Stephenson link motion uses two eccentric rods to move the ends of a slotted expansion link. A die block connected to the valve gear occupies a selectable position in that slot, changing the combined motion and its timing between forward-side, mid-gear and reverse-side settings.
If an actuator adjusts the link setting
An actuator used to adjust a reversing linkage needs a force and stroke calculation for that actual linkage. The interpolation below does not include adjustment loads, mounting positions or the suspension mechanism.
For a separate actuator application, use the FIRGELLI actuator force calculator for its supported mounting arrangement, compare specifications in the FIRGELLI linear actuator range, or consult the linear actuator replacement finder for an existing unit.
Reversing Gear Interactive Calculator
Compare a weighted combination of two sinusoidal motions. The numeric results use the Shaft Angle input; playback moves the illustration separately. This is an interpolation example, not a complete Stephenson valve-gear calculation.
Equation Used
- The endpoint values are sinusoids with equal amplitude r and phase offsets +δ and −δ.
- The output is a weighted average of the two endpoint values.
- The half-length reference sets only the numeric offset sY, not drawing size.
- Complete valve events, real link geometry, forces, clearances and ratings are excluded.
The companion view repeats the same symbolic illustration. Numeric results remain tied to the entered shaft angle during playback.
How Stephenson link motion selects valve motion
Two eccentrics on the engine shaft drive rods attached to opposite ends of a slotted expansion link. A die block in the slot transmits motion to the valve rod, directly or through a rocker. Changing the relative position of link and block changes the motion sent to the valve.
The historical mechanism uses a curved link with defined rod lengths and suspension geometry. The illustration here uses symbolic rods and a straight slot to introduce motion selection; their motion does not solve that rigid linkage.
What the interpolation shows
Use the calculator to see how a weighting changes the contribution of two motions. Moving the block setting toward +100% favors the forward-side value; moving it toward −100% favors the reverse-side value. The setting names relate to link-gear selection, but the result is not a prediction of engine direction or steam admission.
Change Shaft Angle to compare positions through a cycle. Increase Endpoint Amplitude to scale both endpoint values and the interpolated result. The half-length reference affects only the numeric block offset.
Weighted endpoint displacement
Divide the Block Setting percentage by 100 to obtain s between −1 and +1. The assumed endpoint values are xF = r sin(θ + δ) and xR = r sin(θ − δ). Their weighted combination is x = ½(1+s)xF + ½(1−s)xR.
Here θ is the entered shaft angle, δ is the phase offset and r is the sinusoidal amplitude. At s = +1, x equals xF; at s = −1, it equals xR. At s = 0, it is their average. The separate block-offset output is sY.
These equations are evaluated at the entered angle. Playback phase is not used in the numeric results. The formulas describe an interpolation, not the full geometry or valve events of Stephenson gear.
Worked example
At θ = 60°, δ = 30° and r = 30 mm, the endpoint values are 30 mm and 15 mm. A block setting of about +83.33% gives s ≈ 0.8333 and x ≈ 28.75 mm. With Y = 200 mm, the block-offset result is about 166.67 mm.
At a zero block setting, x is the average, 22.5 mm, and block offset is zero. The displacement does not generally vanish at the middle setting.
Reading the illustration and results
The moving drawing and the numeric outputs use different angles during playback. The drawing advances around a cycle, while the outputs stay at the Shaft Angle input. Use Return to start to reset playback phase to zero when comparing the entered angle with the illustration.
Rods, slot and output slider are symbols. Their displayed lengths are not a closed rigid-link solution, the half-length input does not resize them, and the slider can extend beyond its drawn housing at large amplitudes. Do not use the picture for dimensions or clearances.
A real valve-motion calculation needs eccentric positions, rod lengths, link curvature, suspension, rocker geometry, valve lap and lead. This tool does not determine admission, cut-off, exhaust, forces, wear or operating limits.
Link-motion questions
Does mid-gear make every part stop?
No. The eccentrics and rods still move. In this interpolation, a zero block setting gives the average of the two endpoint values, which is generally nonzero.
Does this calculate steam cut-off or valve travel?
It calculates the weighted displacement of two assumed sinusoidal motions. It does not solve actual Stephenson valve travel or port events. Those require the complete mechanism, valve lap and lead.
Why do the result numbers stay still during playback?
They are evaluated at the Shaft Angle input. Playback advances the drawing separately, so the moving slider is not a live indication of those numbers. Return to start sets animation phase to zero; change Shaft Angle to compare calculated positions.
What does link half-length change?
It changes only the numeric block offset, sY. It does not resize the drawing or affect the interpolated displacement. The physical link length and curvature are not solved.
How is the block setting used?
The percentage is divided by 100 to give s. At +100% the result equals the forward-side endpoint; at −100% it equals the reverse-side endpoint. At zero it is their average.
Primary references
- Bilgram, Slide Valve Gears — two eccentrics, eccentric rods, expansion link and sliding block in Stephenson link motion.
- US757411A, Valve-gear — virtual-eccentric paths, block position and combined rocking and translating link motion.
- Zeuner, Treatise on Valve-Gears (1869) — historical Stephenson link-motion arrangement and selection.
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