Mechanism design · Intermittent motion

Geneva Drive

How can a turning input make the output wait? The drive pin engages the wheel for only part of each turn. While the pin is in a slot, it turns the wheel by one slot spacing; once it leaves, nothing drives the wheel, and a separate lock holds it still until the pin comes round again. With four slots, the wheel rests for three quarters of every input turn. More slots give smaller steps and a shorter rest.

Watch a gold pin slide into a radial slot, turn the output wheel by one step and leave it at rest. Change the number of slots, scrub through the engagement and measure how much of each driver turn the wheel spends waiting.

Output angle $0$

Output velocity $0$

Output acceleration $0$

Dwell fraction $0$

Required input torque $0$

Signed load power $0$

Engaged slot residual $0$

Quasistatic power residual $0$

Turn & inspect

Follow the gold drive pin.

Cycle phase

psi

45.00\,{}^circ

Prescribed input speed

omega

60.00\,{}^circ/mathrm s

Radial slot count

n

4.00\,

Pivot spacing

d

1.60\,mathrm m

Signed external output torque

au_o

-1.00\,mathrm{N,m}

Blue is the input crank, gold the drive pin and coral the output. Motion happens in a plane with right and up positive; angles are positive counterclockwise, and the pin axes point along the depth. Drag the gold pin in the separate plan view, or use the cycle-phase slider with the keyboard.

This is an external Geneva drive. The crank radius follows from the pivot spacing and the number of slots, chosen so that the output speed is zero as the pin enters and leaves a slot. Phase zero is the moment of entry, not a horizontal crank. The mint shoes stand for an ideal brake that holds the wheel during the dwell; the classic circular locking surfaces are not modeled. With nothing holding it, the disengaged wheel would turn freely.

As the pin enters and leaves, the velocity is continuous, but the acceleration approaches different values from the two sides. The acceleration at the boundary is undefined and is left blank in the CSV. A curve sampled every half degree may miss the exact boundary; the transition buttons use the analytic phases.

The applied load keeps a fixed signed direction, and for part of each cycle it can supply power. With massless, frictionless parts, the required input torque comes from balancing virtual work. During a Geneva dwell the ideal brake carries the output torque at zero output power, and the input pin transfers no load.

Playback turns the input once and stops; replaying resets the cycle. Lengths are in metres, while widths, thicknesses, supports and the gaps on screen are schematic. Nothing here predicts impacts, wear, structural safety or dynamic drive capability. The CSV holds 721 phase samples, one every half degree, with angles and angular rates in radians.

The motion is that of an ideal external Geneva drive. A schematic, controlled brake holds the wheel during the dwell, and the traditional locking arcs are left out. The input speed is set; impact, inertia, friction, backlash and brake force are not modeled.

Start with the essentials

Focus question: How can a continuously turning input produce a stationary output?
One-sentence intuition: The wheel turns only while the pin is in a slot; for the rest of the turn, something else must hold it still.

Core mathematical model

Geometry of a tangential pin entry

\alpha=\frac{\pi}{n},\qquad r=d\sin\alpha,\qquad\beta=\frac{\pi}{2}-\alpha

The pin is in the slot while the crank angle lies between minus and plus the engagement half-angle.

Output angle while the pin is engaged

\phi=-\alpha-\operatorname{atan2}(r\sin\theta,d-r\cos\theta)

The output angle is zero at entry and has dropped by one slot pitch at exit. During the dwell the wheel is held still.

Step size and dwell fraction

\Delta\phi=-\frac{2\pi}{n},\qquad f_{\rm dwell}=\frac12+\frac1n

These values assume a single driver pin and a constant input speed.

Drive torque with no inertia

\tau_{\rm in}=-\tau_o\frac{\mathrm d\phi}{\mathrm d\theta}

During the dwell the ideal holding brake balances the external output torque, and the input pin transfers no power.

Common difficulties

Smooth motion does not mean smooth forces

Typical misconceptionIf the animation looks smooth, the forces must be smooth too.

Better mental modelThe input speed is imposed, and inertia, impacts, friction and flexibility are left out. The Geneva wheel's acceleration jumps at pin entry and exit.

A constant load can help or resist

Typical misconceptionA constant external load always resists the motion.

Better mental modelA constant force or torque feeds power in when it points along the output velocity and takes power out when it points against it.

Run the experiment

01
Follow the pin
Play one turn, then scrub the cycle or drag the gold pin in the plan.
What to observe: The input pin, output and graph cursors move together.
02
Change the slot count
Compare four, six and eight slots at the same input speed.
What to observe: More slots give smaller steps, and the wheel spends a smaller fraction of each driver turn at rest.
03
Look at the edge cases
Load Pin entry and then Pin exit, look at the dwell brake, and export the cycle.
What to observe: At entry and exit the acceleration is undefined. Once the pin has left the slot there is no contact to check, so the slot residual shows no value.

Theory & apparatus: Carnegie Mellon · Geneva Wheel · Purdue · Scotch Yoke