Mechanism design · Intermittent motion

Geneva Drive

Watch a gold pin enter an open radial slot, index the output wheel and leave it at rest. Change the slot count, scrub through engagement and measure how much of each driver turn is spent 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 is in the horizontal-right, vertical-up plane, with counterclockwise positive angles and pin axes along depth. Drag the gold pin in the separate plan, or use the cycle-phase slider with a keyboard.

This is an external Geneva. Crank radius is derived from pivot spacing and slot count so that pin entry and exit have zero output speed. Phase zero is entry, not a horizontal crank. The mint shoes represent an ideal controlled dwell brake; the classic circular locking surfaces are not modeled. Without a holding constraint the disengaged wheel would be free.

At pin entry and exit the velocity is continuous, but acceleration has unequal one-sided limits. The boundary acceleration is undefined, and is left blank in CSV. The half-degree sampled curve may miss an exact boundary; the live transition buttons use analytic phases.

The applied load keeps its signed direction and can supply power during part of a cycle. Required input torque balances virtual work with massless, frictionless parts. During a Geneva dwell the ideal brake carries the applied output torque at zero output power; the input pin transfers none.

Playback performs one input revolution and stops. Replay explicitly resets the cycle. Lengths use metres; widths, thicknesses, supports and display clearance are schematic. No impacts, wear, structural safety or dynamic drive capability are inferred. CSV contains 721 half-degree phase samples and uses radians for angles and angular rates.

Ideal external Geneva kinematics with a schematic controlled brake holding the dwell. The traditional locking arcs are omitted. Prescribed input speed; no impact, inertia, friction, backlash or brake-force model.

Start with the essentials

Focus question: How can a continuously turning input produce a stationary output?
One-sentence intuition: Only the pin-engaged interval produces an index. An independent holding constraint is essential during the remaining dwell.

Core mathematical model

Tangent entry geometry

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

The pin engages while the crank angle lies between the negative and positive engagement half-angle.

Output index during engagement

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

Output angle is zero at entry and decreases by one slot pitch at exit. The wheel is held fixed during dwell.

Dwell and index

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

These fractions assume one driver pin and uniform prescribed input speed.

Quasistatic drive torque

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

During dwell the ideal holding brake balances the external output torque, with no input-pin power transfer.

Common difficulties

Prescribed motion

Typical misconceptionA smooth-looking animation proves smooth forces.

Better mental modelInput speed is imposed. Dynamic inertia, impacts, friction and flexibility are omitted. Geneva boundary acceleration is discontinuous.

Signed load

Typical misconceptionA constant external load must always resist motion.

Better mental modelA constant signed force or torque can supply or absorb power depending on output velocity.

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 make smaller steps and a smaller fraction of the driver turn is spent dwelling.
03
Check the boundary
Use Pin entry and Pin exit, then inspect the dwell brake. Export the cycle.
What to observe: Boundary acceleration is undefined; the disengaged slot residual is unavailable rather than a fictitious contact check.

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