A circular cam mounted off-centre on a rotating shaft can drive a pump plunger back and forth. In the arrangement shown here, a flat follower touches the cam, a return spring maintains contact, and two check valves direct intake and delivery. Change plunger diameter and stroke to calculate ideal displacement per revolution and see how the motion works.
Reciprocating Pump From Rotary via Cam Interactive Calculator
Vary plunger diameter and stroke length to see the cam pump displacement per stroke and per shaft revolution.
Equation Used
- One single-acting plunger displacement per cam revolution.
- A spring maintains contact between the translating flat follower and eccentric circular cam.
- No volumetric loss, pressure, valve dynamics, spring force, contact stress, torque or speed limit is predicted.
The follower face stays tangent to the circular cam, and the connected plunger moves with it. When the plunger retracts, the inlet check opens; when it advances into the chamber, the delivery check opens. The animation illustrates that sequence with ideal valve states.
How the eccentric cam drives the plunger
The shaft turns about a fixed centre. The centre of the circular cam is offset from that shaft by eccentricity e. As the cam turns, its rightmost edge moves towards and away from the pump chamber. The vertical follower face touches that edge, so the follower and attached plunger translate horizontally.
Advancing the plunger reduces liquid space in the chamber and produces the delivery stroke. Retracting it increases that space and produces the intake stroke. The drawing shows the corresponding check valve open on each stroke and both checks shut at changeover. Real valves respond to pressure differences and have their own dynamics.
Parts shown
- Eccentric circular cam: converts shaft rotation into follower motion.
- Flat follower and plunger: move together along a straight path.
- Return spring: represents the force needed to maintain contact as the cam recedes.
- Plunger seal and chamber: define the liquid space whose volume changes.
- Inlet and delivery checks: direct liquid through the chamber.
The display assumes continuous follower contact. It does not establish the spring force required to achieve it. Materials, clearances, pressure capability and service life are outside this geometric model.
Where this arrangement is useful
A cam-driven plunger illustrates how a rotating machine can produce repeated liquid-displacement strokes. The same principle is useful when considering timed dosing or lubrication: shaft revolutions provide a convenient way to count pumping cycles.
Use the calculator to compare the volume swept by different plunger diameters and strokes. A target dose can then be compared with the ideal volume per revolution. Actual metering needs delivery measurements and the details of the fluid, valves, seals and drive.
The animation represents one eccentric circle with one flat follower. It is not a model of every cam-driven pump, and its displacement results do not establish compatibility with a particular chemical, pressure or commercial pump.
Displacement and motion equations
Let d be plunger diameter and S be the full stroke, both in millimetres. The area A is in mm². Dividing the swept volume in mm³ by 1000 converts it to mL.
One delivery stroke occurs per revolution, so Volume / Rev equals Stroke Volume. Rev / mL is 1/V. These are ideal geometric volumes, without leakage or incomplete filling.
For the illustrated flat follower, x is the horizontal location of its face measured from the shaft centre, R is the circular cam radius and θ locates the cam centre relative to that shaft. The difference between maximum and minimum x is 2e = S. Constant shaft speed therefore produces harmonic follower motion. End positions are momentary stops, not dwells.
If speed N in RPM is supplied separately, ideal average flow is Q = VN in mL/min. If volumetric efficiency eta_v has been established separately, estimated delivered flow is VN × eta_v. Neither speed nor efficiency is an input to this calculator; no flow-rate result is displayed.
Worked example: the default plunger
With diameter d = 6 mm and stroke S = 10 mm:
- Area A = π × 6²/4 = 28.274 mm².
- Swept volume V = 28.274 × 10/1000 = 0.282743 mL/stroke.
- One pumping cycle per revolution gives 0.282743 mL/rev.
- Its reciprocal is 3.5368 rev/mL.
- The physical eccentricity required for this motion is S/2 = 5 mm.
The output cards round these results to 28.3 mm², 0.283 mL/stroke, 0.283 mL/rev and 3.54 rev/mL. If diameter alone is doubled to 12 mm, displacement rises fourfold to 1.131 mL/rev. If stroke alone is doubled to 20 mm, displacement doubles to 0.565 mL/rev.
As a separate arithmetic example, the default displacement at 60 RPM would give an ideal average flow of 16.96 mL/min. This assumes one delivery stroke per revolution and no volume loss. The playback speed is not that operating speed, and the example does not establish a permissible pump speed.
What each input changes
| Change | Calculated effect |
|---|---|
| Increase diameter | Area and displacement grow with diameter squared; Rev / mL decreases. |
| Increase stroke | Displacement grows in direct proportion; area stays constant. |
| Move the cycle-position control | Changes the displayed pose and valve state, without changing displacement per complete cycle. |
| Play or pause | Controls the demonstration; it does not set shaft RPM or pump flow. |
A differently shaped cam can produce a different motion schedule, including a dwell. A crank drive instead imposes a motion law through crank and connecting-rod geometry. Comparing their loads, wear or pressure capability requires more information than diameter and stroke.
Cam-pump questions
Why are Stroke Volume and Volume / Rev the same?
This model has one single-acting plunger and one pumping cycle per shaft revolution. One cycle includes an intake stroke and a delivery stroke. Only the delivery stroke contributes the ideal displaced volume.
What does Rev / mL mean?
It is the reciprocal of ideal displacement per revolution. At the default 6 mm diameter and 10 mm stroke, one revolution displaces about 0.283 mL, so the calculation gives about 3.54 revolutions per mL. It describes average displacement, not a continuous stream without pulses.
Why does diameter have a larger effect than stroke?
Area is proportional to diameter squared, while displaced volume is directly proportional to stroke. Doubling diameter gives four times the volume. Doubling stroke gives twice the volume, with the other input held constant.
Does the circular cam provide a dwell?
No. With a flat follower and constant shaft speed, this eccentric circle produces harmonic reciprocation. The plunger momentarily stops at each end of travel but does not remain there over a finite shaft angle. A cam with a dwell needs a different profile.
Is the return spring sized by this tool?
No. The drawing assumes the spring keeps the follower in contact. Spring preload, stiffness, moving mass, operating speed and fluid loading are not inputs, so follower separation and contact force are not predicted.
Can I calculate flow from the displayed volume?
If shaft speed is known separately, multiply mL/rev by RPM to obtain ideal mL/min. An independently established volumetric efficiency can adjust that estimate. This calculator has neither a speed nor an efficiency input and cannot determine either value.
Will a real pump deliver exactly the displayed volume?
Not necessarily. Leakage, incomplete filling, trapped gas and valve behaviour can change delivered volume. The tool calculates geometric displacement; it does not measure accuracy or diagnose the cause of a delivery shortfall.
Do the input limits specify a suitable pump design?
No. They are exploration ranges for diameter and stroke. Pressure rating, permissible speed, sealing clearances, materials and service intervals must come from the actual pump design and operating conditions.
Technical reference
Carnegie Mellon University, Introduction to Mechanisms, Chapter 6: Cams explains translating followers, follower configurations, contact constraints and cam motion. The displacement equations above follow from the circular-cam and plunger geometry shown here.
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