Smith’s circular bellows has two stacked sections to help maintain an even blast between pumping strokes. A hand lever moves the lower board, while an upper chamber stores air. The animation illustrates this arrangement. The calculator uses entered volume per counted stroke, stroke rate and volumetric efficiency: delivered volume is Vsη and average flow is VsNη.
Smith's Circular Bellows · Selected Flow Ledger
Explore exact selected volume-flow arithmetic without treating the efficiency input as a bellows-performance prediction.
Equation Used
- Vs is ideal volume per counted stroke.
- N uses the same counted-stroke convention.
- η is a selected dimensionless multiplier.
- Valve dynamics, leakage, pressure, pulsation, work and temperature are excluded.
Use the same stroke definition for both the entered volume and stroke rate. The animation shows one lower-board compression per cycle; its proportions do not determine the entered volume.
Two chambers for a steadier blast
Hiscox’s item 622 shows two stacked circular bellows sections with a hand lever and a link to the lower board. The drawing here shows the lower pumping chamber and upper reservoir. A fixed middle board carries the lever fulcrum, and the rigid connecting link raises and lowers the bottom board. Upper-board motion illustrates air storage and delivery; internal valves and air pressure are not shown or calculated.
What the calculator determines
Select ideal volume per counted stroke, counted strokes per minute and an efficiency factor. The calculator reports exact selected delivered, lost and per-minute volumes.
Selected flow arithmetic
Vdel=Vsη; Vloss=Vs(1−η); Q=VsNη. L/min=1000Q.
Selected-input example
For Vs=0.040 m³/stroke, N=30 strokes/min and η=62.5%, delivered volume is 0.025 m³/stroke and selected average flow is 0.750 m³/min.
What the flow result means
Volumetric efficiency is an entered factor, not calculated from valves, leakage, pressure, dead volume or speed. Double-acting event counting, outlet pulsation, pressure rise, operator work and temperature are excluded.
Questions
What is one counted stroke?
It is exactly the event represented by the selected Vs and N inputs; the calculator does not reinterpret cycles or double-acting chamber events.
Does η predict a real bellows?
No. It is a selected multiplier.
Replacing manual motion in Smith's Circular Bellows Mechanism
If smith's circular bellows mechanism is converted to actuator drive, the actuator is no longer just a replacement for a crank or cam. It becomes part of the timing, force, and limit-control system, so the travel must be checked through the full motion.
With leverage, force is traded against travel. A bracket change that improves force can also increase required stroke, slow the output motion, or move the actuator into a poor mounting angle.
A crank or cam may tolerate continuous rotation through a difficult part of the cycle, while a linear actuator has defined end positions and internal limits. That difference matters when the mechanism needs repeatability or must not drive into a hard stop.
- Map actuator stroke to the actual output travel before choosing a model.
- Check for binding, changing leverage, and peak load near the ends of travel.
- Decide whether timed motion is acceptable or position feedback is required.
For a FIRGELLI design review, calculate the load case with the FIRGELLI actuator force calculator and plan the switching or controller arrangement with the linear actuator wiring diagram generator. If an actuator or cylinder is already installed, the linear actuator replacement finder helps keep the comparison tied to real dimensions.
References & Further Reading
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances (1901), page 168, item 622: Smith’s circular bellows, in two parts for a uniform blast.
- Wikipedia contributors. Bellows. Wikipedia
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