Hiscox's toggle-joint duplex air compressor uses a crank to move the common joint of long arms, with toggle straightening increasing piston power near the terminal part of the stroke. The calculator below compares an abstract symmetric two-link free body at two entered angles only.
Toggle-joint Duplex Air Compressor Interactive Calculator
Enter two link angles from the straight axis. Results compare ideal symmetric-toggle force quotients only; they do not predict piston force, pressure, flow, torque or compressor performance.
Equation Used
- Each comparison uses two equal symmetric links at the entered angle from a straight axis.
- Links are ideal two-force members with frictionless pins.
- A transverse force acts at the knee and equal axial reactions act at the ends.
- The two angle states are independent comparisons, not points from a solved crank cycle.
- Actual Hiscox geometry, crank path, pistons, gas pressure, valves, displacement, flow, speed, torque, friction, inertia, deformation, strength, capacity and safety are omitted.
Historical Compressor Arrangement
Gardner D. Hiscox's movement 648 states that the crank moves the common joint of the long arms horizontally on a slide and that straightening the toggle increases piston power during the terminal part of the stroke, when air pressure is greatest.
This historical description explains the linkage arrangement and the increase in leverage near the end of the stroke. Compressor output also depends on cylinder dimensions, speed, pressure and valve behavior, which are outside this calculator.
What This Calculator Does
The tool evaluates the ideal symmetric-toggle force quotient at two independently entered angles. It reports their quotient ratio and the relative change from A to B.
It does not solve Hiscox's crank path, piston motion, cylinder pressure, displacement or air delivery.
Two-angle Comparison
MB = 1/(2 tan thetaB)
Q = MA/MB
D = 100(1-MB/MA)
The factor two is required for the symmetric two-link free body. Both angles must exceed zero.
Worked Ideal Comparison
At theta A=5 degrees, the ideal quotient is about 5.7. At theta B=30 degrees, it is about 0.9. Their quotient ratio is about 6.6, and B is about 84.8% below A.
These dimensionless comparisons do not establish compressor force, pressure or output.
Model Boundary
- Historical arrangement: a crank moves the common joint of long arms and toggle straightening increases piston power late in the stroke.
- Calculated: ideal symmetric-link quotient at two independent angles and direct comparisons.
- Not calculated: actual linkage geometry, crank phasing or motion, piston force or stroke, bore, swept volume, pressure, valves, volumetric efficiency, free-air delivery, torque, energy, receiver behavior, wear, maintenance, materials, ratings or safe operation.
Frequently Asked Questions
Why does the force-ratio equation contain a factor of two?
The displayed symmetric free body has two link-force components, so the correct ideal quotient is 1/(2 tan theta).
Do A and B represent actual compressor positions?
Not unless independently established from real geometry; here they are comparison inputs.
Does the relative-change output predict pressure change?
No.
Does duplex mean two compression strokes per revolution?
This calculator does not establish cycle timing or phasing.
Can it calculate CFM or volumetric efficiency?
No.
Can it diagnose or specify a compressor?
No. Use authenticated machine documentation and qualified service guidance.
References
- Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, movement 648: Toggle-joint Duplex Air Compressor.
- William Rogers, Pumps and Hydraulics, Part Two: historical air-pump and toggle-joint terminal-stroke leverage context.
- University of Maryland, Engineering Mechanics: Statics lecture notes: free-body equilibrium and toggle-mechanism mechanical advantage.
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