An eccentric gear is a spur or helical gear whose bore or pitch axis sits offset from its geometric centre, so that a constant input rotation produces a cyclically varying output motion or stroke. The concept traces back to clockmaking and was formalised in 19th-century kinematics work by Franz Reuleaux, who catalogued eccentric drives alongside cams and linkages. The offset converts uniform rotation into a sinusoidal displacement, useful for stroke generation, variable-speed output, or feeding non-uniform motion into linkages. You see it today in pump drives, shaker screens, and small-engine balancer assemblies producing strokes from 1 mm to 50 mm.
Eccentric Gear Interactive Calculator
Vary nominal and actual bore offset to see the resulting eccentric gear stroke and the effect of offset error.
Equation Used
The eccentric gear stroke is twice the bore offset because the pitch-circle center moves one eccentricity to each side of the shaft axis during a full revolution. Comparing actual offset to nominal offset shows how machining error changes the final stroke.
- Stroke is measured peak-to-peak from the eccentric offset.
- The follower follows the eccentric motion directly.
- Gear body and shaft are treated as rigid.
- Linkage angularity and clearance are ignored.
Operating Principle of the Eccentric Gear
An eccentric gear works because the bore that carries the shaft is deliberately offset from the gear's pitch-circle centre by a distance e — the eccentricity. When the shaft turns at constant RPM, any feature mounted to the gear traces a circle of radius e around the shaft axis, which means a follower, connecting rod, or meshing partner sees a sinusoidally varying position over each revolution. If you couple two eccentric gears together, the meshing forces and angular velocity ratio also fluctuate cyclically, giving you a non-circular gearing effect without machining true elliptical teeth.
The design is built this way because it's the cheapest route to variable angular velocity or stroke output you can get out of standard gear-cutting equipment. A normal involute gear blank goes on the hob, gets cut, and then the bore is machined off-centre — done. The trade is that the cyclic torque variation and pitch line eccentricity load the bearings unevenly, so you have to size the support shaft and bearings for the peak case, not the average.
If the eccentricity tolerance drifts — say the offset bore comes in at 3.2 mm instead of the specified 3.0 mm — the stroke grows by 7%, and any linkage downstream hits its end stop or over-extends a return spring. If the bore is concentric to within 0.05 mm when it shouldn't be, you get effectively zero stroke and the machine just hums. Common failure modes are bore wallow from cyclic radial load, key shear at the offset, and tooth-flank pitting on the side of the gear that carries peak mesh force during the heavy half of each revolution.
Key Components
- Gear Body: A standard involute spur or helical gear, typically module 1 to module 5 for industrial work. The teeth are cut concentric to the pitch circle as normal — eccentricity is introduced only at the bore, not the tooth profile.
- Offset Bore: The shaft hole machined with its centre offset from the pitch-circle centre by the eccentricity distance e. Bore-to-pitch-centre tolerance is usually held to ±0.02 mm because every micron of error scales directly into stroke error at the output.
- Drive Shaft: Carries the gear and transmits torque. Sized for the peak radial load, which equals the tangential tooth force plus the cyclic inertial load from the offset mass — typically 1.5× to 2× what a concentric gear of the same size would impose.
- Support Bearings: Two bearings flanking the gear, rated for the peak cyclic load. L10 life calculations must use peak load, not average — a bearing sized for mean load will fail at roughly 30% of expected service hours.
- Follower or Connecting Rod: The output element that picks up the eccentric motion. On a pump or shaker, this is a wrist-pin connecting rod riding the gear's outer face on a bushing or needle bearing of clearance 0.01 to 0.03 mm.
Where the Eccentric Gear Is Used
Eccentric gears show up wherever a designer needs cheap, repeatable stroke or variable-velocity output from a constant-RPM input, and doesn't want to pay for a true non-circular gear set or a separate cam. They're common in fluid handling, vibratory equipment, small-engine accessories, and any motion where the kinematic asymmetry is actually wanted — not a defect to be designed out.
- Fluid handling: Diaphragm metering pumps such as the ProMinent Sigma series use an eccentric-gear-driven connecting rod to produce a 1.5 mm to 6 mm diaphragm stroke at 60 to 180 strokes per minute.
- Vibratory screening: Rotex screen separators use balanced eccentric gear assemblies to drive the screen deck through a 25 mm to 50 mm horizontal throw at roughly 200 to 250 RPM.
- Small engines: Honda GX-series single-cylinder engines use an eccentric balancer gear driven off the crankshaft to cancel first-order vibration from the piston.
- Watchmaking: ETA 2824-2 automatic movements use an eccentric stud at the regulator to fine-tune the hairspring effective length, adjusting rate by ±20 seconds per day.
- Printing and packaging: Heidelberg sheet-fed presses use eccentric gears in the gripper-bar timing drive to produce non-uniform angular velocity that matches sheet handover at the impression cylinder.
- Textile machinery: Karl Mayer warp knitting machines use eccentric gear segments in the guide-bar shogging mechanism to deliver controlled lateral displacement per course.
The Formula Behind the Eccentric Gear
The most useful formula for an eccentric gear is the peak-to-peak stroke at the follower, which is simply twice the eccentricity. What matters in practice is how the stroke and the cyclic radial load scale with e across your operating range. At low eccentricity (say e = 1 mm on a 50 mm pitch radius gear) the gear behaves almost like a concentric gear and the stroke is small but the bearings barely notice. At nominal e ≈ 5% of pitch radius you get a clean compromise — useful stroke and bearing loads still well inside catalogue ratings. Push e past 10% of pitch radius and the radial load starts dominating bearing selection, the tooth contact pattern walks across the flank, and you're closer to cam territory than gear territory.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| S | Peak-to-peak stroke at the follower | m | in |
| e | Eccentricity — offset between bore centre and pitch-circle centre | m | in |
| Fr,peak | Peak radial bearing load | N | lbf |
| m | Effective mass of gear plus follower offset | kg | lb |
| ω | Angular velocity of the drive shaft | rad/s | rad/s |
| Ftooth | Tangential tooth force from transmitted torque | N | lbf |
Worked Example: Eccentric Gear in a chocolate enrobing line vibratory feeder
You are sizing the eccentric gear drive on the vibratory infeed pan of a Sollich Turbotemper 3 chocolate enrobing line. The pan needs a horizontal throw to walk tempered couverture-coated centres forward at a controlled rate without splashing. Pan effective mass with product is 4.5 kg, the eccentric gear runs off a 1400 RPM motor through a 10:1 reduction, and you've specified a nominal eccentricity of 4 mm on a gear with a 60 mm pitch radius. You need stroke and peak bearing load at low, nominal, and high operating points so you can spec the support bearings.
Given
- enom = 4 mm
- Nshaft = 140 RPM
- m = 4.5 kg
- Ftooth = 180 N
- rpitch = 60 mm
Solution
Step 1 — convert shaft speed to angular velocity at the nominal operating point:
Step 2 — at nominal e = 4 mm (0.004 m), compute peak-to-peak stroke and peak radial load:
An 8 mm throw at roughly 2.3 Hz is the sweet spot for a chocolate feeder pan — the centres walk forward smoothly without bouncing off the pan surface, and 184 N is well inside the rating of a standard 6204 deep-groove bearing.
Step 3 — at the low end of the practical range, e = 2 mm:
A 4 mm stroke barely walks the product — you'd see chocolate centres dribble forward at maybe 30% of nominal feed rate, and the operator would crank the line speed up to compensate, defeating the point.
Step 4 — at the high end, e = 8 mm (the tightest you can push before the offset bore starts compromising the gear hub wall thickness):
16 mm throw looks aggressive on paper but in practice the chocolate centres start launching off the pan at the stroke reversal — you get splash on the side rails and uneven coating thickness downstream of the enrober. Keep e at or below 6 mm for product integrity.
Result
Nominal stroke is 8 mm with a peak radial bearing load of about 184 N, comfortably handled by a 6204 deep-groove ball bearing. The 4 mm low-end stroke under-feeds the line and the 16 mm high-end stroke flings product off the pan, so the usable design window sits between 6 and 10 mm of throw — pick a 4 mm eccentricity and tune line speed for the rest. If you measure a stroke noticeably below 8 mm on the assembled machine, the most likely causes are: (1) a slipping taper-lock bushing on the eccentric gear allowing the offset to drift toward concentric, (2) a worn connecting-rod bushing adding 0.1 mm or more of clearance per cycle which absorbs stroke as lost motion, or (3) an out-of-tolerance offset bore machined at 3.7 mm instead of 4.0 mm, which alone drops stroke by 7.5%.
Eccentric Gear vs Alternatives
Eccentric gears compete against cams, scotch yokes, and true non-circular gears for the same job: convert constant rotation into varying output. The right pick depends on stroke length, accuracy, cost, and how much cyclic load your bearings can absorb.
| Property | Eccentric Gear | Cam-and-Follower | Non-Circular (Elliptical) Gear |
|---|---|---|---|
| Typical stroke range | 1–50 mm | 0.5–200 mm | N/A — produces variable angular velocity, not stroke |
| Stroke accuracy (typical) | ±0.05 mm | ±0.01 mm with ground cam | ±0.5° angular position |
| Speed capability | Up to ~2000 RPM before bearing load dominates | Up to 6000 RPM with positive-drive follower | Up to ~3000 RPM |
| Manufacturing cost (relative) | 1.0× — standard gear with offset bore | 1.5–4× depending on profile | 5–10× — requires CNC profile cutting |
| Bearing life impact | Cyclic radial load reduces L10 by ~30% | Steady radial load, near-catalogue L10 | Cyclic tooth load, L10 reduced by ~20% |
| Best application fit | Pumps, shakers, balancers, low-cost stroke | High-precision motion profiles, valve trains | Continuous variable-ratio drives, printing presses |
| Design complexity | Low — bore offset is the only special op | Medium — profile design is iterative | High — pitch curve must be computed |
Frequently Asked Questions About Eccentric Gear
Increase eccentricity first, but only up to about 10% of pitch radius. Beyond that, the offset bore eats into the hub wall thickness and the cyclic radial load on the support bearings starts dominating L10 life calculations. If you still need more stroke, switch to a larger gear or add a lever-arm linkage downstream rather than pushing eccentricity past the structural limit.
Rule of thumb on a module 2 spur gear with 60 mm pitch radius: 6 mm eccentricity is comfortable, 8 mm is the practical ceiling, and anything above means you should be looking at a scotch yoke or a cam instead.
That's almost always the connecting-rod bushing wearing out, or the key on the offset bore working loose. The cyclic radial load reverses direction every revolution, which is brutal on any clearance-fit joint. A 0.02 mm clearance grows to 0.1 mm in a few thousand cycles once wear starts, and you hear that as an audible knock at top and bottom dead centre.
Pull the assembly and check the bushing bore with a bore gauge. If it's gone oval or grown more than 0.05 mm beyond nominal, replace it and switch to a needle bearing if the duty cycle warrants it.
You probably forgot to include the dynamic amplification from system flexibility. The formula gives you the rigid-body peak load, but real shafts deflect, real housings resonate, and if your operating frequency lands within 30% of a structural natural frequency you'll see 2–3× the calculated load on the bearing.
Quick check: tap-test the housing with an accelerometer and look for a mode within ±30% of your shaft frequency. If you find one, either stiffen the housing or move the operating speed away from it. Adding a tuned mass damper is a last resort.
Sort of, but not really. Two eccentric gears meshing together do produce a cyclically varying ratio, but the centre-distance variation has to be absorbed somewhere — usually by a spring-loaded idler or a slotted shaft mount. The ratio variation is also small (typically ±5–10%) compared to a properly designed non-circular gear set which can hit ±50%.
If you need real variable-ratio behaviour, cut elliptical or oval gears. Eccentric gears are for stroke and balance work, not ratio modulation.
Because the cyclic radial load from the eccentricity tilts the gear slightly on its bearings every revolution. Even with shaft deflection of only 0.02 mm, the tooth contact band shifts toward whichever flank end is loaded heaviest at that moment. Over thousands of cycles you get a diagonal wear pattern instead of an even one.
Diagnose it by inking the teeth with engineer's blue and running the gear for 10 minutes. If the contact patch sweeps from one end to the other across a revolution, the answer is to crown the teeth slightly (5–15 µm) or stiffen the shaft.
3% cycle-to-cycle variation is too much for an eccentric gear running off a constant-speed drive. Real causes are almost always backlash in the upstream reduction, or a flexible coupling between the motor and the eccentric shaft that lets torque ripple modulate the angular position.
Lock a dial indicator to the follower and rotate the shaft by hand through one full revolution in 30° increments. If the stroke profile is repeatable to better than 0.5% by hand but jumps under power, the problem is upstream of the gear — coupling or reducer — not the eccentric assembly itself.
References & Further Reading
- Wikipedia contributors. Non-circular gear. Wikipedia
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