process condition, failure consequences, selected concept, verification method and acceptance criterion. Mark every numerical input as project requirement, verified supplier data, measured value, calculation output or assumption. Review the weakest evidence first. If an assumption can change safety, compliance, interchangeability or capacity, it must be resolved before release rather than buried in a calculation note.

Evidence class	Question	Release expectation
Requirement	What must the design do and under which conditions?	Approved and traceable
Input	Where did the load, property, tolerance or process limit come from?	Source, unit and revision recorded
Analysis	Which model and assumptions connect input to result?	Checkable calculation or simulation
Verification	How will conformity be demonstrated?	Method and acceptance criterion agreed
Validation	Will the solution work for intended users and conditions?	Representative use evidence

Common failure modes and recovery actions

1. Watch for

Starting detailed design before interfaces and operating limits are agreed.

Recovery: Return to the governing definition or requirement and restate the decision in one sentence.

2. Watch for

Using catalogue or typical values as though they were certified project inputs.

Recovery: Separate evidence from assumption, assign an owner and set a date for validation.

3. Watch for

Checking nominal performance while ignoring tolerances, degradation and foreseeable misuse.

Recovery: Run a small counterexample, boundary test, pilot or independent check before proceeding.

4. Watch for

Confusing verification of requirements with validation of user need.

Recovery: Record the consequence, decision and rationale, then update the controlled baseline.

5. Watch for

Releasing drawings or procedures without configuration, inspection and change controls.

Recovery: Escalate when the issue affects safety, compliance, acceptance, material value or an agreed tolerance.