An eccentric converts shaft rotation into reciprocating motion through a connecting rod and guided slider. Use this calculator to find slider position and rod angle for an offset guide. It explains one motion-conversion element; a complete steam-engine reversing gear needs additional linkage and valve geometry.
Eccentric, Rod and Guided-Slider Calculator
Enter guide offset, eccentric radius and rod length, then set shaft angle and phase offset. Results use their combined phase; playback advances the drawing separately.
Equation Used
- The rod is rigid and has fixed length L.
- The slider is constrained to the horizontal guide offset b.
- Inputs are bounded so exact closure exists for all phases.
- The second eccentric/rod, expansion link, die block and all valve events are excluded.
The companion figure shows the same eccentric, rod and guided slider. Playback moves both views; result numbers remain at the entered combined phase.
How the eccentric drives the slider
The eccentric pin moves around a fixed shaft center at radius e. A rod of length L connects it to a slider on a horizontal guide offset by b. As the pin turns, the rod changes angle and pushes or pulls the slider along its guide.
The calculation uses the right-hand position where the rod reaches the guide. It is a geometric example, not a complete reversing valve gear. Stephenson link motion combines two eccentric rods through a slotted expansion link and die block; that larger mechanism also requires its suspension and valve geometry.
Exploring the geometry
Change eccentric radius to compare reciprocating motion, guide offset to change the rod inclination, or rod length to change the slider position. With zero eccentric radius, the pin stays at the shaft center and the slider no longer reciprocates.
Use the output values to compare positions and geometric reach. Forces, steam events, physical interference and component strength are not determined by these dimensions alone.
Slider position and rod angle
Let φ = θ + δ, where θ is shaft angle and δ is phase offset. The vertical separation from pin to guide is d = b − e sinφ. For the right-hand slider position, x = e cosφ + √(L² − d²).
The reference position is x₀ = e + √(L² − b²), evaluated at combined phase φ = 0. Displacement is x − x₀. The rod angle is atan2(d, √(L² − d²)), and closure margin is L − |d|.
Slider coordinate is measured horizontally from the shaft center. The diagram uses a downward-positive vertical direction for guide offset. Over the available input range, L is at least 100 mm and b + e is at most 90 mm, so the rod can reach the guide throughout a revolution.
Worked example
With b = 45 mm, e = 15 mm, L = 150 mm, θ = 60° and δ = 0°, the combined phase is 60°. The slider coordinate is about 154.04 mm, displacement from φ = 0 is −4.05 mm, rod angle is 12.32°, and geometric reach margin is 117.99 mm.
Changing phase offset changes the combined phase at which the results are calculated. The displacement reference remains φ = 0, rather than shifting with the offset.
Reading the drawing and results
The rod and slider positions follow the stated geometric constraint. The surrounding housing and guide line are illustrative, not dimensioned components; the slider can extend beyond the drawn guide segment for some inputs. The fixed disk outline is a symbol, not an entered eccentric size.
Result numbers use the entered combined phase. Playback adds a changing phase to the drawing without updating those numbers. Return to start resets that animation phase; change the angle inputs to calculate other positions.
A complete reversing-gear analysis needs the second drive path, expansion-link shape, suspension, block position and valve dimensions. This calculator does not determine cut-off, expansion ratio, steam use or how to operate an engine.
Eccentric-slider questions
Does this calculate a complete reversing gear?
No. It calculates one eccentric pin, a fixed-length rod and a guided slider. Stephenson reversing gear also needs a second eccentric and rod, an expansion link, suspension and die block, together with the valve geometry.
What is the displacement reference?
Displacement is measured from combined phase φ = 0, where φ = shaft angle + phase offset. It is not measured from shaft angle zero unless the phase offset is also zero.
What does closure margin mean?
It is L − |b − e sinφ|: rod length minus the vertical distance from eccentric pin to guide. Positive margin means the rod can reach the guide at that phase. It is a geometric reach margin, not clearance or a strength allowance.
Why do the numbers stay fixed during playback?
The outputs use the entered shaft angle plus phase offset. Playback advances the drawing separately. Return to start resets playback phase to zero so it uses the entered phase again.
Can slider displacement determine steam cut-off?
No. Steam cut-off is a valve-port event. Slider displacement alone does not establish it without valve lap, lead, port dimensions and the complete valve linkage.
Primary references
- Bilgram, Slide Valve Gears — complete Stephenson topology with two eccentrics, rods, expansion link and block.
- US757411A, Valve-gear — combined link motion and selectable block position.
- Zeuner, Treatise on Valve-Gears — historical full-link geometry showing why a single branch is incomplete.
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