A mutilated bevel gear for opposing intermittent motion is a bevel gear with teeth removed across two opposing sectors of the pinion or driver, so that two perpendicular output gears mesh in alternation — one rotates while the other dwells, then they swap. Henry T. Brown catalogued this layout in his 1868 reference 507 Mechanical Movements as a way to drive two right-angle shafts from one continuously rotating input. The toothed sectors hand off cleanly, giving each output a precise rotational increment per input cycle. You see it in old textile drop-box looms and twin-spindle automatic screw machines where two tools must index in alternating strokes.
Mutilated Bevel Gear for Opposing Intermittent Interactive Calculator
Vary the toothed sector, tooth counts, and number of sectors to see the driven output step, sector teeth, phase spacing, and remaining smooth gap.
Equation Used
The toothed-sector arc selects a fraction of the driver gear teeth. Those teeth advance the driven bevel gear by the same tooth count, so the output step is theta_out = alpha x N_d / N_o. For a two-sector opposing mechanism, the output engagements are spaced 180° apart when the sectors are opposite each other.
- Driver and driven bevel gears have compatible module and pitch geometry.
- Each toothed sector contains a whole number of teeth for practical manufacture.
- Opposing intermittent layout uses two toothed sectors phased 180 deg apart.
- Backlash, impact, and lock-disk clearance are not included in the kinematic result.
The Mutilated Bevel Gear for Opposing Intermittent in Action
The driver is a bevel gear with teeth machined off across two arcs on opposite sides of the cone — the "mutilated" sectors. Two driven bevel gears sit at right angles, both meshed with the driver's pitch line, but only one can engage at a time. As the driver rotates, the toothed half engages output A and rotates it through a fixed arc. The instant that toothed sector clears, the gap rolls past output A and output A dwells. Half a revolution later the second toothed sector engages output B, rotating it the same arc while A continues to dwell. Then the cycle reverses on the next input revolution.
The geometry only works if the tooth-cut sector boundaries align precisely with the dwell-locking features on each output. We typically pair each driven bevel with a partial-disk lock that rides in the gap of the driver's mutilated sector — same principle as a Geneva driving disk locking the slot wheel during dwell. If the lock arc and the tooth-cut arc disagree by more than about 0.5°, you get one of three failures: the output backdrives during dwell because nothing holds it, the next tooth slams into the side of an output tooth instead of rolling into mesh (you hear it as a sharp tick every cycle), or the lock disk binds against the output's hub and stalls the input. Tooth count on the driver's toothed sector must equal a whole number — partial teeth at the sector edges chip within a few hundred cycles.
Because two outputs share one driver, timing between A and B is rigidly mechanical — there is no slip, no electronic sync, no encoder. That's the whole reason the mechanism survived in 19th-century machine tools: one shaft, two perfectly phased outputs, no clutches.
Key Components
- Mutilated Bevel Driver: The input bevel gear with teeth cut away across two opposing sectors, typically 90° toothed and 90° smooth in alternation. The toothed arc length sets how many teeth roll into the output per engagement — a 90° sector on a 24-tooth blank gives 6 driven teeth per cycle. Sector boundary tolerance must hold within ±0.25° or the locking disk hands off rough.
- Driven Bevel Gear A: The first right-angle output. It rotates only while the driver's toothed sector is in contact, then dwells while the smooth arc passes by. The dwell hub carries a concave arc that mates with the driver's smooth sector — this is what physically prevents back-rotation during the dwell phase.
- Driven Bevel Gear B: The second output, mounted opposite A, identical geometry, phased 180° on the input. While A rotates, B dwells locked. While B rotates, A dwells locked. The two outputs never drive simultaneously and never both dwell — the handoff is continuous.
- Locking Disk / Dwell Arc: A circular arc on the driver that sweeps through the concave relief on the dwelling output's hub, holding it stationary against any back-torque. Radial clearance between the lock arc and the relief should be 0.05–0.10 mm — tighter and you get binding, looser and the dwelling output rattles.
- Input Shaft and Bearings: The continuously rotating input. Because torque pulses on and off every quarter revolution, the bearings see cyclic radial loading — use rolling-element bearings rather than plain bushings on anything above about 200 RPM input, or you'll see fretting wear inside 1,000 hours.
Real-World Applications of the Mutilated Bevel Gear for Opposing Intermittent
This mechanism shows up wherever one continuously rotating input has to drive two perpendicular outputs that must alternate cleanly without electronic synchronisation. The opposing layout is what readers usually search for — same idea as a single-revolution gear, but doubled and phased. Below are real machines where the mutilated bevel handoff earns its keep.
- Textile Machinery: Drop-box loom shuttle selectors on Crompton & Knowles W3 looms, where two shuttle boxes must index in alternation to swap weft colours.
- Machine Tools: Twin-spindle Brown & Sharpe No. 2 automatic screw machines, alternating tool-turret indexes between front and rear stations.
- Printing Equipment: Two-colour Heidelberg cylinder press inking-roller advance, where two ink fountains tick over on alternating impressions.
- Agricultural Machinery: Twin-row corn planter seed-disk drivers on John Deere 999 horse-drawn planters, dropping kernels in left and right rows on alternating cycles.
- Clockwork and Automata: Strike-and-chime trains on tower clocks where the strike train and the chime train share one going-train output but must run in alternation, not together.
- Packaging Machinery: Dual-lane biscuit feeders where two parallel conveyors index forward in alternation to keep a downstream wrapper at constant duty.
The Formula Behind the Mutilated Bevel Gear for Opposing Intermittent
The number every designer needs is the angular displacement each output rotates per input revolution — call it θout. It depends on the toothed-sector arc on the driver, the gear ratio at mesh, and how many engagement cycles per input revolution (one for a single mutilated sector, two for opposing). At the low end of typical use — a 60° toothed sector with a 1:1 ratio — each output ticks 60° per engagement, fine for a slow ratchet feed. Nominal is a 90° sector at 1:1, giving a 90° step per cycle. Push the sector to 120° and the output advances 120° per cycle, but you lose dwell margin and the lock-disk arc shrinks below safe handoff angles. The sweet spot for opposing layouts sits at 90°, which leaves equal dwell and drive arcs.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| θout | Angular displacement of the driven output per engagement cycle | degrees | degrees |
| αtooth | Arc length of the toothed sector on the mutilated driver | degrees | degrees |
| ndriver | Tooth count on the full driver pitch circle (if it were not mutilated) | teeth | teeth |
| noutput | Tooth count on the driven bevel gear | teeth | teeth |
Worked Example: Mutilated Bevel Gear for Opposing Intermittent in a brass cartridge case-mouth annealing carousel
You are designing a two-station case-mouth annealing fixture for a small ammunition reloading shop running once-fired .308 Winchester brass. Two flame nozzles sit at right angles. Each nozzle dwell-heats a case for a fixed time, then the fixture must rotate that case out and the opposite case in. One continuous-rotation gearmotor drives both fixtures through a mutilated bevel pair — driver has a 90° toothed sector, 24 teeth on the full pitch circle, and each driven bevel has 24 teeth. Input runs at 6 RPM nominal.
Given
- αtooth = 90 degrees
- ndriver = 24 teeth
- noutput = 24 teeth
- Input speed (nominal) = 6 RPM
Solution
Step 1 — at nominal geometry, compute the per-cycle output rotation:
Each output ticks 90° per engagement, then dwells while the opposite output ticks 90°. With a 24-tooth driver and a 90° toothed sector, exactly 6 teeth roll into mesh per cycle — a whole number, which is what you want. No partial-tooth chipping at the sector boundary.
Step 2 — convert input RPM to dwell time per output. At 6 RPM input, one full revolution takes 10 seconds. The opposing layout gives two engagement cycles per input revolution, so each output gets 5 seconds total per cycle: roughly 2.5 seconds rotating and 2.5 seconds dwelling.
Step 3 — at the low end of the typical operating range, drop input to 3 RPM. Dwell time doubles to 5 seconds per cycle. That's long enough to fully anneal a .308 case mouth without scorching the body — close to the sweet spot for 70/30 cartridge brass. At the high end, push input to 12 RPM:
1.25 seconds is below the heat-soak time the brass needs. You'll under-anneal and the necks will split on the next firing. Above about 10 RPM the mechanism also starts seeing audible tooth-clack at handoff because the lock-disk arc has less time to seat before the next toothed sector engages.
Result
Each output bevel rotates 90° per cycle with a 2. 5-second dwell at 6 RPM input — exactly what a flame anneal needs for once-fired .308 brass. At 3 RPM you get a generous 5-second dwell that wastes throughput but anneals reliably; at 12 RPM the 1.25-second dwell under-anneals and the handoff gets noisy. The sweet spot sits at 5–7 RPM input. If you measure dwell-time variation greater than ±0.2 s between the two outputs, the most likely causes are: (1) the two toothed sectors on the driver were cut to slightly different arc lengths — check both with a sine bar, they must agree within 0.25°; (2) the lock-disk concave reliefs on the two outputs have unequal radii, letting one output creep during dwell while the other holds rigid; or (3) the input shaft has axial float greater than 0.05 mm, which shifts mesh depth between the two driven bevels and changes effective engagement timing.
Choosing the Mutilated Bevel Gear for Opposing Intermittent: Pros and Cons
Opposing intermittent motion is a niche requirement — one input, two perpendicular outputs, alternating. The mutilated bevel is one solution. The realistic alternatives are a pair of opposed Geneva drives sharing an input, or two separate cam-driven indexers with electronic phase control. Here's how they stack up on the dimensions a designer actually decides on.
| Property | Mutilated Bevel Gear (opposing) | Twin Geneva Drives (shared input) | Cam Indexers with Servo Phasing |
|---|---|---|---|
| Max input RPM (practical) | 100–300 RPM before tooth slam at handoff | 300–600 RPM with proper Geneva geometry | 1,000+ RPM, limited by cam follower dynamics |
| Indexing accuracy | ±0.25° per output, set by sector boundary tolerance | ±0.10° per slot, set by Geneva pin fit | ±0.02° with closed-loop servo correction |
| Cost (small batch, 2024) | $400–800 for matched bevel set | $600–1,200 for two Geneva pairs | $3,000+ for two cam boxes plus drive |
| Mechanical phase rigidity | Absolute — outputs locked to input geometry | Absolute — same one-input rule applies | Depends on servo tuning, can drift on power loss |
| Footprint | Compact — one driver, two outputs at 90° | Larger — two slot wheels need radial clearance | Largest — two cam boxes plus motors and drives |
| Wear failure mode | Sector-edge tooth chipping at 5,000–20,000 cycles | Pin and slot edge wear, 50,000+ cycles | Cam follower fatigue, 10⁷ cycles typical |
Frequently Asked Questions About Mutilated Bevel Gear for Opposing Intermittent
The arc length is only half the picture. The phase angle between the two opposing toothed sectors must be exactly 180°, and the leading tooth of sector B must align with the trailing dwell-arc edge of sector A within about 0.1°. If the sectors are correctly sized but mis-clocked on the driver hub, sector B engages while sector A's lock arc still has 1–2° of dwell left to deliver, and you get a brief overlap where both outputs are constrained — the result is a tooth scrape that sounds like chatter.
Check this by indicating the leading edge of each toothed sector against the same reference index pin on the input shaft. The two readings must differ by 180° ± 0.1°.
Pick the mutilated bevel when the two output axes must be perpendicular to the input axis — bevels handle that natively. Twin Genevas keep all axes parallel, so if your machine layout demands two right-angle outputs (like a vertical input driving two horizontal indexing tables) the Geneva forces you to add miter gears or shaft couplers, which adds backlash.
Pick the Geneva when you need more than 90° per index, finer accuracy, or higher input RPM. Above about 300 RPM the mutilated bevel's tooth-edge stresses at handoff exceed what a typical case-hardened steel sector can sustain past 10,000 cycles.
The driver may be symmetric but the driven bevels probably aren't seated at identical mesh depth. Bevel gears are sensitive to axial position — move a driven bevel 0.1 mm closer or farther along its shaft and the effective mesh point shifts, which changes how many teeth fully engage during the sector pass.
Set both driven bevels to the same backlash spec at the pitch line, measured with feeler stock or a dial indicator riding a tooth flank. 0.05–0.08 mm backlash on each, matched within 0.02 mm, will normally bring the two output increments back into agreement.
You can, but the lock-disk geometry usually isn't symmetric for both directions. Most practical designs cut the leading edge of each toothed sector with a slight rolling lead-in (a relieved entry tooth) so the first engagement doesn't slam. Reverse the rotation and that lead-in is now on the trailing side, and the now-leading tooth has a sharp edge that hammers the output gear at engagement.
If you genuinely need bidirectional operation, both sector edges must be relieved symmetrically — and you give up some toothed-arc length to do it, which reduces θout.
The lock arc resists back-torque through pure geometric interference between the driver's circular arc and the output hub's concave relief. With a 0.05 mm radial clearance and case-hardened surfaces, you can typically resist 60–80% of the rated drive torque without measurable creep. Beyond that, the contact line plastically deforms the relief edge over a few thousand cycles and clearance grows.
If the dwelling output sees back-torque approaching the drive torque (common in spring-return applications), add a separate pawl or detent rather than relying on the lock arc alone. The arc is a holding feature, not a brake.
This almost always points to a mis-aligned input shaft. If the input shaft axis is tilted by even 0.5° relative to the design plane, one driven bevel takes the full mesh load on its tooth tips while the other rides on its tooth roots. The tip-loaded gear pits first because Hertzian contact stress at the tip is several times higher than at the pitch line.
Check the input shaft for parallelism with the mounting plane using a precision square against the shaft and the plane. If you measure more than 0.1° tilt, shim the input bearing housings to bring it back. The asymmetric wear should stop within a few hundred cycles after correction.
References & Further Reading
- Wikipedia contributors. Bevel gear. Wikipedia
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