A geared air-pump drive turns motor rotation into a piston’s back-and-forth motion. A pinion drives a crank gear, whose offset pin moves a connecting rod and guided piston. Use the calculator to compare stroke, cycle rate and mean piston speed as crank offset, motor speed and gear ratio change. These motion values do not determine airflow or pressure by themselves.
Air-pump Movement Interactive Calculator
Vary crank offset, motor speed, and gear reduction to see piston stroke, pump cycle rate, frequency, and piston speed.
Equation Used
The crank pin offset r sets the piston travel directly: stroke equals 2r. The gear ratio reduces motor speed to crank speed, so pump cycles per minute equal motor rpm divided by the crank-gear-to-pinion ratio.
- One piston stroke cycle occurs per crank gear revolution.
- Gear ratio is crank gear teeth divided by motor pinion teeth.
- Stroke is set by crank offset only: stroke = 2r.
- Mean piston speed uses total reciprocating travel per cycle: 2 x stroke.
How the geared pump drive works
The motor pinion and crank gear turn in opposite directions. Their tooth-count ratio determines crank speed. The crank pin travels in a circle, while the connecting rod constrains the piston to its cylinder axis.
For the inline crank-slider shown, crank radius r produces stroke 2r. One crank revolution includes an outward and a return stroke: one complete reciprocating cycle. The piston slows to zero at each end and moves fastest between the ends; the Piston Speed card is a cycle average, not its instantaneous speed.
Parts in the animation
- Motor pinion: drives the larger crank gear.
- Crank gear: establishes the output rotation rate.
- Offset crank pin: sets the stroke.
- Connecting rod: links the rotating pin to the guided piston.
- Cylinder guide: keeps piston travel straight.
The animation uses a fixed rod length and an illustrative cylinder bore. Actual pump delivery also requires chamber and valve geometry. Not every air pump has this drive: oscillating-armature diaphragm pumps and rotary pumps use different motion arrangements.
Where this motion is useful
Crank drives are used in reciprocating compressors, inflators and some piston or diaphragm pumps. Gearing lets a designer choose a pump cycle rate independently of motor speed, while crank offset determines the displacement travel.
For a piston pump, a longer stroke increases swept volume at a given bore. Higher cycle rate increases theoretical volume per minute, but real delivery depends on pressure, clearance, leakage, valve behavior and temperature. A diaphragm’s useful chamber displacement also depends on its shape and flexure.
The calculator compares drive motion. Equipment selection still needs manufacturer flow-versus-pressure data, duty limits, gas compatibility and the required air quality. A motion result alone does not establish suitability for medical, breathing-air or other specialized service.
Stroke, frequency and mean speed
Let r be crank offset in millimetres, N be motor speed in rpm, and G be crank-gear teeth divided by pinion teeth. The inline slider stroke S is 2r. Crank rate n = N/G cycles per minute, and frequency f = n/60 hertz.
Mean piston speed = 2Sn/1000 metres per minute when S is in millimetres. The factor two counts travel in both directions during each cycle. For example, a 12 mm stroke covers 24 mm of total piston travel per revolution.
These are kinematic relations. If a separate single-acting piston calculation has bore D, its theoretical swept volume per cycle is πD²S/4. Multiplying by cycle rate gives theoretical displacement flow in consistent units. Actual inlet-referenced delivery needs a suitable volumetric-efficiency model or test data. Bore and efficiency are not controls in this calculator, so it does not display flow.
Rod length influences the instantaneous motion and side loading, but not the 2r stroke of this inline geometry. The model does not calculate motor torque, piston force, air pressure, wear or a maximum permissible speed.
Worked example: a geared crank-slider
Enter crank offset 6 mm, motor speed 3600 rpm and gear ratio 1.8. Stroke is 2 × 6 = 12 mm. Crank rate is 3600/1.8 = 2000 cycles/min, and frequency is 2000/60 = 33.33 Hz.
Mean piston speed is 2 × 12 × 2000/1000 = 48 m/min. Changing the ratio to 3.6 halves crank rate to 1000 cycles/min, frequency to 16.67 Hz and mean piston speed to 24 m/min; stroke remains 12 mm.
At the original speed and ratio, changing offset to 3 mm halves stroke to 6 mm and mean speed to 24 m/min, while cycle rate and frequency remain unchanged. This example describes entered geometry and speed, not a particular inflator’s measured performance or tire-inflation time.
Comparing pump drives
| Drive | Motion | Design consideration |
|---|---|---|
| Geared crank-slider | Gears drive a crank and connecting rod. | Ratio sets cycle rate; crank offset sets stroke. |
| Direct crank-slider | Motor shaft drives the crank directly. | Crank rate follows motor rate without a reduction stage. |
| Scotch yoke | A crank pin moves in a transverse slot. | Sinusoidal travel in the ideal geometry; pin-slot contact needs suitable design. |
| Oscillating-armature diaphragm drive | An electromagnetic drive flexes a diaphragm. | No rotating crank gear is required. |
Service life, noise, cost and pressure capability depend on the complete pump. This table does not assign universal performance ratings to a drive type.
Air-pump drive questions
It is crank-gear teeth divided by motor-pinion teeth. A ratio of 3 means the crank completes one revolution for three motor revolutions.
One crank revolution gives one complete outward-and-return cycle. The piston travels twice the stroke length during that cycle.
Gearing changes crank speed. Crank offset, not gear ratio, sets the inline piston stroke.
No. It is total piston travel per cycle multiplied by cycle rate. Instantaneous velocity changes throughout the cycle and is zero at the travel endpoints.
No. Piston bore, chamber clearance, valves, pressure and volumetric efficiency also matter. The calculator reports motion only.
No. The finite connecting rod gives an inline crank-slider a different displacement curve from the ideal sinusoidal motion of a scotch yoke. Both can have stroke twice their crank radius.
It is slowed 400-fold for viewing. The numerical cycle rate and mean piston speed describe the entered operating speed.
No. They do not model faults, lubrication or thermal behavior. Use the actual pump’s operating and service information; do not infer universal backlash, bearing clearance or valve replacement limits from this diagram.
References and further reading
U.S. Department of Energy: Improving Compressed Air System Performance covers compressor and system performance. It provides broader context for the difference between drive displacement and delivered air; it is not a specification for the illustrative mechanism.
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