A single-tooth small wheel to large intermittent is a step-down indexing pair where the driver carries just one tooth (or pin) and the driven wheel carries many notches, so each full turn of the driver advances the large wheel by exactly one notch. You'll see this on the units drum of a Veeder-Root mechanical tally counter. It gives you a clean integer reduction ratio — 1:N where N is the notch count — without a gear train. The result is precise event counting with mechanical lock between strokes.
Single-tooth Small Wheel to Large Intermittent Interactive Calculator
Vary the count-wheel notch count and driver index arc to see the step angle, dwell angle, and reduction ratio update live.
Equation Used
For a single-tooth driver, each full driver revolution advances the driven count wheel by exactly one notch. With N evenly spaced notches, the angular step is 360/N. The remaining part of the driver rotation after the active index arc is dwell, when the rim-lock holds the count wheel stationary.
- The driver has one tooth or pin.
- One full driver revolution advances the count wheel by one notch.
- The index arc is the active engagement portion of the driver revolution.
How the Single-tooth Small Wheel to Large Intermittent Actually Works
The driver is a small disc carrying one engagement feature — usually a single tooth, pin, or roller — sitting at a fixed radius. The driven wheel is larger and carries N evenly spaced notches around its rim. Once per driver revolution the tooth sweeps into a notch, drags the large wheel through one pitch angle of 360°/N, then disengages. The rest of the driver revolution is dwell — the large wheel does nothing and must stay locked in place. That lock is what separates a real intermittent from a sloppy gear pair. Most designs use a rim-locking arc on the driver: a circular shoulder concentric with the driver shaft that rides against a matching concave scallop between every pair of notches on the count wheel. While the rim arc is engaged, the count wheel cannot rotate even if you push on it.
Get the geometry wrong and the mechanism either jams or skips. The tooth tip radius, the notch entry chamfer, and the rim-lock clearance all have to agree within roughly 0.05 mm on a counter-sized build. If the tooth enters the notch too deep, you get binding at the bottom of the stroke and the driver stalls. If the rim-lock clearance opens past about 0.1 mm, the count wheel can drift under vibration and you read a wrong count after a few hundred cycles. The single-tooth pinion geometry forces a 1:N step-down ratio in one stage, which is why it's the workhorse for the units digit on every mechanical tally drum from a 1920s grain-elevator counter to a modern turnstile.
Failure modes are predictable. The tooth wears first because it carries every drive impulse — when its leading flank rounds off past about 0.2 mm of wear, the count wheel starts to lag-engage and you'll occasionally drop a count. The notch corners chip second, especially if the count wheel is hardened steel and the tooth is brass. And the rim-lock arc polishes smooth over years of dwell contact, eventually losing its grip and letting the count wheel creep.
Key Components
- Single-tooth driver disc: A small disc with one tooth, pin, or roller projecting at a fixed radius. The tooth profile is typically an involute or simple radial flank, 2-4 mm tall on a counter-sized build, with the tip radius matched to the notch root within 0.05 mm. One full rotation of this disc produces exactly one index event on the count wheel.
- Large count wheel: The driven member, carrying N notches evenly spaced at 360°/N. N is typically 6 to 100 depending on the count base — 10 for a decimal digit drum, 60 for a seconds wheel, 100 for a percentage display. Notch flank angles run 20-30° to accept the tooth without slamming.
- Rim-lock arc: A concentric circular shoulder on the driver, occupying roughly 270-340° of the driver's circumference depending on tooth engagement angle. This arc rides against scalloped lock faces between notches on the count wheel and physically prevents the wheel from rotating during the dwell phase. Clearance must stay below 0.1 mm to prevent count drift.
- Detent or anti-backlash spring: Optional but common — a leaf spring or sprung roller that bears on the count wheel rim between notches. It eliminates the small free angle that exists at the moment the rim arc disengages and the next tooth has not yet engaged. On a Veeder-Root style counter the detent is integrated into the digit drum saddle.
- Driver shaft and bearing: Carries the input torque. On a hand-tally counter this is just a pivot in two pierced plates. On a powered indexer the driver shaft sees the full reaction torque during the engagement arc, which is roughly N times the count-wheel resistance torque due to the 1:N reduction.
Real-World Applications of the Single-tooth Small Wheel to Large Intermittent
You see this mechanism anywhere a designer needs an integer-reduction count without a gear train, with positive lock between events. It's cheap, it's compact, and it's been in service for over a century in the same basic form. The single-tooth driver geometry suits low-speed, high-precision counting — typically under 200 RPM input — where each input event must register as exactly one output increment with no possibility of half-counts.
- Mechanical counters: Veeder-Root Series 7000 hand-tally counter — single-tooth pinion drives the units digit drum, 10-notch wheel for one decimal digit per click.
- Vintage pinball restoration: Williams and Bally score reels from the 1960s use single-tooth drivers on the units reel, with carry pawls cascading to the tens reel.
- Industrial turnstiles: Perey full-height turnstile head counter — one tooth per pedestrian rotation drives a 6-notch index wheel locked to the turnstile axle.
- Textile machinery: Pick counters on Picanol air-jet looms — a single-tooth wheel on the main shaft drives a 100-notch tally drum to log shed cycles for warp inspection intervals.
- Postage and ticketing: Pitney Bowes meter strip-counter modules use single-tooth drivers on the impression-units drum, with 36-notch wheels matching the print roller circumference.
- Agricultural equipment: John Deere baler bale-count meters — single-tooth driver triggered by the knotter cycle, advancing a 5-digit Veeder-Root style register.
The Formula Behind the Single-tooth Small Wheel to Large Intermittent
The fundamental relationship is the step-down ratio between input revolutions and output index angle. At low notch counts (N=6 to 10) you get a coarse, snappy index with strong lock and forgiving tolerance — this is the sweet spot for hand-tally counters and turnstiles. At high notch counts (N=60 to 100) the index angle shrinks to a few degrees per event, which demands tighter machining but lets you fit more counts per drum revolution before a carry pulse is needed. Past N≈120 the notch pitch on a reasonable-diameter wheel falls below the practical machining tolerance and the mechanism loses positive engagement.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| θstep | Angular advance of the count wheel per driver revolution | degrees | degrees |
| N | Number of notches on the count wheel | count (integer) | count (integer) |
| ωin | Driver angular velocity (input) | RPM or rad/s | RPM |
| ωout | Average count-wheel angular velocity | RPM or rad/s | RPM |
| Pnotch | Linear notch pitch at count-wheel rim | mm | in |
Worked Example: Single-tooth Small Wheel to Large Intermittent in a sawmill log-tally counter
You are designing a log-tally counter for a small cedar mill on Vancouver Island. Each log passing the trim saw triggers a cam that rotates a single-tooth driver one full revolution. The driver must advance a 12-notch count wheel by exactly one position per log, with the wheel diameter set to 60 mm so the operator can read the count from across the deck. Logs cross the trim saw at a peak rate of about 90 per hour, with typical operation 30-60 per hour and bursts to 120 per hour during a busy shift.
Given
- N = 12 notches
- Dwheel = 60 mm
- Ratenom = 60 logs/hour
- Ratelow = 30 logs/hour
- Ratehigh = 120 logs/hour
Solution
Step 1 — compute the index angle per log. With 12 notches the count wheel advances:
Step 2 — compute the linear notch pitch at the rim. This sets the minimum machining tolerance for the notches:
15.71 mm is comfortable — you can mill these notches on a manual rotary table with ±0.1 mm and the tooth will still drop in cleanly. If you'd specified N=60 the pitch would collapse to 3.14 mm and you'd need a CNC indexer.
Step 3 — at nominal 60 logs/hour, compute driver speed. The driver turns once per log:
1.0 RPM is glacially slow — the cam barely moves between logs, lock-arc dwell is essentially permanent, and wear is dominated by the engagement event itself rather than dwell sliding.
Step 4 — at the low end of the operating range, 30 logs/hour:
The mechanism barely runs. Stiction in the detent spring becomes the dominant resistance and you may see the count wheel hesitate at the start of an index. Specify a detent preload under 0.5 N at the rim.
Step 5 — at the high end, 120 logs/hour during a burst:
Still slow in absolute terms, but the engagement event itself happens in roughly 50 ms because the tooth only sweeps through about 30° of the driver's revolution to fully index the wheel. At 2 RPM that 30° takes 2.5 seconds — fine. The real concern at the high end is operator confidence: if two logs arrive within 1 second the cam linkage must reset cleanly. Size the cam return spring for at least 3 Hz response.
Result
Nominal step angle is 30° per log with a driver speed of 1. 0 RPM, and notch pitch on the rim is 15.71 mm. At 30 logs/hour the wheel is essentially static between events and you'll fight detent stiction; at 120 logs/hour during a busy shift the cam linkage timing — not the indexer geometry — becomes the limiting factor. If you measure dropped counts in service, check three things in order: (1) cam linkage failing to complete a full driver revolution under fast triggering, which means the tooth never fully clears the previous notch — symptom is occasional double-counts followed by a missed count; (2) detent spring preload too high, causing the wheel to stall mid-index at low log rates — symptom is a wheel that sits at +15° instead of +30° after the driver returns; (3) tooth tip radius worn past 0.2 mm rounding, which lets the wheel slip back as the tooth disengages.
Single-tooth Small Wheel to Large Intermittent vs Alternatives
The single-tooth-to-large-wheel intermittent competes with a few other indexing approaches when you need integer reduction with positive lock. Here is how it stacks up on the dimensions that actually matter when you're choosing between them for a counter or low-speed indexer.
| Property | Single-tooth driver to large count wheel | Geneva drive | Ratchet and pawl |
|---|---|---|---|
| Reduction ratio per stage | 1:N (any integer N from 6 to ~120) | 1:N (typically 4 to 12 slots) | 1:1 per stroke, no fixed reduction |
| Practical input speed | Up to ~200 RPM | Up to 600 RPM with proper design | Limited by stroke return — typically under 60 cycles/min |
| Index accuracy | ±0.5° on a counter-sized build | ±0.1° with rim lock | ±1-2° depending on pawl tip wear |
| Dwell as fraction of cycle | ~85-95% (most of driver rev is dwell) | ~67% for 6-slot, 75% for 8-slot | 100% between strokes (input is bidirectional) |
| Cost and complexity | Low — two parts plus detent | Medium — precise slot geometry required | Lowest — pawl and toothed wheel only |
| Typical lifespan | 10⁶ to 10⁷ counts before tooth wear matters | 10⁷ to 10⁸ cycles in proper steel | 10⁵ to 10⁶ strokes — pawl tip is the wear item |
| Best application fit | Decimal digit drums, low-speed event counters | Continuous-rotation indexers, turret stations | Hand-operated tools, one-way clutches |
Frequently Asked Questions About Single-tooth Small Wheel to Large Intermittent
Look at your input motion first. If your input is continuous rotation you want a Geneva — its slot geometry gives smooth tangential entry and you get controlled acceleration into the index. If your input is one discrete revolution per event (like a cam pulse from a sensor or lever), the single-tooth driver is simpler, cheaper, and tolerates rougher input timing because the rim-lock arc covers most of the cycle.
Speed is the second factor. Above about 200 RPM the single-tooth driver starts hammering the count wheel at engagement because the tooth flank has no smooth approach geometry. A Geneva will run to 600 RPM in the same envelope. Below 60 RPM the single-tooth wins on cost every time.
That's almost always inertia overrun combined with insufficient detent. When the tooth disengages, the count wheel is still rotating and carries past the next lock face. If your detent spring is weak or missing, or the rim-lock arc has a gap before re-engaging, the wheel coasts an extra 30° and seats in the wrong notch.
Fix it by checking that the rim-lock arc engages the next scalloped face before the tooth fully clears the current notch — there should be a small overlap of 2-5° of driver rotation where both the tooth and the rim arc are simultaneously constraining the wheel. If the geometry shows a gap instead of overlap, you've either machined the rim arc short or the wheel notches are too widely spaced.
Around 30 to 40 notches before the geometry stops working. Notch pitch at N=40 on a 50 mm wheel is about 3.9 mm, which is the lower bound for a tooth profile that can carry meaningful load and still self-locate at engagement. Below 3 mm pitch the tooth tip can ride over the lock face instead of dropping into the notch, especially if there's any radial play in the driver bearing.
If you need higher counts on a small wheel, use two stages — a single-tooth driver into a 10-notch wheel, then a carry pawl into a second 10-notch wheel for the tens digit. That's how every Veeder-Root register is built.
That's a classic sign of tooth-flank wear or backlash between the rim-lock arc and the scalloped lock face. 0.3° is small enough that the mechanism is still functional, but it accumulates as visible misalignment of the printed digit on a reading drum.
Diagnostic: rotate the driver backwards by hand and watch the count wheel. If it moves at all before the tooth re-engages, you have rim-lock backlash and you need to either shim the arc outward or replace the count wheel. If the wheel doesn't move backwards but still indexes short, the tooth leading flank has worn — measure tip radius with pin gauges and replace the driver if it's past 0.15 mm rounding from the original sharp profile.
Only if you design the tooth profile symmetrically and use a symmetric notch geometry — both flanks 25-30° from radial, no chamfer bias. Most off-the-shelf single-tooth drivers are asymmetric because they're designed for one-way counting, with a steep leading flank for positive engagement and a relieved trailing flank to disengage cleanly.
If you need bidirectional counting, you also need a bidirectional detent — typically a sprung roller riding in scalloped pockets between notches rather than a leaf-spring pawl. The Veeder-Root reversible counter range uses exactly this approach.
Because the 1:N reduction works in reverse for torque. Whatever resistance torque the count wheel sees — detent friction, drum drag, ink-roller load if it's a printing counter — gets multiplied by N at the driver shaft during the engagement arc. With N=12 and a 0.05 N·m count-wheel resistance, your driver needs at least 0.6 N·m of input torque just to overcome it, and you should size for 1.5× that to handle the inertia spike at engagement.
The torque isn't constant either — it spikes during the 30° engagement arc and drops to near zero during the rim-lock dwell. Size your motor or cam linkage for the peak, not the average, or the driver will stall right at the moment the tooth bottoms in the notch.
References & Further Reading
- Wikipedia contributors. Geneva drive. Wikipedia
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