Concealed cabinet hinge: the cup hinge hidden in furniture
Open any kitchen cabinet and look at the hinge from the inside: there's no axle. Inside the door sits a round cup, an articulated arm reaching out from the cabinet wall, and between the two a tangle of links and pins that folds in on itself as the door shuts. That hidden hinge does three things a simple pivot can't: it opens past 90° without the door's corner biting into the side of the cabinet, it stays completely invisible with the door closed, and it lets you adjust in three axes with a handful of screws. It's neither magic nor showing off: it's a four-bar linkage, and understanding the four-bar is understanding why this hinge exists and why it's one of the hardest parts you'll ever print.
Not a pivot: a four-bar with a moving center of rotation
A normal hinge turns about a fixed line. The door sweeps a perfect arc around that axis, and that arc is the problem the cup hinge solves: if the axis sits in the plane of the door, the inner corner swings into the cabinet as it opens and hits the side wall long before reaching 90°. That's why a cheap edge-mounted hinge won't open all the way, or forces you to shim the door off the side wall — and the shim gets in the way.
The concealed cup hinge changes the rule because it doesn't turn about a fixed point: it turns about an instantaneous center of rotation that moves as the door opens. That's what defines a four-bar linkage. You have four links — the fixed body anchored to the cabinet, the cup fixed to the door, and two intermediate arms joining them — connected by four pins. Because the two arms have unequal lengths and pivot at different points, the door doesn't follow a circular arc but a compound path: at the start of the travel the door moves outward, away from the side wall, before it really begins to rotate. That initial retreat opens exactly the gap the corner needs to avoid hitting, and it's what lets the door swing past 90° — typically up to 110°, and 165° or more on wide-opening models — while sitting flush with the side wall.
That center of rotation isn't a fuzzy point either: at each instant it sits where the extensions of the two intermediate arms cross, outside the body of the hinge. It coincides with no pin, but it has an exact geometric position, and that crossing point shifts as the door moves. That moving crossing point is the whole mechanism.
The over-center spring: why it stays closed on its own
Real hardware has a behavior almost nobody notices until it's missing: the door closes itself over the last stretch and stays shut with no latch. That's not friction; it's an over-center spring. The hinge integrates a spring acting on the chain of links, and the four-bar geometry has a dead point: an angle beyond which the spring's line of action crosses to the other side of a pivot. Before that point the spring pushes the door open; past it, it pushes the door closed. That's why beyond a certain angle — some 30 to 40° from closed — the door closes the rest of the way on its own and stays pressed against the cabinet.
This is the most characteristic feature and the hardest to reproduce in a printed part. A printed cup hinge with no spring opens and closes, but won't stay closed: it stalls halfway, ajar, because it's missing exactly the over-center action that drives it to the stop. If you want that behavior you have to add a real spring — steel — anchored to two points on the mechanism chosen so its line of action crosses a pivot somewhere within the travel. The bistability comes from the four-bar geometry, but the force has to come from a spring you won't be printing.
Three-axis adjustment comes from the plate, not the kinematics
It's worth clearing up a common misconception: that the door's fine adjustment is a consequence of the four-bar. It isn't. On a real kitchen hinge you turn three screws — one moves the door up and down, another in and out in depth, another left and right — and the door shifts without your having to touch anything else. But those three degrees of freedom don't live in the articulated mechanism: they live in the mounting plate and in the interface between the plate and the hinge body.
Height is set with slots or a cam on the plate screwed to the side wall; depth, with a screw that slides the body over the plate; lateral position, with an eccentric screw that moves the body relative to the plate. These are mounting degrees of freedom introduced on purpose with slots and eccentrics, entirely independent of whether the mechanism is a four-bar. You'd get exactly the same three-axis adjustment on a simple pivot hinge mounted on the same plate. If you print the hinge and want adjustment, don't look for it in the links: design it where it actually lives, in slots and eccentrics on the face that bears against the cabinet. And conversely: simplifying the four-bar removes the wide opening, but not the adjustment, because the adjustment never depended on it.
Printing it is the problem, not designing it
This is, plainly, one of the hardest joints to pull off in FDM, and the reason is purely one of manufacturing, not mechanics. A four-bar has four small pins close together, and each one is an interface that rotates. You have two paths, and neither is without cost.
If you go print-in-place — printing the mechanism already assembled, with the pins formed in situ — every pivot needs a real clearance between male and female, and the reason is direct: the slicer only generates two separate walls if the gap between them is wider than a single bead. Draw a gap narrower than the line width and the walls of the male and female print touching and weld layer to layer, and the pivot prints solid. That's why the clearance has to be equal to or greater than one bead width — on the order of 0.3–0.4 mm for a 0.4 mm nozzle — and why the effective gap in the part ends up smaller than what you drew: some of it is lost in printing. The physical detail of why this happens is in Tolerances for moving parts; here what matters is that you have to apply it four times, on tiny pins, and that a single pivot that prints fused renders the whole assembly useless. If you go separate axles — printing the links individually and assembling them with pins — you gain precision at each joint in exchange for four assembly operations on small parts and a through-hole that has to print clean and cylindrical.
Compactness brings its own trap. Because the four pins sit very close together, in print-in-place the risk isn't only that each pivot welds to itself: neighboring pivots can fuse to each other if their walls end up less than one bead width apart. The same closeness that makes the mechanism elegant also glues one joint to the next.
The cup, finally, is a hollow volume — a buried cylinder — and inside that cavity sits the geometry that holds the anchors. Orient it wrong and the interior fills with unsupported overhangs that collapse as they print, right where you need dimensional precision for the pivots to seat. Orient the cup so the cavity prints like a well — mouth up, vertical walls — and you minimize the material hanging in the air on the inside. The face that rests on the bed and the direction of the cavity decide whether the pivots print round or flattened.
Play accumulates, and the door amplifies it
The failure mode that defines this hinge is wobble from accumulated play. Each of the four pivots has its clearance — it needs it to turn — and each clearance allows a small amount of lost motion at its joint before the link actually starts to push. That lost motion chains along the kinematic chain, and it doesn't add up as lengths but as angles: a pin's diametral play translates into angular play, and that angle turns into displacement multiplied by the length of the link hanging from it. Four joints with clearance, chained and with growing lever arms, let the cup shift relative to the body before anything reaches a stop. And that shift at the root of the arm becomes several millimeters at the free edge of the door, because the door is a long lever: the play is amplified by the distance from the pivot, just as a small wobble at the wrist becomes a wide sweep at the fingertip.
That's why the generous clearance of a crude hinge won't do here. Each interface has to be controlled separately and tightened as far as the process allows without seizing, because the total error is amplified by the lever, not diluted by it. And that's why it's worth considering metal axles in the most heavily loaded pivots: a steel pin in a well-calibrated printed hole gives a joint that's more precise, more repeatable, and wears less than plastic against plastic, which abrades a little each cycle and keeps opening up the play with use. Embedding a metal axle is a technique that pays for itself in high-cycle mechanisms; how to house it — and why a printed hole receives it better than gluing one in afterward — is in Embedded hardware: magnets, bearings, and inserts.
The other two failure modes are geometric. One is breakage of a thin link: the intermediate arms of a compact four-bar are thin by necessity — they have to fit inside the cup when folded. In normal operation they work mostly in axial tension and compression, as two-force links, but it only takes a lateral load — the weight of the door twisting the plane of the mechanism — or a knock against the stop to put them into bending. Printing them with their weak interlayer grain aligned with that bending is asking for delamination. The other is the imprecise printed closure: if the four-bar geometry deforms — because a link came out warped, because a pivot ended up ovalized, because the cup shrank unevenly as it cooled — the door's path stops being the one you calculated, and the door closes misaligned or never seats flush. The kinematics is only exact if the four lengths and the four pivot centers are the ones you drew; every tenth of a millimeter the print deviates throws it off.
When it's worth printing
Print a cup hinge when you need the two things no simple pivot gives you at once: that the hinge stay invisible with the door closed and that it open wide without hitting the side of the cabinet. That's its reason for being: cabinet doors where you don't want to see hardware, where the door has to swing past 90° flush with the side wall. For a lid that only has to lift 70° and doesn't mind showing its axle, this is using a sledgehammer to crack a nut: a simple pin hinge is stronger, easier to print, and accumulates no play.
There's a second motive, perfectly legitimate: printing it as an advanced four-bar exercise. It's the place where the theory of the instantaneous center of rotation stops being a drawing and becomes a part in your hand that either opens as it should or doesn't open at all. If you get it working — the four pivots turning, the door tracing its curve, the flush closure — you've handled at once the kinematics of a planar mechanism and the manufacture of several small pivots in series, which is exactly the skill set you need for any complex printed joint.
Before you size the first pin, fix your real clearance number: this whole hinge rests on four interfaces that rotate, and each one depends entirely on the tenths of a millimeter of gap that actually remain in the part. That number comes from measuring your printer, not from a table, and how to obtain it is in Tolerances for moving parts.