An Eccentric Spur-gear with Link Control is a spur gear mounted on an off-centre pivot whose output is constrained by a swinging link, producing a non-uniform output rotation from a uniform input. Throw eccentricity typically runs 5-25 mm with output-speed ratios varying ±40% across one revolution. The mechanism trades constant velocity for a built-in dwell-and-snap profile, which is exactly what feeders, indexers and quick-return slotting heads need. You see it in machines like the Schuler TMK transfer press feed drive.
Eccentric Spur-gear with Link Control Interactive Calculator
Vary the velocity-ratio swing, dwell angle, and cycle angle to see the dwell-snap speed envelope and eccentric gear/link motion.
Equation Used
This calculator follows the article example by treating the mechanism as a normalized velocity-ratio envelope. A 35% swing about a mean ratio of 1.0 gives a dwell-side minimum of 0.65 and a snap-side maximum of 1.35. The dwell angle is also shown as its share of one full revolution.
- Velocity variation is represented by a first-harmonic dwell-snap envelope.
- Mean ratio is normalized to the article chart value of 1.0 unless changed.
- Dwell angle is converted directly to percent of one 360 deg cycle.
Inside the Eccentric Spur-gear with Link Control
The driving spur gear sits on the motor shaft and turns at constant speed. The driven gear is the eccentric one — its rotation centre is offset from the gear's geometric centre by a fixed distance e, typically 5-25 mm depending on the size of the unit. A control link pins one end to a fixed ground point and the other end to a crank pin on the eccentric gear. As the gear tries to rotate, the link forces its instantaneous centre of rotation to wander along an arc, so the output shaft sees a varying angular velocity even though the input is steady.
The result is a programmable non-uniform rotation. During part of the cycle the output speeds up — that's the snap or quick-return phase. During another part it slows down or nearly stops — the dwell. By picking the eccentricity, the link length, and the ground-pivot location, you tune where the dwell sits in the cycle and how aggressive the snap is. A typical paper-feed unit gets you a 60° dwell with a velocity ratio swing of about ±35%.
Tolerances matter more than people think. If the crank-pin bore drifts past 0.05 mm clearance the link starts hammering at the velocity-reversal point, and you'll hear it as a tick on every revolution. If the eccentricity is machined off-spec by even 0.2 mm on a 10 mm throw, the dwell window shifts by several degrees and downstream timing breaks. Common failure modes are crank-pin bushing wear, link-rod fatigue at the small end, and tooth-face pitting on the eccentric gear because the load isn't constant — it spikes hard at the snap point.
Key Components
- Driving Spur Gear: Standard involute spur gear running on the constant-speed input shaft. Module typically 1-3 mm, AGMA quality 8 or better. It transfers torque uniformly to the eccentric gear; any backlash above 0.1 mm shows up as output-position chatter at the velocity-reversal points.
- Eccentric Driven Gear: Spur gear mounted on a shaft whose axis is offset from the gear's geometric centre by eccentricity e (commonly 5-25 mm). The offset must hold ±0.05 mm or the dwell timing drifts. This part is the heart of the non-uniform rotation.
- Control Link: Rigid two-pin link connecting a fixed ground pivot to a crank pin on the eccentric gear. Length sets the velocity-ratio swing and where the dwell sits. Made from hardened steel, often 4140 at 28-32 HRC, with bronze or needle bushings at each end.
- Crank Pin: Hardened pin pressed into the eccentric gear at a defined radius from the gear's rotation centre. Surface finish must be Ra 0.4 µm or better — anything rougher chews bushings inside 2,000 hours.
- Ground Pivot: Stationary mounting boss for the far end of the control link. Position relative to the gear-centre line determines the angular phase of the dwell. Must be doweled, not just bolted, or the dwell phase walks under repeated thermal cycles.
- Output Shaft & Bearings: Carries the eccentric gear and delivers the non-uniform rotation downstream. Needle bearings handle the radial load spikes during the snap phase, which can hit 2-3× nominal torque.
Real-World Applications of the Eccentric Spur-gear with Link Control
You find this mechanism wherever a machine needs constant input rotation but non-constant output — feeding, indexing, dwell-and-snap motion, or quick-return strokes. It's mechanically simple, holds timing well, and runs forever if the link bushings are kept tight.
- Metal Stamping: Feed-roll drive on Schuler TMK transfer presses, where the strip must dwell while the dies close, then snap forward during the open phase.
- Textile: Take-up drive on Karl Mayer warp-knitting machines, generating the variable yarn-tension profile needed during loop formation.
- Paper Converting: Sheet-feed timing drive in Heidelberg Speedmaster offset presses, controlling when the gripper bar accelerates and decelerates.
- Packaging: Index drive on Bosch Pack 403 cartoners, holding the carton stationary at the load station then snapping it to the next position.
- Machine Tools: Quick-return ram drive on shaping machines like the Cincinnati 24-inch shaper, giving a slower cutting stroke and faster return.
- Glass Forming: Plunger-drive timing in Emhart IS bottle machines, where the gob press cycle needs a controlled dwell at bottom of stroke.
The Formula Behind the Eccentric Spur-gear with Link Control
The headline number you size against is the output-to-input angular velocity ratio at any crank angle θ. At small eccentricities the ratio barely deviates from 1.0 — fine for gentle timing tweaks but useless if you need a real dwell. Push the eccentricity past 20% of the link length and you get sharp snap-and-dwell behaviour, but tooth-load spikes climb fast and the gear-mesh life drops. The sweet spot for most production machines sits at e/L between 0.10 and 0.18, where you get a useful ±25-35% velocity swing without abusing the gear teeth.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| ωout | Instantaneous output angular velocity | rad/s | rad/s |
| ωin | Constant input angular velocity | rad/s | rad/s |
| e | Eccentricity — offset between gear geometric centre and rotation axis | mm | in |
| L | Effective control-link length from ground pivot to crank pin | mm | in |
| θ | Crank angle measured from the line through ground pivot and rotation axis | rad or deg | rad or deg |
Worked Example: Eccentric Spur-gear with Link Control in a tea-bag tag-attachment indexer
You are sizing the eccentric spur-gear link drive on the tag-and-string attachment indexer of a Teepack Compack III tea-bag machine running at 200 bags per minute. The indexer needs to hold the bag stationary for roughly 30% of each cycle while the heat seal closes, then snap forward to clear the seal head. Input shaft runs at 200 RPM constant. You're choosing eccentricity e on a control link of L = 80 mm.
Given
- ωin = 200 RPM
- L = 80 mm
- e (nominal) = 12 mm
- Cycle rate = 200 bags/min
Solution
Step 1 — at the nominal eccentricity e = 12 mm on an L = 80 mm link, the ratio e/L = 0.15. Compute the velocity ratio at θ = 0° (peak of the snap phase):
Step 2 — compute the ratio at θ = 180° (the dwell side of the cycle):
So the output swings between 0.87× and 1.18× the input speed — a ±15% swing around the mean. At 200 RPM input that's an output range of 174-235 RPM, which gives roughly the 30% effective dwell window the seal head needs.
Step 3 — at the low end of the typical operating range, drop to e = 6 mm (e/L = 0.075):
That's only ±8% swing — the bag barely pauses, and at 200 BPM the seal head will land on a moving bag and produce a wrinkled seam. Useless for this duty.
Step 4 — at the high end, push e = 20 mm (e/L = 0.25):
±33% swing, deep dwell — but tooth-load spikes climb to roughly 1.7× nominal at the snap point, and the crank-pin bushing on a stock 8 mm pin will see surface pressure above 25 MPa. You'd need to upsize the pin to 10 mm and use a needle bearing instead of a bronze bushing. For a 200 BPM line the 12 mm nominal is the right pick.
Result
Nominal output velocity ratio swings from 0. 87× to 1.18× input, giving roughly a 30% effective dwell window at 200 BPM — exactly what the heat-seal cycle needs. At the low end (e = 6 mm) the dwell collapses to nothing and you'll see wrinkled seams; at the high end (e = 20 mm) the dwell is generous but tooth-pitting and crank-pin wear become the limiting factors inside 3,000 hours. If your measured dwell window comes in shorter than the predicted 30%, the most common causes are: (1) crank-pin bushing wear over 0.1 mm clearance, which lets the link lag at the velocity-reversal point and shaves degrees off the dwell; (2) ground-pivot bracket flexing under the snap-phase load spike, shifting the effective L; (3) eccentric-gear bore machined oversize so the gear walks on its shaft and e drifts.
Choosing the Eccentric Spur-gear with Link Control: Pros and Cons
Several mechanisms produce non-uniform rotation from constant input. The eccentric spur-gear with link control sits between the simple offset-crank and the full Geneva drive in cost, complexity, and motion sharpness.
| Property | Eccentric Spur-gear with Link Control | Geneva Drive | Elliptical Gear Pair |
|---|---|---|---|
| Output speed swing (±% of mean) | ±15-35% | Full stop with hard snap | ±20-50% |
| Dwell quality | Soft dwell, 20-40% of cycle | True dead stop, sharply defined | No true dwell, just slow zone |
| Max input RPM (typical) | 600 RPM | 300 RPM (impact-limited) | 1500 RPM |
| Tooth-load peak factor | 1.3-1.7× nominal | 3-5× nominal at engagement | 1.2-1.5× nominal |
| Manufacturing cost (relative) | Medium — standard spur gear plus link | Medium-high — slotted star + driver | High — non-circular gear cutting |
| Bushing/bearing service life | 8,000-15,000 hours | 3,000-6,000 hours (impact wear) | 12,000+ hours |
| Best application fit | Soft dwell + quick return | Hard indexing with full stop | Smooth variable-velocity drives |
Frequently Asked Questions About Eccentric Spur-gear with Link Control
The textbook formula assumes the control link is rigid and the ground pivot is fixed in space. In reality both flex under the peak tooth load that hits at the velocity-reversal point. A 6 mm steel link in a typical machine deflects 0.1-0.2 mm under the snap-phase load, which shows up as a few degrees of lost dwell.
Quick check: pin a dial indicator on the ground-pivot bracket and run the machine at half speed. If you see more than 0.05 mm motion on the bracket, the bracket is the problem, not the gearing. Stiffen the mounting or move to a gusseted casting.
Ask whether you need a true dead stop or just a slow zone. Geneva gives you a hard zero-velocity dwell with sharply defined start and end — perfect when a robot has to enter a stationary pocket. The eccentric spur-gear gives a soft dwell where the output slows to maybe 20% of mean speed but never fully stops. If your downstream operation tolerates a small residual motion (heat sealing, gluing, light pressing) the eccentric drive runs smoother, costs less, and lasts longer because nothing impacts. If you need the carton stone-still for a robotic load, use Geneva.
Almost always the small-end bushing on the control link has opened up past 0.08-0.1 mm clearance. The link reverses direction twice per revolution and at one of those reversals the load goes through zero — the pin lifts off one side of the bushing and slaps back. That's your tick.
Pull the link, mike the pin and bore. Replace the bushing if clearance exceeds 0.05 mm. If the noise persists with a fresh bushing, check the crank-pin surface finish — anything above Ra 0.8 µm will hammer a new bushing back to loose inside a few hundred hours.
Yes, and this is one of the underrated strengths of the mechanism. The angular position of the dwell is set by where the ground pivot sits relative to the line between input and output centres. Move the ground-pivot bracket angularly around the output axis and the dwell rotates with it. On most production machines the bracket is doweled at one of several pre-machined hole patterns so a fitter can reposition it during changeover.
You can't change the magnitude of the dwell this way — only the phase. Magnitude requires changing e or L.
Because the load isn't symmetric. During the snap phase the driving gear pushes hard against one tooth flank; during the dwell phase the load reverses and the link actually drives the gear, loading the opposite flank lightly. Over time the snap-side flank pits while the back flank stays nearly polished.
If you see severe pitting on only the loaded flank within 2,000 hours, your eccentricity is probably set too aggressive for the gear quality. Drop e by 20% or upgrade the gear from AGMA 8 to AGMA 10 with case-hardened teeth.
The ratio formula is purely geometric — it depends on e, L, and θ, not on RPM. Whatever ratio you calculate at 100 RPM input applies at 500 RPM input. What changes with RPM is the dynamic load: peak tooth force scales roughly with the square of input speed because angular accelerations scale with ω². That's why a mechanism that runs sweetly at 200 RPM can self-destruct at 600 RPM with the same geometry. Always size the gear teeth and bushings against the worst-case acceleration at maximum operating RPM, not against nominal torque.
References & Further Reading
- Wikipedia contributors. Non-circular gear. Wikipedia
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