Internal ring gear: teeth facing inward

Flip a spur gear inside out—point the teeth inward instead of outward—and you have a ring gear: a toothed ring whose inner face meshes with a pinion seated inside it. It looks like a geometric detail, but it changes the kinematics at the root and lets you fit a whole reduction into the space a single gear used to occupy. It's the part that closes the planetary train, and the one that delivers large ratios in very little space. And like almost everything in FDM, its problem isn't the tooth profile but whether the ring around it carries the load without springing open.

Why the pinion and the ring turn the same way

When two external gears mesh, their teeth push against each other along the line of contact and the shafts turn in opposite directions: one turning clockwise drags the other counterclockwise. That's the default mental image of any mesh, and with a ring gear it no longer holds. Here the ring's teeth point toward the center, toward the pinion, so contact happens on the inner side of the ring. The result is that the ring and the pinion turn in the same direction: if the pinion is mounted on a fixed axle inside a fixed-axle ring, both rotate the same way about their respective centers.

That matching direction is exactly the reason to choose a ring gear over a single-stage pair of external gears. Two external gears reverse the direction once: if the input turns clockwise, the output turns counterclockwise. To bring the output back to the input's direction you'd have to insert a third, idler gear, which takes up space and adds play to the train. Internal meshing gives you that same co-rotation with a single pair of wheels, no intermediate gear, purely from geometry.

Don't confuse this case—a fixed-axle pinion inside a fixed-axle ring—with the planet that orbits around the inside of a ring, which is the planetary case and has different direction and speed relationships. In the fixed-axle pair, all that matters is that internal contact does not reverse the rotation.

What doesn't change is the meshing condition. The ring and the pinion have to share module and pressure angle, exactly as two external gears do. The module sets the tooth size and pitch; the pressure angle sets the flank slope that transmits the force. If they don't match, the teeth don't fit and contact degenerates into pounding and wear. The only difference is the direction the tooth faces, not the rules that define it.

The ring gear closes the planetary set

The ring gear becomes indispensable in the planetary gear set. There you have a central pinion—the sun—several planet gears that roll around it mounted on a carrier, and the ring that wraps the assembly from the outside. Each planet is an external gear, with all its teeth pointing outward, and it meshes at the same time in two places: on one side against the sun and on the diametrically opposite side against the ring's internal teeth. The two contact zones end up nearly 180° apart around the planet's perimeter. The ring is what closes the force loop; without it, the planets would have nothing to push against and the train would transmit nothing.

That architecture is what gives the planetary its two advantages: high reduction ratios in a small diameter, and torque split across several contacts instead of one. But the planetary doesn't close with just any tooth counts. The coaxiality condition forces the three elements to share an axis, and that fixes the relationship:

Without the first, the planetary simply doesn't fit: the ring's diameter doesn't square with that of the sun and the planets. Without the second, you can't space three or four planets at equal intervals around the sun, and you'll assemble with positional stresses from the very first turn.

Even outside the planetary, it's worth remembering that a ring against a simple pinion gives you a large reduction ratio in a space that a parallel-shaft train couldn't match.

Print it flat and reinforce the ring

In FDM the golden rule for the ring gear is to print it flat on the bed, with the axis vertical. That way each internal tooth is built layer by layer with the same profile top to bottom, with no overhangs to degrade the flank. If you print it lying down, with the axis horizontal, the problem concentrates in the upper arc of the ring, where the teeth become overhangs facing downward and come out with supports or a deformed flank; the lower arc and the equatorial zone suffer less, but one badly formed sector is enough to make contact irregular and introduce play you can't control. Flat, the tooth profile comes out consistent and repeatable, which is exactly what a mesh needs. It's the same orientation logic that governs any printed moving part, developed in Layer orientation for motion.

That orientation has a ceiling. With the axis vertical, the tooth flank is defined by the XY resolution and the extrusion width, so very small modules—below ~1 mm on a typical FDM machine—lose flank definition even printed flat: the vertices round over and the involute blurs at the tips. That's the real miniaturization limit of a ring gear, not the overhang.

The second rule is the outer ring. The mesh transmits mostly tangential force—the one that delivers the torque—and a smaller radial component, F_r = F_t·tan(α), that pushes from the center toward the ring. Both load the ring: the radial one tends to bow it outward and the tangential one tensions it in a circle. If the ring is thin, it flexes, deforming from round to slightly oval under load: it pulls the teeth away from the pinion in some zones and presses them tighter in others, opening the mesh. The result is a train that runs fine with no load and jams or skips teeth the moment you ask it for torque. As a starting rule, give the ring a wall thickness of at least 1.5 to 2 times the tooth height, built as continuous perimeters all the way around the contour, because it's the perimeter—the bead that closes the entire circle—that truly resists the ring springing open, not the loose infill inside. In a planetary this matters even more, because several planets push the ring outward at once.

Those perimeters only work if they're continuous and concentric, and the slicer often breaks them with the seam: the point where each loop starts and closes cold leaves a weak joint. If the seam always falls at the same point on the ring, that's where the ring will fail. Move the seam or scatter it so the joint line doesn't stack up on a single meridian.

Backlash and concentricity: no room to improvise

As in any printed mesh, the teeth of the ring gear and those of the pinion need backlash—the play between flanks: a clearance that lets the incoming tooth fit into the gap without seizing against the wall of the opposite gap. Zero backlash in the model is interference in the part, because the printer widens the flanks and narrows the gaps; the mesh binds. That gap is designed on purpose, starting from the real clearance your machine gives you—the method for measuring it is in Tolerances for moving parts—and not from the theoretical nominal of a pair of machined gears. The backlash you need scales with the module and with the printer's scatter.

Internal meshing also tolerates tight backlash worse than external meshing does. The flanks of the ring and the pinion are conformal—concave against convex, with similar radii of curvature—so they trap each other more easily when the play is insufficient. Where an external pair would still slide, the ring gear already seizes. Lean toward leaving a bit more backlash than you would on an external gear of the same module.

The ring gear adds a variable that a spur gear doesn't have so prominently: the ring's stiffness enters the clearance equation. With two external gears, the backlash you left is essentially the backlash you have. With a ring gear, a ring that yields under load changes the effective mesh in service: what was correct backlash unloaded can turn into seizing or excessive play depending on which way the force deforms the ring. That's why a thin ring and tight backlash is a treacherous combination: they look like two independent decisions and they're actually coupled.

The other half is concentricity. The pinion has to turn centered with respect to the ring; if its axle ends up off-center, the mesh tightens on one side and loosens on the opposite one, and you go through the whole turn alternating between seizing and play. Make sure the pinion's axle housing is well centered with respect to the ring gear's circle, because an offset that on an external gear would only produce a tight spot shows up across a whole sector of the turn on a ring gear.

How a printed ring gear fails

A printed ring gear fails in a few specific ways, and recognizing them in advance is half the battle.

The first, and the most characteristic of this part, is deformation of the outer ring when it's thin: the ring springs open under the mesh load, ovals, and skews the contact, with the already-described consequence of skipping and seizing under torque. It's the failure that sets the ring gear apart from a spur gear, and it's almost always fixed with more wall and more perimeters.

The second is breakage of an internal tooth, usually at its root, when the torque concentrates too much force in a single contact. It's typical if only one tooth meshes at a time for lack of contact ratio, or if the ring flexed and dumped all the load on one point. Contact ratio—how many teeth are in contact at once—works in the ring gear's favor here: internal meshing has a higher contact ratio than the equivalent external one, splits the torque across more teeth, and lowers the load per contact. You lose that advantage the moment the ring flexes and shifts all the force onto a single tooth.

The third is seizing, which comes not from the tooth but from its surroundings: insufficient backlash, poor concentricity between pinion and ring, or the deformed ring narrowing the mesh.

The fourth is specific to internal meshing and isn't shared with external gears: trimming interference between the tips of the teeth. When the ring and the pinion have tooth counts that are too close—differences smaller than about 8 to 10 teeth, depending on the pressure angle—the tooth tips get in each other's way during meshing: the pair won't assemble or it scrapes, regardless of backlash, wall, or concentricity. It's a design failure, not a manufacturing one. The ring gear needs quite a few more teeth than the pinion; if you want an aggressive reduction, get it from the module and the diameter, not by bringing the tooth counts closer together.

Almost every problem with a ring gear reduces to one of these four failures, and almost all of them are prevented with the same discipline: print it flat, reinforce the ring, give it its measured backlash, center the pinion well, and leave enough tooth-count difference.

If you're going to mount this ring gear inside a planetary train, the next step is to orient and size the planets and the sun that mesh against it. There, the same tolerance discipline from Tolerances for moving parts decides whether the assembly runs cleanly or binds.