This calculator gives the ideal maximum axis swing of an oscillating-cylinder geometry whose trunnion lies outside the crank-pin circle. The difference C−r shows whether the trunnion lies outside the crank-pin circle.
Inverted Slider-crank Interactive Calculator
Explore ideal tangent-limited swing from crank radius and crankshaft-to-trunnion spacing, with a clear C>r validity condition.
Equation Used
- Crank pin follows a circle of radius r about a fixed crankshaft center.
- Oscillating cylinder/guide axis always passes through the fixed trunnion and crank pin.
- Crankshaft center and trunnion are separated by fixed distance C.
- Bounded tangent extrema require C>r; C<=r is flagged as invalid for this interpretation.
- No piston length/stroke/dead centers, cylinder bore/ports, slider fit, trunnion dimensions, clearance/interference, force, pressure, torque, friction, leakage, dynamics, strength, wear or safety model.
The relation theta_max=asin(r/C) applies to the line from a fixed trunnion to a crank pin moving on a circle only when C>r. If C<=r, the trunnion lies on or inside the crank-pin circle and the assumed bounded oscillating-axis geometry is invalid; the displayed 90-degree cap is only a limit indicator.
Crank-pin and trunnion geometry
The crank pin moves on a radius-r circle about the crankshaft. A line from the fixed trunnion to the pin represents the oscillating cylinder or guide axis. Its extreme angle occurs when that line is tangent to the crank circle, giving sin(theta_max)=r/C.
The axis passes through the trunnion and crank pin, and its illustrated swing changes with the entered r/C ratio.
Use as a first-principles swing check
The result can verify the ideal angular envelope of the specified two-center geometry. It cannot define piston stroke, port timing, steam admission, force, speed or a complete engine.
Validity condition
For C>r, tangent geometry gives peak swing asin(r/C) and total symmetric sweep twice that value. C/r is a spacing ratio and C−r is the radial separation from the crank circle.
If C<=r, the trunnion is not outside the crank circle, so there is no pair of external tangents and the bounded-swing formula does not apply.
Worked example
For r=9.5 mm and C=25 mm, r/C=0.38, peak axis swing is 22.33 degrees, total sweep is 44.67 degrees, C/r is 2.632 and bounded-geometry margin is 15.5 mm.
Limits of the geometry calculation
The two entered dimensions determine an angular envelope, not a complete engine. Piston travel, cylinder clearance and port timing need further geometry. Loads, bearing reactions and pressure are not calculated.
Questions
What does a zero or negative margin mean?
C<=r, so the assumed bounded oscillating-axis geometry is invalid.
Does total sweep equal piston stroke?
No. Stroke is a length requiring complete cylinder/piston geometry.
Does this determine port timing?
No. Port positions and cylinder dimensions are absent.
References & Further Reading
- Wikipedia contributors. Slider-crank linkage. Wikipedia
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