An eccentric crank replaces a projecting crank pin with a circular sheave whose center is offset from the rotating shaft. A surrounding strap follows the sheave center and drives a rod. In the aligned, guided arrangement shown here, an offset e produces exactly 2e of slider stroke.
The gold sheave turns with the shaft while the blue split strap rocks slightly with the rod. The animation solves the rod’s fixed-length connection to the straight-guided slider. It does not make the strap rotate rigidly with the sheave.
Eccentric Crank Interactive Calculator
Adjust the offset, rod ratio and input speed. The gold sheave turns inside the blue rocking strap; an exact rigid-rod solution drives the guided slider.
Equation Used
- Circular sheave and ideal frictionless enclosing strap.
- Rigid strap/rod with its center-to-pin length fixed.
- Straight slider guide aligned with the input shaft.
- No stress, wear, lubrication or dynamics prediction.
Hiscox 1115 strap-driven variant with an aligned slider. Body sizes and fasteners are illustrative; no fit, load or speed rating.
A sheave rotating inside a rocking strap
The fixed input shaft is the small dark-centered circle. The gold sheave’s geometric center is a separate marked point displaced from that shaft by the entered offset. As the shaft turns, the sheave center moves in a circle of radius e.
The blue strap surrounds the sheave like a plain bearing. It moves with the sheave center but takes its angular orientation from the connected rod and slider. Its two joint blocks and split lines help distinguish the rocking strap from the continuously rotating gold sheave.
The rod and strap act as one rigid body in this planar model. L is measured from sheave center to slider pin, not just the visible straight portion of the rod. The slider guide passes through the shaft center. The detailed strap fasteners and overall body proportions are illustrative.
What this eccentric model represents
Hiscox figure 1115 illustrates an eccentric and strap for valve motion and other crank applications. This calculator shows that strap-driven variant with an aligned output slider. It does not reproduce a particular engine, treadle or valve timing system.
The input shaft can pass through the offset sheave while the strap transfers its center motion to the rod. Actual valve travel may be altered by additional levers or links, which are outside this model.
Exact guided-rod motion
Let e be eccentric offset, L the fixed sheave-center to slider distance, and θ the input angle. With the shaft at (0,0), the sheave center is C=(e cosθ,e sinθ). The right-hand slider coordinate is:
x=e cosθ+√(L²−e²sin²θ)
Its extreme positions are L−e and L+e, so full stroke is 2e and total distance traveled in one revolution is 4e. At N rpm, cycle rate is N/60 and mean absolute slider speed is 4eN/60. Mean signed velocity over a full cycle is zero.
The strap angle from the guide is β=−asin[(e/L)sinθ], so its maximum magnitude is asin(e/L). The input range keeps L/e between 6 and 15, ensuring a continuous full revolution for this ideal alignment.
The plot compares exact slider displacement x−L with the long-rod sinusoidal approximation e cosθ. Rod length affects intermediate positions and strap rocking, while the exact stroke and total distance remain fixed by e.
Stroke and rocking example
With e=12.5 mm and L/e=9, the sheave-center to slider distance is 112.5 mm. The slider stroke is 25 mm, total travel is 50 mm per revolution, and the strap rocks through a maximum angle of about 6.38° on either side of the guide.
At 200 rpm the mechanism completes 3.33 cycles per second and the slider’s mean absolute speed is 166.67 mm/s. A longer rod reduces the rocking angle and brings the intermediate motion closer to a sine wave without changing that 25 mm stroke.
At zero rpm, calculated speed and cycle rate are zero. The geometry remains displayed and can be inspected with the cycle scrubber.
Geometry and practical limits
The model assumes a rigid strap and rod, a circular sheave, an aligned frictionless slider and no bearing clearance. It does not calculate lubrication, wear, rod force, torque, inertia or a permissible operating speed.
The sheave radius and shaft diameter are proportioned for the illustration. They are not manufacturing inputs or recommendations. Fits, lubrication, wear limits and permissible speed depend on the actual sheave, strap and operating conditions.
Autoplay is slowed for inspection. Changing the entered rpm changes the numerical cycle rate and mean speed; the illustration is not presented as a real-time high-speed machine.
Eccentric-crank questions
Does the strap turn with the sheave?
No. The sheave rotates inside it. The strap’s orientation follows the rod, so it rocks rather than making full revolutions.
Is stroke always twice the offset?
It is for the aligned full-rotation slider arrangement modeled here. Added levers or a different guide geometry require their own calculation.
Why does the rod-length slider not change stroke?
Rod length changes the intermediate motion and rocking angle. The two aligned endpoints remain separated by 2e.
What does mean speed mean?
Total distance traveled divided by time. It counts both outward and return travel, rather than averaging the signed velocity to zero.
Construction reference
Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 274, figure 1115, depicts the eccentric sheave, enclosing split strap and rod attachment. The illustration uses an aligned slider guide and adjustable offset and rod length.
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