Uniform Intermittent Motion is a power transmission scheme where a continuously rotating input shaft produces an output that moves at constant angular velocity for a defined fraction of each cycle, then dwells motionless for the remainder. It solves the problem of converting steady motor rotation into stop-and-go indexing without using a clutch or servo. The output advances by a fixed angle per cycle — typically 30°, 45°, 60° or 90° — then holds station while a downstream operation runs. You see this on rotary indexing tables, film projector pulldowns, and bottle-filling carousels indexing thousands of cycles per shift.
Uniform Intermittent Motion Interactive Calculator
Vary the Geneva slot count, driver cycles, and index fraction to see index angle, travel, and dwell timing update on an animated mechanism diagram.
Equation Used
The calculator uses the worked 4-slot Geneva relationship: each driver revolution creates one index step plus one dwell. The step angle is 360 divided by the number of slots, total output travel is the number of driver cycles times that step angle, and dwell percentage is the remaining portion of the cycle after the index phase.
- One driver revolution equals one index cycle.
- Output speed is uniform during the index phase.
- Output is stationary during dwell.
- Ideal timing only; backlash, acceleration blends, and pin clearance are ignored.
How the Uniform Intermittent Motion Works
The core idea is mechanical — split each input revolution into two distinct phases. During the index phase, a driver engages the output and rotates it through a fixed angle at constant angular velocity. During the dwell phase, the driver disengages and a locking surface holds the output rigid. The classic implementations are the Geneva wheel, the cam-driven indexer (parallel or barrel cam with a roller-gear follower), and the ratchet and pawl. Each gives you a different index-to-dwell ratio, but they all share the same goal — uniform output velocity during motion, zero motion during dwell, and a clean handoff between the two.
Why uniform during the index? Because the downstream tooling — a filling head, a welder, a vision camera — needs a predictable arrival profile. If the output accelerates and decelerates inside the index window like a Scotch yoke or a slider-crank, you lose precision at the entry and exit of the dwell. A true uniform-velocity indexer crosses its index window at constant angular velocity and only adds the accel/decel ramps inside short blend zones at each end. On a cam indexer this is done with a modified-sinusoidal or modified-trapezoidal motion law, picked to control jerk.
Tolerances matter. On a Geneva drive the centre distance between driver and Geneva wheel must match (Rd2 + Rg2) = C2 within roughly ±0.05 mm on a 100 mm centre, or the pin enters the slot off-axis and you get a velocity bump at engagement. On cam indexers, follower preload that drops below 30% rated torque causes the rollers to lift off the cam flank under load — the index then arrives with an audible clack and the dwell position drifts by 0.1° to 0.3°. Get those wrong and the symptoms are loud — pin galling, backlash growth, missed indexes during high-cycle runs.
Key Components
- Driver (input crank or cam): Carries the engagement feature — pin, cam lobe, or pawl — and rotates continuously at the input speed. On a Geneva drive the driver pin sits at radius Rd typically 30 to 80 mm; on a roller-gear cam indexer the cam lobe profile is ground to ±0.005 mm to hit the motion-law specification.
- Output (indexed shaft or table): Carries the load and advances by a fixed angle each cycle. The output must be stiff in torsion — angular deflection under peak index torque should stay below 0.05° or the dwell position wanders. Rotary indexing tables from CAMCO and Sankyo specify this as the position repeatability figure.
- Locking surface: Holds the output stationary during the dwell phase. On a Geneva wheel this is the concave arc on the driver hub mating against the convex arc between Geneva slots. On a cam indexer, the dwell arc on the cam keeps the rollers preloaded against both flanks simultaneously, giving zero backlash.
- Engagement feature: The pin, roller, or pawl that transfers torque during the index phase only. Pin diameter on a Geneva drive must match the slot width within H7/g6 — about 0.013 mm clearance on a 6 mm pin. Looser than that and you get backlash; tighter and you get galling at the slot entry.
- Index-to-dwell controller: On a cam indexer this is the cam profile geometry itself; on a Geneva drive it is fixed by the number of slots (4-slot = 25% index, 75% dwell; 6-slot = 33% index, 67% dwell). You pick the ratio at design time — you cannot adjust it later without swapping the whole driver-output pair.
Who Uses the Uniform Intermittent Motion
Uniform Intermittent Motion shows up anywhere the process needs a steady index between fixed work stations — packaging lines, assembly cells, optical instruments, watch escapements. The reason it dominates over servo-indexing in high-cycle applications is simple: a mechanical indexer running off a continuous AC motor has no encoder to drift, no firmware to crash, and the dwell position repeats to within arc-seconds for hundreds of millions of cycles. The downside is that the index-to-dwell ratio is fixed in hardware, so if your downstream cycle time changes you change the motor speed, not the cam.
- Pharmaceutical packaging: Rotary tablet press turrets on a Korsch XL400 use a cam indexer to dwell each die under the compression rollers, then index 30° to the next station at constant angular velocity.
- Cinema and film: The Maltese cross (a 4-slot Geneva) drives the film pulldown in a Cinemeccanica Victoria 8 35 mm projector — 24 frames per second with a precise dwell while each frame is illuminated.
- Beverage filling: Krones Modulfill rotary fillers use a roller-gear cam indexer to step bottles through filling, capping, and inspection stations at up to 72,000 bottles per hour.
- Automotive assembly: Sankyo Precision rotary indexing tables on Bosch fuel-injector assembly cells dwell each fixture at 8 stations, indexing 45° per cycle with ±15 arc-second repeatability.
- Horology: The Swiss lever escapement in an ETA 2824-2 movement is a uniform intermittent drive — the escape wheel advances one tooth per oscillation of the balance, holding station between impulses.
- Conveyor indexing: Stelron parallel-cam indexers drive walking-beam conveyors in Heinz tomato-paste canning lines, advancing the chain a fixed pitch each cycle while the can is filled.
The Formula Behind the Uniform Intermittent Motion
The dominant design equation is the index-to-dwell ratio, which sets how much of each cycle is motion and how much is hold. At the low end of the typical range — say a 4-slot Geneva at 25% index, 75% dwell — you get a long dwell that suits slow downstream operations like glue cure or vision inspection, but the output accelerates hard during the short index window, putting peak torque on the pin. At the high end — an 8-slot Geneva or a cam indexer at 50% index, 50% dwell — peak torque drops and the index is gentler, but you have less time for the downstream operation. The sweet spot for most rotary assembly is 33% index, 67% dwell (a 6-station setup), giving a workable hold time and manageable peak acceleration.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| ωout,avg | Average output angular velocity during the index phase | rad/s | rev/min |
| n | Number of index stations per output revolution (e.g. 4, 6, 8) | dimensionless | dimensionless |
| tindex | Time spent in the index phase per cycle | s | s |
| β | Driver rotation angle during which the index occurs | degrees | degrees |
| Tcycle | Total time for one driver revolution (one full cycle) | s | s |
Worked Example: Uniform Intermittent Motion in a chocolate praline depositing carousel
You are sizing the cam indexer that drives a 12-station rotary depositing carousel on a Sollich Turbotemper praline line at a confectionery plant in Bruges, Belgium. Each station receives a shot of tempered couverture from a fixed depositor head, then indexes 30° to the next station. The continuous-input motor runs at 90 RPM, and the cam profile gives a 50% index / 50% dwell split. You want the average output angular velocity during the index phase, plus a feel for what happens if you push the line speed up or slow it down for a softer chocolate.
Given
- n = 12 stations
- Input speed = 90 RPM
- Index fraction = 0.50 of cycle
- β = 180 degrees
Solution
Step 1 — convert the 90 RPM input to cycle time. Each cam revolution drives one station index.
Step 2 — at the nominal 50% index split, the index phase lasts:
Step 3 — the output rotates 30° (one station) during that time. Convert to angular velocity:
That is the sweet-spot operating point — the depositor has 0.333 s of dwell to drop a clean shot, and the index ramp is gentle enough that the chocolate does not slosh in the moulds.
At the low end of the typical operating range, slow the motor to 45 RPM for a thicker dark couverture:
The dwell stretches to 0.667 s — generous, lets a viscous shot settle — but throughput halves to 5400 deposits/hour. At the high end, push the motor to 150 RPM for a thin milk chocolate:
In theory you get 18,000 deposits/hour, but in practice the index acceleration above ~120 RPM input flings the chocolate off-centre in the mould — you get tail-out splatter on the carousel deck above roughly that speed unless the cam is reground to a modified-sine profile with longer blend zones.
Result
The nominal average output angular velocity during the index phase is 15 RPM, with a 0. 333 s dwell at each station — clean depositing at 10,800 pralines per hour. At 45 RPM input the carousel creeps with a luxurious 0.667 s dwell good for thick ganache; at 150 RPM input the predicted 25 RPM index speed is achievable mechanically but the actual chocolate behaviour fails above ~120 RPM input due to centrifugal tail-out. If you measure dwell-position drift greater than 0.1° at nominal speed, the most likely causes are: (1) cam-follower roller preload below 30% rated torque, letting rollers chatter at index entry; (2) a worn driver bearing letting the cam shaft wander, which shows up as audible clack at index handoff; or (3) loose mounting bolts on the indexer base — torque-check to spec before assuming the cam profile itself is at fault.
When to Use a Uniform Intermittent Motion and When Not To
Pick the indexer family by index-to-dwell ratio, peak acceleration, and cycle rate. Geneva drives are cheap and bulletproof but the index curve is geometrically fixed and acceleration is harsh. Cam indexers cost more but you choose the motion law. Servo indexing wins on flexibility and loses on long-term cost-per-cycle.
| Property | Cam indexer (uniform intermittent) | Geneva drive | Servo-indexed table |
|---|---|---|---|
| Typical cycle rate (indexes/min) | up to 600 | up to 300 | up to 200 (load-dependent) |
| Position repeatability | ±15 arc-sec | ±2 arc-min | ±5 arc-sec (encoder-dependent) |
| Capital cost (relative) | 3-5× | 1× | 4-8× |
| Index-to-dwell ratio flexibility | fixed at design (any ratio specified) | fixed by slot count (4/6/8) | fully programmable |
| Peak acceleration on output | low (motion-law optimised) | high (geometric step at engagement) | low (profile-shaped) |
| Maintenance interval | 20,000+ hr (oil bath) | 5,000-10,000 hr (pin/slot wear) | encoder service every 2-3 yr |
| Lifespan at rated load | 109 cycles | 107-108 cycles | limited by motor bearings |
Frequently Asked Questions About Uniform Intermittent Motion
The Geneva motion law is geometrically uniform in driver angle, but it is NOT uniform in output velocity — output angular velocity peaks in the middle of the index and is zero at entry and exit. What you are likely seeing is the cosine-of-engagement-angle curve, which is intrinsic to the Geneva. If the spike is sharp rather than smooth, the pin is entering the slot off-tangent — check that the centre distance equals √(Rd2 + Rg2) within 0.05 mm and that the pin axis is parallel to the Geneva-wheel axis. A 0.5° pin tilt on a 6 mm pin shows up as a 200 µm offset at the slot entry and creates exactly that spike.
Pick by dwell time first, peak acceleration second. At 120 cycles/min you have 0.5 s per cycle. A 4-slot gives 75% dwell (0.375 s) but peak acceleration is roughly 4× that of an 8-slot — hard on the pin and the load. A 6-slot at 67% dwell (0.333 s) is the usual workhorse for filling and capping. An 8-slot drops peak accel further but only gives 62.5% dwell (0.313 s) — less time for the downstream operation. If your dwell window needs to exceed about 70%, you should be looking at a cam indexer rather than a Geneva, because the Geneva index-to-dwell ratio can only be lengthened by going to fewer slots, and a 3-slot Geneva has unacceptable peak acceleration.
Almost certainly torsional windup in the output shaft, not a cam profile error. Cam indexers are designed for zero backlash via dual-flank roller contact, but the output shaft and table flange still flex elastically under index torque. When the cam reaches the dwell arc, the stored elastic energy releases as a small overshoot-and-settle. Measure the angle change at the table edge with a dial indicator at peak index torque — if it exceeds 0.05° you need a stiffer output coupling, a larger output shaft, or a hub-mounted table flange instead of a keyed boss. CAMCO and Sankyo both publish torsional stiffness figures for their indexers — match them to your load inertia.
Yes — three cases. First, when index angle or dwell time needs to change between recipes (think contract packaging running 4 SKUs per shift), a servo wins on changeover time. Second, when index distance is large compared to dwell — a cam indexer with 80% index and 20% dwell is awkward to manufacture, while a servo handles it trivially. Third, when total cycles per year are below about 107, the capital cost of a precision cam indexer never pays back versus a good servo. Cam indexers win at high cycle rates, fixed recipes, and lifetimes above 108 cycles where servo encoder drift becomes the limiting factor.
Check the input shaft speed under load first. AC induction motors slip — a nameplate 1500 RPM motor on a heavy indexer may run at 1440 RPM under torque, which is a 4% reduction in cycle rate and lengthens index time proportionally. If the motor speed checks out, look at the cam-to-output coupling. A flexible jaw coupling between the cam shaft and the indexer input shaft adds 1° to 3° of windup at peak torque, which on a 50% index span becomes 5-15 ms of apparent index extension. Replace with a rigid coupling or use a steel-disc coupling rated for the peak index torque, not the average.
On a quality roller-gear indexer (Sankyo, CAMCO, Stelron) running within rated torque and oil-bath lubricated, expect under ±30 arc-seconds of dwell-position drift over 109 cycles. The dominant wear mechanism is roller fatigue spalling on the cam flanks, not the rollers themselves — once a flank pits, the roller bridges the pit and the dwell position shifts by the pit depth divided by the cam radius. Drift accelerates rapidly once the first pit appears, so monitor with a dial indicator monthly on critical lines. If you see drift rising past 1 arc-min before 50% of rated life, the indexer is running over-torque or under-lubricated — both are user-correctable, the cam is rarely the root cause.
References & Further Reading
- Wikipedia contributors. Geneva drive. Wikipedia
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