A two-toothed pinion — sometimes called a cam pinion — is a small driving gear that carries only two engaging teeth (often diametrically opposed) plus a locking arc that holds the driven wheel still between engagements. You'll find it inside mechanical odometers, totalizing counters, and Veeder-Root style register heads where one decade wheel must advance the next by exactly 1/10 of a turn per revolution. The two teeth deliver the carry, the locking arc prevents creep, and the result is a clean, repeatable digit step with zero drift between counts.
Two-toothed Pinion (Cam Pinion) Interactive Calculator
Vary the number of driving teeth and driven-wheel teeth to see the output index angle, speed ratio, and locking interval update in the animated cam-pinion diagram.
Equation Used
The calculator uses the article relationship that the output speed ratio equals the number of active pinion teeth divided by the number of driven-wheel teeth. Each engagement advances the wheel by one tooth pitch, so a 10-tooth decade wheel indexes 36 degrees per step.
- Each driving tooth advances the driven wheel by exactly one tooth pitch.
- Driving teeth are evenly spaced around the pinion.
- No slip, backlash, missed counts, or impact torque effects are included.
- The locking arc holds the driven wheel stationary between index events.
The Two-toothed Pinion (cam Pinion) in Action
The two-toothed pinion solves a problem that plain spur gears cannot: you need the input shaft to rotate continuously, but the output wheel must move only during a tiny window of that rotation and stay locked the rest of the time. We do that by cutting away every tooth on the pinion except two, and shaping the remaining hub into a circular locking arc. When one of the two teeth sweeps past the driven wheel, it engages a single tooth space and pushes the wheel forward by one pitch — typically 36° on a 10-tooth decade wheel. The instant that tooth disengages, the locking arc rides into a matching concave cutout on the wheel and holds it dead solid until the next engagement.
Geometry tolerances are tight and unforgiving. The locking arc radius must match the wheel cutout radius within roughly 0.05 mm — too loose and the wheel creeps under vibration, too tight and the arc binds and stalls the input shaft. The two driving teeth must be cut to standard involute form so they mesh cleanly with the driven wheel's full tooth set, but they sit on a hub whose outside diameter equals the wheel's root circle minus running clearance. If you machine the locking arc 0.1 mm undersize, you'll see digit creep between counts — the meter reads 7.3 when it should read 7.0. If you cut it 0.1 mm oversize, the input torque spikes every half revolution and a small clock motor will stall.
The two-toothed pinion fails in three predictable ways: tooth wear at the leading edge from repeated impact loading (the tooth strikes a stationary wheel every cycle), locking arc scoring from grit embedded in the wheel cutout, and pinion shaft wobble that shifts engagement timing. A worn unit shows up as missed counts at low input speed or double-stepping at high input speed.
Key Components
- Driving teeth (×2): Two involute teeth, usually 180° apart, that engage the driven wheel and push it forward by exactly one tooth pitch per engagement. Tooth profile must match the driven wheel module — typically 0.3 to 0.8 module on counter applications. Hardened to 55-60 HRC on metal builds because each tooth absorbs an impact load every cycle.
- Locking arc (cam segment): Circular hub segment between the two teeth that rides in a concave cutout on the driven wheel and holds it stationary between indexes. Arc radius must match the cutout radius within 0.05 mm — looser and the wheel creeps, tighter and it binds. Arc length sets the dwell time, typically 160-170° of pinion rotation per dwell.
- Driven wheel (decade or count wheel): The output wheel with a full set of teeth and matching concave cutouts between every tooth space. On a 10-position decade wheel each cutout sits at 36° spacing. The cutout depth must equal the locking arc radius plus 0.02-0.05 mm clearance for free running.
- Pinion shaft: Carries the two-toothed pinion and runs in a bearing or jewelled pivot. Radial play above 0.05 mm shifts the engagement point and causes timing errors that compound across multi-decade registers. On gas meter index heads we hold shaft runout under 0.02 mm TIR.
- Carry-over flag or finger (optional): On multi-decade counters, a small flag fixed to the lower decade wheel that triggers the two-toothed pinion of the next decade only once per ten counts. This is what gives a register its '9 rolls to 10, then carry the 1' behaviour.
Real-World Applications of the Two-toothed Pinion (cam Pinion)
You see two-toothed pinions wherever a continuous rotation has to drive a stepped, locked, drift-free output — and where a Geneva drive would be too bulky or a ratchet too imprecise. They dominate mechanical metering, totalizing, and analog readout devices because the locking arc gives them positional security a ratchet cannot match.
- Utility metering: Itron 250A and Sensus R-275 residential diaphragm gas meter index heads use a stack of two-toothed pinions to drive cubic-foot decade wheels, with each decade carrying the next via a single flag tooth.
- Fuel dispensing: Veeder-Root mechanical totalizer heads on Gilbarco gasoline pumps used cam pinions on every digit wheel from the 1960s through the 1990s before electronic registers replaced them.
- Automotive instrumentation: Stewart-Warner mechanical odometer assemblies in Ford and GM vehicles up to the late 1990s use two-toothed pinions to carry tenths-of-a-mile to miles to tens of miles.
- Industrial production counters: Hengstler 0.835 and Durant 5-Y series stroke counters mount on punch presses and packaging lines, indexing one count per ram cycle through a cam-pinion stack.
- Postal and ticketing equipment: Pitney Bowes meter date-stamp heads and Globe Ticket numbering presses use single- and two-toothed pinions to advance serial-number wheels between impressions.
- Horology and timing: Mechanical chronograph minute-recorder wheels in ETA 7750-based movements step once per minute via a cam pinion driven off the chronograph runner.
The Formula Behind the Two-toothed Pinion (cam Pinion)
What a designer actually needs from a two-toothed pinion is the relationship between input shaft RPM and output digit-step rate, plus the peak torque the input shaft has to deliver during the brief engagement window. At the low end of the typical operating range — say 5 RPM input on a slow utility meter — the engagement is gentle and torque demand is dominated by friction in the wheel cutout. At the high end — 200 RPM input on a fast production counter — the engagement becomes an impact event, and peak torque can spike 3 to 5× the static value because the wheel has to be accelerated from rest to angular velocity in a fraction of a degree of pinion rotation. The sweet spot for most counter applications sits between 30 and 90 RPM input, where engagement is firm but not impulsive.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Nout | Output wheel rotational speed (full revolutions per unit time) | rev/s | rev/min |
| Nin | Input pinion shaft rotational speed | rev/s | rev/min |
| nteeth_pinion | Number of engaging teeth on the pinion (2 for a standard cam pinion, sometimes 1) | teeth | teeth |
| Zwheel | Total tooth count on the driven wheel (10 for a decade wheel) | teeth | teeth |
| fstep | Step frequency — number of digit advances per unit time = Nin × nteeth_pinion | steps/s | steps/min |
Worked Example: Two-toothed Pinion (cam Pinion) in a textile loom pick counter
You are sizing the two-toothed pinion that drives the units decade wheel on a Picanol OmniPlus 800 air-jet loom pick counter, where the input shaft runs off the loom's main crankshaft via a 1:4 reduction. The loom runs nominally at 600 picks per minute, and the pick counter must advance one digit per pick on the units wheel, then carry to the tens wheel every ten picks. The decade wheel has 10 teeth at module 0.5, and the cam pinion carries 2 teeth.
Given
- Loom pick rate = 600 picks/min
- Reduction ratio (crank to counter input) = 4:1 —
- nteeth_pinion = 2 teeth
- Zwheel = 10 teeth
- Wheel module = 0.5 mm
Solution
Step 1 — find the cam pinion input speed at the nominal 600 picks/min loom rate. The counter input runs at the pick rate divided by the reduction:
Step 2 — compute the step frequency at nominal speed. Each pinion revolution delivers 2 engagements:
That is exactly half the loom pick rate, which is wrong if you want one digit per pick. The fix: either drop the reduction to 2:1 so the counter input runs at 300 RPM and delivers 600 steps/min, or use a single-tooth pinion at 600 RPM input. We'll continue with the 2:1 reduction option because the impact loads are gentler with two teeth than with one.
Step 3 — corrected nominal step rate at 2:1 reduction:
At the low end of the loom's operating envelope — 350 picks/min during heavy fabric runs — the step rate drops to 350 steps/min or 5.83 steps/s. Engagement is firm and you can hear each digit click distinctly. At the high end — 750 picks/min on light cottons — step rate climbs to 750 steps/min or 12.5 steps/s, and the engagement transitions from audible click to continuous rattle. Above roughly 900 picks/min the impact load on the leading tooth flank exceeds the fatigue limit of unhardened brass, which is why Picanol specs hardened steel pinions on high-speed variants.
Step 4 — output decade wheel speed at nominal:
So the units decade wheel makes one full revolution per second, and the carry-over flag triggers the tens pinion 60 times per minute. That matches the design intent — every 10 picks rolls a tens digit.
Result
Nominal output is 600 steps per minute on the units wheel, which is exactly one digit advance per loom pick at 600 picks/min crankshaft speed. At the 350 picks/min low end the counter ticks at a leisurely 5.8 Hz and digit registration is dead clean; at the 750 picks/min high end you're pushing 12.5 Hz and the locking arc starts to whine — that's the sweet-spot ceiling for an unhardened brass build. If your measured count differs from the actual pick count, the three failure modes to check first are: (1) locking arc undersize causing digit creep between picks, which shows up as the units wheel reading 0.5 high after a heavy production run; (2) pinion shaft radial play above 0.05 mm, which lets the engagement skip every 20-30 cycles and the counter under-reads; and (3) carry-over flag bent or worn flat, so the tens wheel fails to advance on the 9-to-0 transition and the counter stalls at xx9 indefinitely.
When to Use a Two-toothed Pinion (cam Pinion) and When Not To
The two-toothed pinion competes with three other mechanisms for low-rate intermittent indexing: the Geneva drive, the ratchet-and-pawl, and the single-tooth pinion. Each has a different sweet spot, and choosing wrong gets you either premature wear or mechanism that won't fit in the available space.
| Property | Two-toothed pinion | Geneva drive | Ratchet & pawl |
|---|---|---|---|
| Indexing accuracy (positional drift between steps) | ≤ 0.1° with proper locking arc fit | ≤ 0.05° — best in class | 0.5-2° depending on pawl spring preload |
| Maximum practical step rate | ~15 Hz before impact wear dominates | ~5 Hz limited by Geneva slot acceleration | ~25 Hz but with audible chatter |
| Package size for a 10-position index | Smallest — fits in a 12 mm OD register stack | Largest — Geneva needs ≥ 25 mm OD for 10 stations | Compact but needs separate detent |
| Cost (production, mid-volume) | Low — single machined or moulded pinion | Medium — Geneva slots need form-cutting or EDM | Lowest — stamped pawl and ratchet wheel |
| Reverse-direction holding | Excellent — locking arc holds both directions | Excellent — geometric lock | Poor — pawl only resists one direction |
| Typical lifespan at 1 step/sec | 10-50 million cycles in hardened steel | 50-200 million cycles | 5-20 million cycles before pawl spring fatigue |
| Best application fit | Counters, registers, decade wheels, odometers | Film advance, indexing tables, turret tools | Winding mechanisms, cable reels, one-way drives |
Frequently Asked Questions About Two-toothed Pinion (cam Pinion)
This is almost always engagement-window timing, not tooth wear. At high speed the driven wheel has to accelerate from zero to engagement velocity in a fraction of a degree of pinion rotation. If the pinion shaft has more than about 0.05 mm of radial play, the tooth strikes the wheel slightly off-centre and the wheel rotates about its own pivot rather than indexing forward — you get a half-step that the locking arc then forces back, and the count is lost.
Diagnostic check: spin the input at half normal speed and watch a single decade. If the skip disappears at low speed but returns at full speed, it's bearing play, not tooth geometry. Replace the pinion shaft bushing.
Two teeth at half the speed wins almost every time. The single-tooth pinion delivers twice the impact energy per engagement because all the wheel acceleration happens in one event per revolution instead of two, and the leading tooth flank takes the full hit alone. Tooth fatigue scales roughly with impact energy squared, so a single-tooth design at 2× RPM has 4× the per-tooth wear rate of a two-tooth design at 1× RPM delivering the same step frequency.
The exception is when package length matters more than longevity — single-tooth pinions can be ground thinner because there's no diametrical tooth-pair geometry to maintain.
Creep under vibration with a visually good locking arc is almost always a surface finish problem on the wheel cutout, not a dimensional one. If the cutout radius was machined with a worn end mill or the wheel was sintered without a finish operation, the arc rides on a few high spots rather than the full curved contact line. Vibration walks the wheel across those high spots one micron at a time.
Check the cutout surface with a 10× loupe — you want to see a continuous polished band where the arc has burnished it. If you see only spotty contact marks, lap the cutout with the actual locking arc and a touch of fine valve-grinding compound for 50 cycles. Creep usually disappears.
The arc length is set by the angular gap between the two teeth on the pinion. Standard symmetric designs put teeth 180° apart, giving a 160-170° dwell on each side after you subtract the engagement sweep. If you want longer dwell, you go to a single-tooth pinion (one engagement per revolution, ~340° dwell) or you space the two teeth asymmetrically — say 90° and 270° — to get one short dwell and one long dwell per revolution.
Watch the load balance: asymmetric tooth spacing means the input shaft sees an uneven torque demand, which can excite resonance in light clock-motor drives. We don't recommend asymmetric spacing on anything driven by a synchronous AC motor under 5 W.
This is a flag-tooth alignment issue, not a pinion problem. The carry-over flag on the units wheel has to engage the tens-wheel pinion at exactly the moment the units wheel passes from 9 to 0. If the flag is bent inward by even 0.3 mm, it misses the engagement entirely on every tenth count. If it's bent outward, it engages every count and the tens wheel runs ten times too fast.
Quick check: rotate the units wheel slowly by hand through a 9-to-0 transition and watch the tens pinion. It should rotate exactly one tooth pitch — no more, no less. If it stutters or fails to move, straighten the flag with a small pair of pliers, working in 0.1 mm increments.
Plastic works fine for low-cycle applications — mechanical bath scales, cheap stroke counters, kitchen timers — up to maybe 100,000 cycles. Acetal (Delrin) and PBT are the standard choices because they have low coefficient of friction against steel and don't cold-flow under the locking arc's continuous radial load.
Where plastic fails is high-vibration environments. The locking arc puts a small but constant radial preload on the wheel cutout, and over thousands of hours that preload causes creep deformation in the cutout, which then enlarges and lets the wheel drift between counts. For utility meters and odometers — anything that has to read accurately over 10+ years — use a brass or zinc decade wheel even though the cost is higher.
References & Further Reading
- Wikipedia contributors. Pinion. Wikipedia
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