Mutilated gear: missing teeth to drive only part of a turn

A normal gear drives its mate through the entire revolution. Strip the teeth from one sector of the circumference and you no longer have a continuous transmission: in exchange you gain something far more useful when what you want is motion in chunks. The gear moves the driven wheel only while the remaining teeth are in contact, and for the rest of the turn the driven wheel sits still. It is the cheapest way to manufacture intermittent motion without building a whole Geneva cross. But that simplicity hides the real problem, which is not in the teeth you add but in what happens to the driven wheel while nothing is driving it.

The kinematics: drive by sectors, not by full turn

The idea is geometrically trivial, and it is worth being clear about it before you size anything. You have a driving gear that turns continuously but keeps teeth on only an arc of its outline — say a third, or a quarter, depending on how much motion you want to deliver per turn. While that toothed sector is meshing with the driven wheel, everything works like an ordinary pair of gears: the gear ratio is the usual one, the tooth count rules, and the driven wheel advances the angle it is due. As soon as the last tooth of the sector leaves the mesh, the driven wheel stops receiving any push and, in theory, should stay exactly where it was left until the toothed sector completes its turn and takes it up again.

That is the key word: should. A gear does not impose position, it only transmits motion while there is contact. The moment the smooth sector faces the driven wheel, nothing holds it. And a free wheel, in a real mechanism, does not stay still because you want it to: the inertia left by the last tooth tends to make it overshoot, and then any vibration, the torque of a hanging load, or the rebound from the disengagement impact itself moves it without anything intervening. Inertia, far from holding it, is one of the causes of displacement during the pause. If the driven wheel shifts even by one tooth, then when the sector comes back around it will not find the gap where it left it, and that is where the trouble starts.

Re-engagement is the real problem

The whole design of a mutilated gear is decided in the instant the teeth come back into contact. For that re-engagement to be clean, two things have to be true at once: the driven wheel must be at the correct angular position (its gap right where the first incoming tooth is going to land), and the first tooth must enter without slamming flat against the tip of a driven-wheel tooth. If the driven wheel has moved during the pause, you fail the first condition: the incoming tooth strikes a crest instead of dropping into a valley, and you get a metal-on-metal collision — plastic on plastic, here — that either jams the mechanism or breaks the tooth.

It helps to separate two functions that are easily confused. One thing is to define the stop position, another is to hold it. What defines where the driven wheel ends up is the exit geometry of the last tooth: the way that flank leaves it sets the wheel at a specific angle, not one degree more or less. If the last tooth releases it two degrees out of phase, that error is already made, and no purely concentric retention system corrects it; it only freezes it. That is why the exit profile matters as much as the entry one: the stop must end up centered with respect to the first tooth that is going to return.

Holding that position is the job of a retention system that keeps the driven wheel pinned during the rest. The classic solution, and the one that prints best, is a retention arc — a "moon", a smooth concentric sector of circumference — that protrudes from the driving gear in the region where it is missing teeth. But be careful how it blocks: a perfectly circular arc seated in an equally circular concave surface prevents nothing, the driven wheel rolls inside it as in a bearing. What actually blocks is for that arc to fill a local recess between two teeth of the driven wheel — not its whole circumference — and stop it by geometric abutment. It is exactly the same principle as the locking disc of a Geneva cross: the moon of the mutilated gear is the equivalent of that locker, not a dispensable add-on. And it is synchronized with the teeth by construction: the moon releases the driven wheel just as the first tooth of the active sector is about to enter, neither before nor after.

Sizing the moon and the play without seizing

A mutilated gear has two settings that coexist, and it is worth not confusing them because they work in opposite directions. On one side there is the backlash of the toothed zone: the play between flanks that any printed gear needs in order not to seize. But watch out, because in a mutilated gear this number matters less than in an ordinary gear: there any play turns into angular error during the pause, exactly what ruins the re-engagement, so here you do not want the generous end of the range but the low one. On the other side there is the fit of the retention arc against the driven wheel, which is the opposite: there you do not want play, you want the moon to hug the recess tightly enough that it does not move even a degree during the pause.

The conflict is that this moon has to hold firmly and yet release smoothly at the moment of transition. Too much grip and the arc brakes the driven wheel just when the teeth are trying to start it, which loads the first tooth of the sector with the full torque of overcoming the moon's friction; too much play and the retention does not retain. The reasonable balance is to give the moon a light-rubbing contact — neither interference nor free play — counting on FDM narrowing that gap (the same extra material that fattens the teeth). The clearance you draw is not the one that comes off the bed. Reason out the fit per side and measure it on your printer before trusting a number, with exactly the same method as any other sliding fit; you have it in Tolerances for moving parts.

Teeth in contact: the contact ratio of the sector

Before deciding what fraction of the outline keeps teeth, make sure the active sector has enough of them to keep at least one pair of flanks engaged at all times while it is driving. It is what in any gear is called the contact ratio, and here it is not a refinement but a condition: if the sector is so short that between one tooth leaving and the next entering there is an instant with nobody engaged, the driven wheel goes free mid-drive, not only in the pause, and the advance turns jerky. Always keep a tooth entering before the previous one leaves the mesh.

And within the sector, the first and last teeth are not full teeth like the rest: they usually call for a modified or partial profile. The first because it has to gather up the driven wheel without ramming it, the last because it must release it at exactly the right position. Do not copy them straight from the rest of the outline; they are the teeth that define the mechanism's behavior at its two critical moments.

The end teeth take the impact

Within the active sector, not all teeth work the same. The middle ones enter and leave the mesh with the driven wheel already moving, in a smooth regime, as in any gear. But the first tooth of the sector is the one that breaks the inertia of the stopped driven wheel — it has to accelerate it from zero — and the last is the one that manages the separation. The first, moreover, is the one that suffers the re-engagement: if, because of play or a degree of phase error, the driven wheel was not perfectly positioned, that tooth takes the collision. It is no coincidence that, when a mutilated gear fails, it almost always breaks right there.

The defense is twofold. Geometrically, it is worth easing the entry of the first tooth: a slightly more relaxed starting flank, or a small chamfer at the tip, turns a sharp blow into a ramp that guides the driven wheel into place instead of ramming it. And structurally, those end teeth appreciate a bit more root — a generous fillet radius where the tooth springs from the wheel — because it is there, at the base, that the impact concentrates the stress. A tooth with a sharp corner at the root is a fracture line drawn in; round it as you would round the root of any arm loaded in bending.

In FDM this crosses with anisotropy. The gear is printed flat on the bed, like any gear, so the teeth end up working along the beads and not between layers: a tooth whose load pulls on the interlayer bond delaminates at the first hard impact, and the re-engagement is precisely a hard impact. Laid in the plane of the layers, the fiber of the bead runs along the tooth and absorbs the blow in the good direction. This holds for every gear, but in a mutilated gear it is critical because the end teeth take impact loading, not spread, smooth loading. One caveat if the gear face is wide: part of that impact also loads the bond between the tooth and the body in Z, so on wide gears orientation alone is not enough — it also pays not to peel that bond with thin walls. The why of the orientation is developed in Layer orientation for motion.

When it suits you and when it does not

The mutilated gear is the right tool when you want a wheel to advance only during part of the cycle and to stay stopped the rest of the time: intermittent advances, mechanisms that give a stretch of motion per turn of the driver, counters that flip a digit and wait, cams that fire an event once per revolution. Against a Geneva cross — which delivers a more controlled intermittent motion with cleaner stops — the mutilated gear wins on simplicity: it is a gear with teeth missing, it prints as one piece, and it does not need the roller or the precise slots of the Geneva. In exchange, its stop depends entirely on the retention moon — which is the same principle as the locking disc of the Geneva itself, so do not think that one saves itself the retention — and its re-engagement is harsher. If you need very repeatable, smooth stops, or high torques, the Geneva is better; if what you want is a simple, robust intermittent advance, this mechanism is enough.

It is worth keeping its three failure modes in mind, because designing is above all about avoiding them. The first is fracture of the re-engagement tooth by impact, which you attack with the eased entry, the reinforced root, and the correct layer orientation. The second is the incorrect position of the driven wheel during the pause, which you avoid by defining the last tooth's exit well and holding it with a well-fitted retention moon — neither loose, which lets it wander, nor tight, which loads the first tooth. And the third is collision or jam at re-engagement from bad timing: if the moon releases the driven wheel too late, the tooth enters against a still-blocked surface; if it releases too early, the driven wheel goes free for an instant before the tooth takes it and can shift. The synchrony between the end of the moon and the first tooth is pure geometry, and it is resolved in the model before you print anything: that is where a mutilated gear is really designed.