Intermittent motion of a spur gear is a drive arrangement where a partial-tooth (or mutilated) spur gear meshes with a full spur gear so that the output rotates only while teeth are engaged, then dwells while the toothless arc of the driver passes by. The toothless arc — usually paired with a locking plate — holds the output stationary between steps. Designers use it to convert continuous input rotation into a step-and-pause motion, which is what indexing turrets, film projectors, and packaging dials need to load, work, and discharge a part at every station.
Intermittent Motion of Spur Gear Interactive Calculator
Vary the toothed and locking arcs to see the motion fraction, dwell fraction, cycle closure, and animated step-and-pause gear action.
Equation Used
The calculator follows the article dwell-ratio idea: the toothed arc is the motion phase and the locking arc is the dwell phase. For a complete one-revolution timing layout, the two arcs should add to 360 deg; the closure error shows any mismatch.
- The toothed and locking arcs define one driver cycle.
- At constant input speed, angular fractions equal time fractions.
- Ideal engagement is assumed with no backlash, compliance, or impact loss.
Operating Principle of the Intermittent Motion of Spur Gear
The driver gear has teeth cut on only part of its circumference — say 6 teeth across a 90° arc, with the remaining 270° left as a smooth circular boss. The driven full spur gear sits at standard centre distance. While the toothed arc passes through the mesh zone, the driven gear advances exactly the angle dictated by the gear ratio. The instant the last tooth disengages, a concentric locking plate on the driver — machined to the same root radius as the driven gear's outside diameter — slides into a matching scallop on the driven gear and holds it dead still until the next toothed arc arrives. That's the dwell. The ratio of dwell time to motion time is fixed by the angular split between toothed and toothless arcs.
Designers pick this layout over a Geneva drive when they need more than 6 stations per revolution, or when station count must be reconfigured by simply swapping the partial gear. The kinematic dwell is rock-solid because the locking plate physically blocks rotation — there's no reliance on friction or detents.
If the centre distance drifts more than about 0.05 mm on a Module 1 set, the first tooth engagement gets ugly — you'll hear a hard click and see witness marks on the leading flank. If the locking-plate scallop radius is even 0.1 mm undersized, the driven gear won't rotate into the next step cleanly and the indexing turret will hesitate or back-drive. The most common failure modes are: chipped leading-edge teeth from impact at re-engagement, worn scallops from repeated lock-plate contact under load, and gradual phase drift if the driver is keyed with sloppy fit.
Key Components
- Partial (Mutilated) Spur Gear: The driver. Teeth occupy only a defined arc — commonly 60° to 180° — with the remaining circumference machined down to the root circle. Tooth count and arc length together set the step angle of the driven gear per input revolution.
- Full Spur Gear (Driven): Standard spur gear on the output shaft. Receives motion only while meshed with the toothed arc. Often has scalloped flats machined between every tooth group to clear the locking plate during dwell.
- Locking Plate (Lock Disc): Concentric disc fixed to the driver, radius equal to driven gear's addendum circle minus a 0.05–0.10 mm running clearance. Blocks the driven gear from rotating during the dwell phase. Without it, the driven gear coasts under inertia.
- Leading Tooth (Engaging Tooth): The first tooth on the partial gear's toothed arc. Takes the full impact of re-engagement and is usually relieved or tip-rounded by 0.2–0.3 mm to prevent corner-loading damage at start of mesh.
- Driven Gear Scallop: Concave arc cut into the driven gear's outside diameter, matching the lock plate radius. There is one scallop per indexed station. Scallop centre must align with the tooth gap, or the lock plate will skid against a tooth tip during dwell.
Where the Intermittent Motion of Spur Gear Is Used
You see this mechanism wherever a continuous input shaft has to drive a stop-and-go output — pharmaceutical fillers, rotary indexers, film cameras, ticket dispensers, and any low-cost machine where a Geneva would be overkill. It's especially common where station count is non-standard (5, 7, 9, 12 stations) because a partial gear is cheap to redesign, where a Geneva drive locks you into discrete slot counts.
- Packaging: Bottle indexing turret on a Pneumatic Scale Angelus CB100L liquid filler — partial gear driving the 8-station carousel between fill and cap stations
- Cinema & Imaging: Film transport sprocket drive in legacy Bell & Howell 16mm projectors, where a 4-tooth partial gear advances the film one frame per shutter cycle
- Vending & Dispensing: Coin-mech ticket advance on Wurlitzer-style jukeboxes and similar mechanical dispensers, where each input revolution releases exactly one ticket or coin
- Assembly Automation: 6-station rotary indexing dial on a Sortimat assembly cell that pauses each fixture for screwdriving, vision, and test
- Textile Machinery: Pattern-card advance drum on dobby and jacquard looms, where one shed cycle equals one card step
- Watch & Clock Movements: Calendar-wheel advance in mechanical date complications — a finger on a 24-hour driver engages a partial-tooth date star once per day
The Formula Behind the Intermittent Motion of Spur Gear
The key number is the dwell ratio — how much of each input revolution the output spends stationary versus moving. At the low end of the typical range (toothed arc around 30°, dwell ~92%), the output gets a quick kick and a long rest, ideal for a slow assembly station that needs settling time. At the high end (toothed arc around 270°, dwell ~25%), the motion is nearly continuous with brief pauses — fine for a film advance where dwell time only has to exceed shutter open time. The sweet spot for most indexing turrets sits at 60–120° of toothed arc, giving 67–83% dwell, which is enough station-stopped time for a pneumatic operation to complete (typically 0.3–0.8 s per station at 30–60 RPM input).
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| θout | Output (driven gear) angular step per input revolution | degrees | degrees |
| θarc | Angular extent of the toothed arc on the partial gear | degrees | degrees |
| Ndriver | Equivalent full-tooth count of the partial gear (as if teeth covered all 360°) | teeth | teeth |
| Ndriven | Tooth count of the driven full spur gear | teeth | teeth |
| Dratio | Dwell fraction — portion of each input revolution the output is stationary | dimensionless | dimensionless |
Worked Example: Intermittent Motion of Spur Gear in an 8-station rotary indexing turret on a tea-bag tag stapler
You are sizing the partial-gear indexer that drives the 8-station turret on a benchtop tea-bag tag stapler similar in scale to a Maisa C21 tag-and-string machine. The continuous input shaft runs at 45 RPM. Each station must dwell long enough for the staple head to fire (measured 0.6 s minimum) and the driven gear has 48 teeth. You need to pick a toothed-arc angle on the partial driver that gives an exact 45° step per input revolution and confirm dwell time at the operating range of 30–60 RPM input.
Given
- Ndriven = 48 teeth
- θout (required step) = 45 degrees
- Stations per turret revolution = 8 stations
- Ndriver (equivalent full tooth count) = 48 teeth
- Input speed (nominal) = 45 RPM
Solution
Step 1 — with Ndriver = Ndriven = 48, the gear ratio is 1:1, so the toothed arc on the driver equals the required output step:
Step 2 — compute the dwell fraction. The toothed arc is 45° of the driver's 360°, so the toothless arc covers the remaining 315°:
Step 3 — at nominal 45 RPM input, one input revolution takes 60 / 45 = 1.333 s. Dwell time per station:
That is comfortably above the 0.6 s staple-fire requirement — roughly 2× margin, which is the sweet spot for a benchtop machine where the operator might bump the input belt or the staple head occasionally hesitates. At the low end of the operating range, 30 RPM input gives one revolution every 2.0 s, so tdwell,low = 0.875 × 2.0 = 1.75 s — almost three staple cycles' worth of dwell, fine but slow on throughput. At the high end, 60 RPM input gives one revolution every 1.0 s and tdwell,high = 0.875 × 1.0 = 0.875 s. That's still above the 0.6 s minimum, but the safety margin has dropped from 2× to 1.45×, and any wear in the staple solenoid timing will start producing missed staples. Above 75 RPM input, dwell falls below 0.7 s and you'll see intermittent misses.
Result
Pick a 45° toothed arc on the partial driver, giving an 87. 5% dwell ratio and 1.167 s of stationary time per station at the nominal 45 RPM input. At nominal speed the operator sees a clean step-pause-step rhythm with the staple firing well within the dwell window. Across the operating range, dwell drops from 1.75 s at 30 RPM to 0.875 s at 60 RPM — the sweet spot is 40–50 RPM where throughput is decent and staple-cycle margin stays above 1.7×. If your measured step lands short of 45° (say 43–44°) the most common causes are: (1) the partial gear's first tooth has been chamfered too aggressively at manufacture, losing roughly half a pitch of useful engagement; (2) the lock plate is dragging at the end of dwell because its radius is 0.1 mm oversized, back-driving the driven gear by 1–2°; or (3) the keyway between partial driver and input shaft has spread to a 0.15 mm slop, letting the driver lag under load. Check the lock-plate clearance with a feeler gauge first — it's the fastest diagnosis.
Intermittent Motion of Spur Gear vs Alternatives
Partial spur gear indexing is one of three common ways to convert continuous rotation into intermittent motion. Geneva drives and cam-driven indexers are the main alternatives. Each one wins on different axes — station-count flexibility, smoothness, load capacity, and cost.
| Property | Intermittent Spur Gear | Geneva Drive | Cam-Driven Indexer (Roller-Gear) |
|---|---|---|---|
| Typical input speed | 10–120 RPM | 20–300 RPM | 30–600 RPM |
| Indexing accuracy (repeatability) | ±0.2°–0.5° | ±0.05°–0.1° | ±15 arc-sec (±0.004°) |
| Station count flexibility | Any integer, easily reconfigured by swapping partial gear | Practically limited to 3–12 slots | Custom cam profile per station count, expensive to change |
| Relative cost (per indexer) | Low — $50–$300 for fabricated | Medium — $200–$800 stock | High — $1,500–$8,000 (CamCo, Sankyo) |
| Shock at engagement | High — leading tooth takes impact | Moderate — pin enters slot tangentially | Very low — cam profile shapes acceleration |
| Load capacity | Low to moderate (<200 N·m output) | Moderate (up to ~500 N·m) | High (1,000+ N·m, rated for 24/7) |
| Service life before tooth/scallop wear | 1–5 million cycles | 10–50 million cycles | 100+ million cycles |
| Best application fit | Light-duty indexing, film advance, low-volume packaging | Mid-speed turrets, mechanical counters | High-speed automated assembly, precision turret lathes |
Frequently Asked Questions About Intermittent Motion of Spur Gear
The leading tooth carries an impact load at every re-engagement that doesn't show up in static torque calculations. When the toothless arc finishes its pass, the driven gear is dead still and the driver is rotating at full speed — the first tooth has to accelerate the driven gear from zero in a fraction of a millisecond. Peak instantaneous force on that one tooth flank can be 5–10× the steady-state mesh force.
Two practical fixes: chamfer or tip-relieve the leading tooth by 0.2–0.3 mm so contact starts on a stronger part of the flank, and add a small acceleration ramp by tapering the lock plate's exit edge so the driven gear is already turning slowly when the first tooth bites. Most off-the-shelf partial gears skip this and pay for it in tooth chipping.
At 50 RPM with 6 stations, both work mechanically. The decision comes down to three factors: dwell-to-motion ratio, accuracy, and budget. A 6-slot Geneva gives you a fixed 66.7% dwell — you cannot tune it. A partial spur gear lets you set dwell anywhere from 50% to 95% by choosing the toothed-arc angle, which matters if your station operation needs 1.0+ seconds of pause time.
Geneva wins on accuracy (±0.05° vs ±0.3°) and on smooth engagement. Partial gear wins on cost (typically half the price for a fabricated set) and on station-count flexibility if you ever need to convert to 5 or 7 stations later. For light-duty packaging, partial gear. For a precision optical indexer, Geneva.
Back-drive during dwell almost always means lock-plate clearance is wrong, not lock-plate strength. The plate radius should be the driven gear's addendum radius minus 0.05–0.10 mm. If clearance exceeds about 0.15 mm on a Module 1 set, the driven gear has room to rock under any residual torque from the workpiece, and you'll see exactly the symptom you describe.
Check the radial gap with a feeler gauge at four positions around the driven gear. If the gap is uniform but oversize, the plate was machined wrong. If the gap varies around the circumference, the lock plate or driven gear is running eccentric — usually a bearing issue or a bent shaft.
Yes, but only at low speed and only if you've designed for it. Two issues bite you in reverse: first, the lock-plate-to-scallop entry geometry is usually optimised for one direction, so reverse engagement can wedge the plate tip into the scallop wall. Second, the leading tooth becomes a trailing tooth and any tip relief you cut for forward operation now sits on the wrong flank, so reverse engagement starts on a weaker corner.
If reverse capability matters — for a jam-recovery cycle, say — symmetric tip relief on both flanks of the first and last toothed-arc teeth, plus a symmetric lock-plate scallop profile, will let you reverse at 25% of forward speed without damage.
With a short toothed arc (say 3–4 teeth), the driven gear continues rotating briefly after the last tooth disengages because of inertia. Until the lock plate catches the next scallop, there's a small angular window — typically 1–3° — where the driven gear coasts. On a long toothed arc this coast is invisible because dwell time absorbs it, but on a short arc it adds directly to your measured step.
Compensate by either trimming the toothed arc by the coast angle, or — better — by tightening lock-plate clearance to under 0.05 mm so the plate catches the scallop almost the instant the last tooth releases. The second approach also reduces step variability cycle-to-cycle.
For a fabricated steel partial gear with a 60–120° toothed arc, the practical ceiling is around 150 RPM input. Above that, three things start to fail in sequence: leading-tooth impact stress climbs faster than tooth-bending strength can absorb (chipping starts around 180 RPM on Module 1 unhardened steel), the lock plate's entry shock noise becomes unacceptable in any environment with humans nearby, and dwell time drops below the threshold most pneumatic or solenoid actuators need to complete a stroke.
If you genuinely need >150 RPM intermittent indexing, switch to a roller-gear cam indexer. Sankyo and CamCo units run reliably at 600 RPM input because the cam profile shapes acceleration instead of slamming a tooth into engagement.
References & Further Reading
- Wikipedia contributors. Intermittent mechanism. Wikipedia
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