Designing a Geneva Drive That Prints

A Geneva drive turns a crank that never stops into a wheel that moves in steps and is locked between them. A pin on the crank enters a slot in the wheel, turns it by one slot, and leaves. For the rest of the turn a disc on the crank sits in a matching arc on the wheel and holds it still.

The name comes from its early use in mechanical watches, Geneva being a centre of watchmaking, and a four-slot wheel is also called a Maltese cross. Film projectors used it to pull each frame into the gate and hold it steady, and it still indexes tool changers, turret lathes and plotter pens.^[1]

This article works through the geometry, shows what the wheel's motion looks like, and builds a parametric model in Rig Cad that stays correct from 4 to 10 slots, passes a clearance check at every crank angle, and prints without supports.

Two numbers fix the mechanism: the slot count $n$ and the centre distance $C$ between the axles. The pin has to enter each slot moving straight along it, or it would strike the slot wall. So at the moment of entry the crank is at right angles to the slot, and the crank, the slot and the line between the axles form a right triangle with hypotenuse $C$ and angle $\pi/n$ at the wheel:^[2]

Here $a$ is the crank radius, the circle the pin runs on, and $b$ is the distance from the wheel centre to where the pin enters. The pin stays in a slot while the crank is within $\pi/2 - \pi/n$ of the line between the axles, so it drives for $180^\circ - 360^\circ/n$ of every turn, and the wheel is locked for the rest:

While the pin is engaged, the wheel angle $\beta$ follows from the crank angle $\varphi$, measured from the line between the axles, with $\lambda = \sin(\pi/n)$:^[3]

The speed ratio is zero at the moment of entry, so the pin picks the wheel up without a knock. It peaks at mid-index, where $\varphi = 0$, at $\lambda/(1-\lambda)$.

Table: What the slot count decides. None of it depends on size.

Fewer slots means a bigger step squeezed into a shorter part of the turn, so the wheel has to move faster. A four-slot wheel covers 90° in a quarter of a turn and briefly runs at 2.4 times crank speed.

The model takes four mechanism inputs, the slot count $n$, the centre distance $C$, the pin diameter $p$ and the print clearance $t$, and derives every other dimension from them. With the defaults, $n = 4$, $C = 50$ mm, $p = 6$ mm and $t = 0.4$ mm:

Table: Derived dimensions at the default settings.

The wheel radius is a little more than $b$, so the slot walls reach out to where the pin enters. The stop arc and the locking disc use the standard proportions:^[4] the disc sits one clearance inside the arc, and that is what holds the wheel during the dwell. The slot runs slightly deeper than the pin reaches, so the pin never bottoms out.

Validators block combinations that cannot work: a pin too thick to leave room for a locking disc, or a centre distance too short to fit the wheel's pedestal and the knob. At the default 50 mm centre distance that allows 4 to 8 slots; 9 and 10 need a larger one.

Each part is one branch of the scene tree, and every dimension in it is an expression of the four inputs.

Diagram: the four inputs feed the derived geometry, which shapes the base, the driver and the wheel. The crank angle turns the driver directly, and the wheel through its solved angle.

flowchart TD
  V["slotCount, centerDistance, pinDia, clearance"] --> G["Derived geometry"]
  G --> B["Base: plate and two axles"]
  G --> D["Driver: crank disc, pin, locking disc, knob"]
  G --> W["Wheel: disc minus slots and stop arcs"]
  A["crankAngle"] --> D
  A --> R["Solved wheel angle"]
  R --> W

• The wheel is one 2D profile, extruded once. It is a disc minus a Radial Repeat of one slot and one stop arc. The repeat count is the slot count, so changing it rebuilds the wheel.
• Offsets round the tips. Sharp slot mouths and wheel tips print as thin, fragile points. Offsetting the profile in by 0.6 mm and back out by 0.6 mm rounds every convex corner and leaves the rest of the outline where it was.
• The wheel angle is solved, not animated. The driver's rotation is the crank angle plus 180°, which puts the pin on the far side at 0°. While the pin is engaged, the wheel angle comes from the $\tan\beta$ formula above. Outside that window it holds at $\pm 180^\circ/n$, where the locking disc keeps it.
• A handle on the pin. An angular control point sits over the drive pin, so you can drag the crank round in the viewport as well as use the slider.
• Readouts give the wheel step, dwell share, peak speed ratio, wheel diameter and base length for the current settings. Expressions and Variables in Rig Cad covers readouts, validators and handles.

A mechanism that looks right in one pose can still bind in another. Each modelling stage went in with verification requirements that have to keep holding: no overlap between the parts, each part a single watertight solid, and overall sizes tied to their formulas. Then the crank was swept through a full turn, with an interference and clearance check at each step.

Table: Smallest gap between the moving parts at the default settings.

The same sweep, repeated for 4 to 10 slots and at the ends of the size and clearance ranges, found no overlap anywhere. The gaps are what the formulas promise: half the clearance on each side of the pin, and the full clearance at the lock.

All three parts print as modelled at 0.2 mm layers with no supports: the base flat, the driver crank disc down, the wheel flat. At the default size that is about 54 g of filament and five and a half hours (base 26.4 g, driver 19.9 g, wheel 8.0 g). The only bridge is the roof of the driver's blind axle bore, about 8 mm across. The base plate is chamfered on its top edge only, so nothing on any part overhangs.

The default 0.4 mm clearance leaves 0.2 mm on each side of the pin. If your printer makes holes tight, raise it; Clearances for 3D-Printed Parts That Have to Move has a coupon that finds the right value for your machine. The axles and the drive pin print upright, with layer lines across them. That is fine here: they are short, thick pegs under light load, and nothing in the drive flexes.

Nothing needs glue. Gravity holds the driver and the wheel on their axles, and the knob on the driver is for turning it by hand.

Try six slots in the model above: the peak speed drops to crank speed, and the wheel spends a third of each turn moving instead of a quarter. Then try eight: the crank shrinks and the wheel grows, because the pin circle is $C\sin(\pi/n)$.

The techniques behind the model each have their own article: Repeats and Arrays for the repeat that cuts every slot from one, Sketches to Solids for the 2D profile and the offsets that round it, Expressions and Variables in Rig Cad for the readouts, validators and drag handle, and Clearances for 3D-Printed Parts That Have to Move for the gap every moving part here depends on.

The slot count fixes a Geneva drive's motion. For motion you design yourself, see Designing a Cam and Follower That Prints: a grooved cam drives a sliding follower through a rise, dwell and return you set, built and printed the same way as this drive.