An external/internal mutilated gear reverse is a single-input gear arrangement that flips output rotation direction by alternating engagement between an external sector and an internal ring sector cut on the same driver wheel. It solves the problem of producing automatic forward-then-reverse motion from a continuously rotating shaft without a clutch, brake, or electrical control. The driver's toothed sectors mesh in turn with the output pinion — external teeth drive it one way, internal teeth drive it the other. The result is a self-cycling reversing drive used on cable reels, traversing winders, and small reciprocating feed tables.
External/internal Mutilated Gear Reverse Interactive Calculator
Vary the sector arc, gear radii, and master speed to see output stroke rotation, dwell time, and mesh speed for the reversing gear.
Equation Used
The calculator converts the toothed-sector angle from degrees to radians, then multiplies by the pitch-radius ratio. The result is the output pinion rotation during one external or internal toothed engagement. With equal forward and reverse sectors, each locking dwell arc is 180 deg minus the sector angle.
- External and internal toothed sectors use the same arc angle.
- Two equal locking dwell arcs complete each master revolution.
- Pitch rolling is ideal with no slip or backlash allowance.
- Sector angle is entered in degrees and converted to radians.
The External/internal Mutilated Gear Reverse in Action
The trick of this mechanism lives on one master wheel. Cut external teeth across one arc, cut internal teeth across another arc on the same disc, and leave smooth (mutilated) sectors between them. The output pinion sits at a fixed centre distance and engages the external arc when that arc rotates past it — the pinion turns one way. As the wheel keeps rotating, the toothless sector passes the pinion, holding it stationary on a locking radius, and then the internal-tooth arc sweeps in. Internal mesh reverses the relative rolling direction, so the pinion now rotates the opposite way. One full turn of the master gives one forward stroke, one dwell, one reverse stroke, one dwell. No clutch. No solenoid.
Geometry decides whether this works or rattles itself apart. The pitch circles of the external sector and the internal sector must be concentric to the master's axis within roughly 0.05 mm on a 100 mm wheel — drift beyond that and the pinion either jams at handover or skips a tooth. The transition from toothed to mutilated arc has to carry a locking radius — a smooth arc that matches the pinion's addendum circle and holds it still during the dwell. If you skip the locking radius the pinion will free-wheel under load and arrive at the next mesh out of phase, which sounds like a rifle shot and shears teeth.
The common failure modes you'll see in real builds are tooth-tip clipping at the entry to each sector (caused by lead-in chamfers being too short, under 0.3 × module is the usual culprit), pinion lift during the internal-mesh phase if the support bearing has more than about 0.02 mm radial play, and progressive wear on the locking radius if dwell-phase load isn't held by an external detent. Get the entry chamfers right, take play out of the pinion bearing, and add a spring-loaded detent on the output if your load can backdrive — and the mechanism runs for tens of millions of cycles.
Key Components
- Master wheel (mutilated driver): A single disc carrying both an external-tooth sector and an internal-tooth sector with smooth locking arcs between them. Concentricity of the two pitch circles must hold to ≈0.05 mm on a 100 mm OD wheel, otherwise the output pinion binds at sector handover.
- Output pinion: A standard spur pinion sized to mesh with both sectors at the same centre distance. Module and pressure angle must match both arcs exactly — typically module 1 to module 2.5 in light-duty builds, with 20° pressure angle the safe default.
- Locking arc / dwell radius: The smooth toothless sector machined to the pinion's addendum circle. It carries the pinion through the dead zone between meshes and prevents free-wheeling. Surface finish ≤Ra 1.6 µm keeps wear low across millions of cycles.
- Lead-in chamfer: A short relief at the first tooth of each sector, typically 0.3-0.5 × module deep. Without it the pinion tip clips the leading tooth flank during handover, producing the characteristic ticking sound and accelerated wear.
- Output detent or anti-backdrive spring: A spring-loaded plunger or wrap spring on the output shaft holding it against the locking radius during dwell. Required whenever the output load can backdrive — for example a tensioned cable reel or a return-spring-loaded slide.
- Pinion support bearing: A bushing or ball bearing carrying the pinion at fixed centre distance from the master. Radial play above ≈0.02 mm lets the pinion lift during internal-tooth engagement and skip teeth, so we usually run a preloaded angular-contact pair on production builds.
Who Uses the External/internal Mutilated Gear Reverse
You see this mechanism wherever a single continuously rotating input has to produce automatic reciprocation without electrical control — cable winders, dispensing reels, small print-feed tables, and old-school textile traverse drives. The reason it survives in those niches is honesty: one moving part on the input side, no clutch wear, no solenoid coil to burn out, no controller to crash. If your duty cycle is fixed and you don't need adjustable stroke, this beats a servo every time on cost and reliability.
- Textile machinery: Yarn traverse drives on Leesona-style cone winders where the guide must stroke back and forth across a 150 mm package face at 200-300 strokes per minute, driven from the spindle takeoff through a mutilated reverse.
- Cable and hose reels: Level-wind drives on Hannay Reels electric cable reels — the level-wind carriage must reverse at each flange, and a mutilated gear reverse off the reel-shaft chain drive does this without any external sensors.
- Vending and dispensing: Coil-feed drives in older Crane National snack vendors where a partial-rotation reverse retracts the helix briefly to release jammed product, triggered by the same input cam that drives the dispense rotation.
- Toy and educational mechanisms: Reciprocating-action wind-up tin toys built by Schuco and later Tomy, where a single mainspring-driven gear train produces forward-walk then reverse-shimmy via a mutilated reverse stage.
- Process equipment: Reagent dosing pumps on legacy Prominent metering units that use a mechanical reverse to alternate between fill and discharge strokes from a constant-speed motor input.
- Print and paper feed: Sheet-return mechanisms on small Heidelberg windmill platen presses, where a dwell-and-reverse gear stage retracts the gripper bar between impressions.
The Formula Behind the External/internal Mutilated Gear Reverse
What matters most to a designer here is how long the output pinion spends in each phase per master revolution — forward mesh, dwell, reverse mesh, dwell. That phase split sets the stroke length, the dwell time available for any auxiliary action (clamp, eject, sense), and the peak angular velocity the pinion has to handle. At the low end of the typical operating range, with each toothed sector spanning around 90° of master arc, you get balanced symmetric strokes with long dwells — comfortable for heavy loads but slow. Push the toothed sectors out toward 150° each and the dwell collapses to 30° — fast cycling but almost no rest period for the output to settle. The sweet spot for most reel and traverse drives sits at 120° toothed / 60° dwell on each side. The formula below gives output pinion rotation per master revolution as a function of the toothed-sector angle.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| θout | Output pinion rotation during one toothed-sector engagement | rad | rad |
| αsector | Master-wheel arc angle covered by one toothed sector (external or internal) | rad | rad |
| Rmaster | Pitch radius of the master sector (external or internal arc) | mm | in |
| Rpinion | Pitch radius of the output pinion | mm | in |
| nm | Master wheel input speed | rev/min | rev/min |
Worked Example: External/internal Mutilated Gear Reverse in a Hannay-style level-wind cable reel
Suppose you are sizing the level-wind reverse on a Hannay-style 600 mm flange diameter electric cable reel feeding 12 mm welding cable across a 250 mm package width. The master wheel is driven off the reel shaft at 40 RPM nominal, with operating range 20-80 RPM. Master pitch radius is 90 mm on the external sector, 90 mm on the internal sector, both arcs spanning 120° of the master. The output pinion that drives the level-wind leadscrew has pitch radius 18 mm. You need to know how much leadscrew rotation you get per stroke and whether the geometry holds across the speed range.
Given
- αsector = 120 ° (= 2.094 rad)
- Rmaster = 90 mm
- Rpinion = 18 mm
- nm = 40 RPM nominal (range 20-80)
Solution
Step 1 — convert the sector arc to radians and compute output pinion rotation per stroke at nominal speed:
So each forward (or reverse) stroke spins the leadscrew 1.67 turns. With a 5 mm pitch leadscrew that gives a stroke of 8.35 mm of carriage travel per master half-cycle — enough to advance the cable lay one cable diameter (12 mm wraps with a small overlap is what we want, so we'd actually open the sector to 130° in production, but 120° is fine for a first cut).
Step 2 — at the low end of the operating range, 20 RPM master speed, compute the pinion peak speed during mesh:
At 20 RPM master the level-wind carriage tracks slowly and gently — the cable lays cleanly into the package with no overshoot. This is the safe operating point for setup and for thick stiff cable.
Step 3 — at nominal 40 RPM master:
This is the design sweet spot — leadscrew runs at a comfortable 200 RPM during each stroke phase, dwells reset cleanly, and the carriage reverses without slamming. You can hear the handover as a soft click, not a crack.
Step 4 — at the high end, 80 RPM master:
In theory fine, in practice the dwell collapses to about 0.125 s per side at 80 RPM, which is below the time the leadscrew/carriage assembly needs to settle if the carriage carries any meaningful inertia. Above roughly 60 RPM you'll see the carriage overshoot at each reverse, the cable will start crossing previous wraps, and the pinion lead-in chamfers will take a beating because they're now absorbing the inertia of a still-moving output pinion at every handover.
Result
Each stroke produces 1. 67 leadscrew revolutions, giving 8.35 mm of carriage travel per stroke at the assumed 5 mm leadscrew pitch — roughly two-thirds of a cable diameter, so you'd widen the sector to 130° in production for clean lay. At 20 RPM master the system creeps and lays cable perfectly; at 40 RPM nominal it's at the sweet spot with clean reversals; push to 80 RPM and you're fighting carriage inertia at every handover, with overshoot and lead-in tooth wear setting in above about 60 RPM. If your measured leadscrew rotation per stroke comes out 10-15% short of 1.67 rev, the usual causes are: (1) pinion tip-clipping the first sector tooth because the lead-in chamfer is under 0.3 × module, robbing you of the first half-tooth of engagement, (2) the master wheel's two pitch circles being non-concentric beyond 0.05 mm, which forces a backlash gap at one handover, or (3) the dwell-radius surface worn below the addendum-matching profile so the pinion creeps backward during dwell and starts the next stroke out of position.
External/internal Mutilated Gear Reverse vs Alternatives
Three mechanisms compete for the same job — automatic reversing drive from a continuous input. Mutilated gear reverse, planetary-with-clutch reversing, and electronic servo reversing. Each wins on a different axis. Pick the one that matches your duty cycle, your stroke-adjustability needs, and your control-system budget.
| Property | External/Internal Mutilated Gear Reverse | Planetary Reversing Gearbox with Clutch | Servo Motor with Electronic Reversing |
|---|---|---|---|
| Typical input speed range | 20-300 RPM master | 0-3000 RPM input | 0-6000 RPM motor |
| Stroke adjustability | Fixed by sector geometry — must re-machine to change | Adjustable via clutch timing | Fully adjustable in software |
| Cycle accuracy / repeatability | ±0.1° at output, mechanically locked | ±2-5° depending on clutch wear | ±0.01° with encoder feedback |
| Cost (small production volume) | Low — two machined parts plus pinion | Medium — clutch pack adds 5-10× cost | High — drive, motor, controller, cabling |
| Maintenance interval | 10+ million cycles before measurable wear | Clutch faces typically 1-3 million cycles | Motor brushes 5,000 hr, electronics minimal |
| Load capacity (rated torque at output) | High — full tooth engagement during mesh | Medium — clutch slip-limited | Sized to motor; can be very high |
| Application fit | Fixed-stroke reciprocation, reels, traverse | Variable-timing reversing in vehicle drives | Adjustable-stroke production machinery |
| Mechanical complexity (part count) | 3 parts (master, pinion, detent) | 15-30 parts (clutch pack + planetary) | Mechanically simple, electrically complex |
Frequently Asked Questions About External/internal Mutilated Gear Reverse
That crack is almost always the pinion arriving at the next sector slightly out of phase, so the first tooth-pair makes contact tip-to-tip instead of flank-to-flank. Two causes dominate: the dwell radius is undersized by 0.05 mm or so, letting the pinion drift backward during dwell, or the toothed-sector entry is missing its lead-in chamfer.
Quick check — rotate the master by hand and watch the pinion through the dwell zone. If it rocks at all, your locking radius is undersized or the pinion bearing has play. Add a light wrap-spring detent on the output shaft and the noise usually disappears immediately.
Yes, and this is one of the genuinely useful design freedoms here. Make the external-sector arc 150° and the internal-sector arc 90° and your output gets a long forward stroke and a short fast reverse — useful for things like return-quick feed tables or dispensing where the working stroke is slow and the reset can snap back.
The constraint is that the two toothed arcs plus the two dwell arcs must still sum to 360°, and the dwell arcs each need at least 20-30° to give the pinion time to seat against the locking radius. Asymmetric sectors also create asymmetric output speeds — the short sector spins the pinion faster, so check that the leadscrew or output shaft inertia can handle the higher peak RPM.
Geneva drives give intermittent forward-only motion. To get reverse out of a Geneva you need a second Geneva or a directional cam stack, which doubles the part count and centre-distance footprint. Mutilated gear reverse delivers reverse natively from one master wheel.
For a reel winder where you need symmetric stroke timing, mutilated gear wins on cost and packaging. For applications where you need precise dwell-stroke-dwell-stroke timing with adjustable indexing — for example a rotary table indexer — Geneva is the right tool. Don't confuse intermittent indexing (Geneva's job) with reciprocating reverse (mutilated gear's job).
Internal mesh reverses the contact-force direction on the pinion bearing. On external mesh the separating force pushes the pinion away from the master; on internal mesh it pulls the pinion toward the master centre. If your pinion bearing is a plain bushing with one-sided wear, that wear pattern only supports one direction of load.
Measure the pinion bearing radial play with a dial indicator. If it's above 0.02 mm in the direction of internal-mesh thrust, replace the bushing or switch to a preloaded ball-bearing pair. The skipping will stop. This is the single most common build failure on shop-built mutilated reverse drives.
The locking radius sees sliding contact from the pinion addendum during every dwell, so its surface finish drives long-term wear directly. For up to 1 million cycles, Ra 1.6 µm ground is fine. For 10 million cycles plus — typical of textile traverse drives running 24/7 — you want Ra 0.4 µm and case-hardened to HRC 55 or above.
Rule of thumb: if you can feel any ridge with a fingernail at the toothed-to-mutilated transition, the entry geometry is too sharp and will wear the pinion tip prematurely regardless of the radius finish. Blend that transition with a 0.3-0.5 × module radius.
This is run-in of the lead-in chamfers. Fresh chamfers cut at exactly 0.3 × module deep are slightly proud of the ideal handover profile, and the first few thousand engagements polish them to the natural contact line. Stroke length will shorten by 1-3% during this period and then stabilise.
If the drift continues past about 5,000 cycles, the cause is no longer run-in — check pinion bearing play, master-wheel concentricity, and whether your dwell detent (if fitted) is holding the output without backdrive. Continued drift past run-in always means a real geometric problem, not wear-in.
You can, but you lose the main advantage of the mechanism. The whole point of mutilated gear reverse is converting continuous rotation into automatic reciprocation with no control system. If you've already got a stepper and driver in the build, you can produce reverse motion directly by reversing step direction in software.
The legitimate case for stepper-driven mutilated reverse is when you want a fixed mechanical reciprocation timing that survives controller failure — the mechanism keeps cycling correctly even if the stepper just runs free. That's a real reliability argument in safety-related auxiliary drives, but it's a niche.
References & Further Reading
- Wikipedia contributors. Gear. Wikipedia
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