Stephenson link motion uses two eccentric rods and a slotted expansion link to vary the motion delivered to a valve rod. Explore those components and a separate ideal illustration of blending two opposite motions.
Stephenson Link Motion Source-Selection Explorer
Select an idealized gear coordinate and axle phase. The output shows weights for two equal-and-opposite normalized source motions; it is a teaching abstraction, not a dimensional valve-gear solution.
Equation Used
- The two illustration sources are normalized, equal and exactly opposite.
- The selected coordinate g is not a reverser-notch calibration or physical die-block distance.
- Valve travel, lap, lead, port opening, cutoff, forces, wear and safe adjustment are outside the model.
The upper diagram identifies the expansion link, die block and valve connection. The lower illustration blends two equal-and-opposite motions to explain source selection; it does not calculate valve events for an engine.
Stephenson link-motion topology
Two eccentrics on the shaft drive two eccentric rods connected to opposite ends of a curved, slotted expansion link. A die block in that slot is connected directly or through a rocker to the valve rod. Raising or lowering the link places the die block nearer the forward-gear rod, the back-gear rod or an intermediate point.
The animation's upper view is a labelled schematic of those parts. The lower view is an intentionally separate normalized interpolation, not a geometric simulation of the rods and link.
Historical reversing and expansion gear
Historical engineering texts describe Stephenson link motion as widely used on locomotives and other steam engines. The page is for mechanism identification. Inspection, setting and operation require the exact engine drawings, procedures and qualified steam-locomotive practice.
Ideal symmetric teaching model
The two illustrative sources are defined as xF=cos(phi) and xR=-cos(phi). Their weighted sum reduces to g cos(phi). This only visualizes full-forward, mid and full-reverse source selection. It is not a Stephenson valve-event equation.
Reading the ideal illustration
At g=+1 the forward-source weight is 100 percent. At g=0 the two ideal opposite sources have equal weight and cancel. At g=-1 the reverse-source weight is 100 percent. A real gear can retain lead and other motion at mid-gear, so the illustration must not be used for dimensions or timing.
Model boundary and safety
The page does not predict valve travel, port opening, lap, lead, cutoff, tractive effort, coal use, wear limits, tolerances, fault causes or adjustment. Those depend on the exact gear proportions, suspension, eccentric setting, valve geometry and operating conditions.
Stephenson link-motion questions
Is this the same topology as Walschaerts gear?
No. This page is limited to the two-eccentric Stephenson arrangement; Walschaerts combines different motion sources and geometry.
Does mid-gear always mean zero real valve motion?
No. The zero shown is a property of the defined symmetric illustration, not a universal real-engine result.
Can the weights be converted directly to cutoff?
No. Complete valve-event analysis is required.
Historical engineering references
- William E. Bilgram, Slide Valve Gears: figure 24 and description of the two eccentrics, expansion link, sliding block and valve connection.
- Gustav Zeuner, Treatise on Valve-Gears, Stephenson Link Motion: historical primary technical treatment and component arrangement.
- Cylinders, Valves, and Valve Gears: locomotive Stephenson gear, link-block positions and forward/back motion description.
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