Haven's Planetary Crank Gear is a 2:1 epicyclic mechanism in which a planet gear rolls inside a fixed internal ring gear of twice the diameter, so a pin set in the planet's pitch circle traces a straight line across the ring's diameter. Railway signalling and slow-acting pump-drive trades relied on it to turn continuous rotation into a long, smooth reciprocating stroke. The pin's straight-line travel drives a connecting rod with no Scotch yoke or crosshead. The result is a compact rotary-to-linear converter delivering strokes of 100–600 mm with very low side load.
Haven's Planetary Crank Gear Interactive Calculator
Vary ring size, tooth ratio error, and pin offset to see stroke length and straight-line error for the Haven hypocycloid drive.
Equation Used
The Haven gear is the 2:1 hypocycloid case: a planet with half the ring tooth count rolls inside the fixed ring, and a pin on the planet pitch circle traces a straight diameter. This calculator lets small ratio and pin-radius errors bow that line so the resulting side error can be seen.
FIRGELLI Automations - Interactive Mechanism Calculators.
- Internal ring and planet use the same gear module.
- The exact Haven case is planet teeth equal to N/2.
- Ratio error changes the effective planet pitch radius.
- Stroke and lateral deviation are sampled over one carrier revolution.
How the Haven's Planetary Crank Gear Actually Works
The mechanism is a special case of hypocycloidal straight line motion. You fix an internal ring gear with N teeth, and you mesh a planet gear with exactly N/2 teeth inside it. Drive the planet carrier with a crank, and any point on the planet's pitch circle traces a perfect straight line that is a diameter of the ring. Drop a pin on that pitch circle, attach a connecting rod, and you have rotary input to pure linear output — no slot, no slider, no crosshead. That is the trick Haven patented for slow signal-wire pulls and water-lift pumps in the late 19th century.
Why build it this way instead of a Scotch yoke or a slider-crank? Because the planet pin does not slide against anything. All the relative motion happens at gear teeth and bearings, which means the wear surfaces are rolling, not sliding. On a Scotch yoke the slot wears oval after a few thousand cycles under any real side load. On Haven's gear, the same duty just polishes the tooth flanks. For low-speed, high-cycle service — 20 to 60 strokes per minute pumping water out of a brick cistern — that matters.
Tolerances rule the build. The planet pitch diameter must be exactly half the ring pitch diameter. If the ratio drifts by even 0.5%, the pin trace opens into a narrow ellipse instead of a straight line, and the connecting rod sees a transverse oscillation that hammers the small-end bearing. Backlash above roughly 0.15 mm at the gear mesh shows up as a tick at each stroke reversal — you hear it before you see it. Pin location error on the planet (radial position off the pitch circle by more than ~0.2 mm on a 200 mm ring) bows the trace into a figure-of-eight near the dead centres. Get the centres and the gear ratio right, and the mechanism runs for decades. Get them wrong, and the connecting rod's small end is scrap inside a season.
Key Components
- Fixed internal ring gear: The stationary outer gear with internal teeth, pitch diameter D. It defines the straight-line path of the pin — the trace lies along a diameter of this ring. Tooth quality grade ISO 8 or better is needed; coarser grades let backlash open up and the line becomes an ellipse.
- Planet gear (half-diameter): The internal gear meshes with this planet, whose pitch diameter is exactly D/2. Tooth count must be exactly half the ring's; a 60-tooth ring takes a 30-tooth planet, never 29 or 31, because the 2:1 ratio is what generates the straight line.
- Crank carrier (input shaft): Drives the planet's centre around the ring centre at radius D/4. This is what you connect the prime mover to — typically a slow gearmotor at 30–80 RPM for pump duty, or a hand-cranked input on heritage signal frames.
- Trace pin: Set into the planet face exactly on its pitch circle (radius D/4 from the planet centre). This pin is the output point — it traces the straight line. Radial location tolerance ±0.05 mm on a 200 mm ring; any further out or in and the trace bows.
- Connecting rod: Pinned to the trace pin at one end and to the driven load at the other. Because the pin moves on a true straight line, the rod can be long and slender with no transverse loading — unlike a slider-crank rod which carries side thrust.
- Planet bearing: Carries the planet on the crank carrier. Usually a bronze bushing or needle roller, sized for the pin reaction force. At 60 RPM a 25 mm bushing in oil-impregnated bronze runs 20,000+ hours; spec a needle bearing if you push past 100 RPM.
Where the Haven's Planetary Crank Gear Is Used
Haven's gear shows up wherever a long, smooth, slow stroke is needed and side loads on the rod must stay near zero. Railway signal mechanisms drove it for decades because signal wires running 800 m down the right-of-way needed a stroke long enough to clear lost motion in the wire, but slow enough not to snap fittings. Slow-cycling reciprocating pumps in mining and waterworks used it for the same reason — long stroke, low speed, low side load on the rod stuffing box. You will also find it inside mechanical animation rigs, paper-mill couch-roll oscillators, and the occasional piston-engine demo model where a Scotch yoke would be too crude.
- Railway signalling: Mechanical lever-frame signal box drives, e.g. Saxby & Farmer and McKenzie & Holland frames in UK Midland Railway boxes, used planetary crank gears to convert wheel rotation into the long pull needed for distant home signals.
- Water and mine pumping: Slow-stroke reciprocating lift pumps on Cornish and Welsh mining sites, where a 30 RPM gearmotor drove a 400 mm stroke pump rod through a Haven-style planetary gear to lift water from 12 m sumps.
- Paper manufacturing: Couch-roll and felt-shaker oscillators on Fourdrinier paper machines, where a 50 RPM input produces a 150 mm cross-machine reciprocation to even out fibre alignment.
- Mechanical animation and museum exhibits: Beamish Museum and Science Museum London demonstrators use planetary crank gears in cutaway form to show hypocycloidal straight-line motion for visitors.
- Engine demonstration models: Cardan-gear piston engines (a related layout) and the Wiseman Hypocycloid engine kit use the same 2:1 internal-planet geometry to drive a piston with no crosshead.
- Stage and theatre rigging: Slow-cycle scenic effect drives — moving cloud panoramas and slow-moving prop tracks — where a 20–40 RPM motor needs to deliver a 500 mm reciprocation without belt or cable slip.
The Formula Behind the Haven's Planetary Crank Gear
The output is the straight-line displacement of the trace pin as a function of crank angle. What you really want from this formula is a feel for stroke length and instantaneous velocity, because those decide your pump flow, your rod-end bearing load, and whether the gear teeth see acceptable Hertzian stress. At the low end of the typical operating range — say 20 RPM on a heritage pump rebuild — the peak rod velocity is gentle and tooth loading is dominated by static reaction. At the nominal 60 RPM most industrial duties run at, peak velocities are still under 1 m/s and the mechanism feels almost silent. Push past 120 RPM and inertia of the planet gear starts dumping cyclic loads into the bearing that wear it faster than the teeth.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| x(θ) | Linear position of the trace pin along the diameter, measured from the ring centre | m | in |
| D | Pitch diameter of the fixed internal ring gear | m | in |
| θ | Crank carrier angle measured from the line of the trace | rad | rad |
| v(θ) | Instantaneous linear velocity of the trace pin | m/s | in/s |
| Nrpm | Crank input speed | RPM | RPM |
| Stroke | Total peak-to-peak travel = D | m | in |
Worked Example: Haven's Planetary Crank Gear in a heritage waterworks lift pump rebuild
Your industrial heritage workshop in Bendigo, Victoria is rebuilding the Haven's-pattern planetary crank drive on an 1898 Tangye-built reciprocating lift pump that originally moved 110 L/min from a 9 m mine sump. The fixed internal ring gear has a pitch diameter D = 0.400 m (60 teeth, module 6.67). The planet gear is 30 teeth on a 0.200 m pitch diameter. The trace pin drives a connecting rod to a single-acting pump piston with a 0.080 m bore. Your gearmotor is rated 60 RPM nominal but the operator wants to know what changes if the pump is run at 30 RPM for gentle museum demonstrations or short-bursted at 120 RPM for tank-fill duty.
Given
- D = 0.400 m
- Stroke = 0.400 m
- Nrpm,nom = 60 RPM
- Bore = 0.080 m
- Nrpm,low = 30 RPM
- Nrpm,high = 120 RPM
Solution
Step 1 — confirm the stroke. With the 2:1 ratio, stroke equals the ring pitch diameter:
Step 2 — peak pin velocity at nominal 60 RPM. Maximum v occurs at θ = 90°, where sin(θ) = 1:
Step 3 — flow rate at nominal speed. Pump piston area A = π × (0.080)2 / 4 = 0.00503 m2. Volume per stroke = A × Stroke = 0.00503 × 0.400 = 2.01 L. At 60 RPM that is 60 single-acting strokes per minute:
Step 4 — low end of the operating range, 30 RPM. Halve the speed and you halve the velocity and the flow:
That is exactly the regime the museum wants for demonstrations. The piston barely whispers, the gear teeth load almost statically, and visitors can see the connecting rod pause cleanly at each dead centre.
Step 5 — high end, 120 RPM:
In practice you will not reach the theoretical 242 L/min. Above roughly 90 RPM the suction valve cannot open fully before the piston reverses, so volumetric efficiency drops below 0.85 and you bottom out near 200 L/min real flow. The planet bearing also starts to feel the cyclic inertia of the 12 kg planet gear — peak bearing reaction roughly triples between 60 and 120 RPM because it scales with Nrpm2.
Result
At nominal 60 RPM the rebuilt pump delivers 121 L/min — a hair above the original Tangye spec of 110 L/min, which makes sense because the gear set was re-cut to within 0. 05 mm of design pitch instead of the worn original. At 30 RPM you get a calm 60 L/min suitable for crowd demonstrations; at 120 RPM you reach roughly 200 L/min real flow before valve lag and bearing inertia eat the rest. The sweet spot sits around 50–70 RPM where tooth loading is benign and valve timing is unhurried. If your measured flow comes in 15% below the predicted 121 L/min, check three things in this order: (1) gear-mesh backlash above 0.15 mm letting the pin trace open into an ellipse and shorten effective stroke; (2) connecting-rod small-end clearance over 0.10 mm, which causes the piston to lag through dead centre and lose suction time; (3) a worn ring-gear tooth-flank profile, which you can spot as bluing wear bands on alternating teeth — that asymmetry alone can cost you 8–10% of stroke length.
Haven's Planetary Crank Gear vs Alternatives
The Haven's gear is one of three common ways to convert continuous rotation into a long, repeatable straight-line stroke. Each has different speed limits, side-load behaviour, and cost. Pick by stroke length, RPM, and how much side load the driven rod can tolerate.
| Property | Haven's Planetary Crank Gear | Scotch Yoke | Slider-Crank with Crosshead |
|---|---|---|---|
| Typical operating speed | 20–120 RPM | 30–600 RPM | 60–4000 RPM |
| Side load on driven rod | Near zero (true straight-line trace) | Zero, but heavy slot wear | Significant (rod swings; needs crosshead) |
| Stroke-length range typical | 100–600 mm | 20–250 mm | 10–500 mm |
| Wear surfaces | Gear teeth (rolling) + bearings | Yoke slot (sliding) + pin | Crosshead slipper (sliding) + bearings |
| Service life at nominal load | 20,000+ hours | 3,000–8,000 hours before slot rework | 10,000–15,000 hours |
| Build cost (relative) | High — precision internal gear | Low — simple slot and pin | Medium — needs guideways |
| Tolerance sensitivity | Critical: gear ratio exactly 2:1, pin on pitch circle ±0.05 mm | Loose; runs even when sloppy | Moderate; crosshead alignment matters |
| Best application fit | Slow, long-stroke, side-load-sensitive duty | Cheap reciprocating drives, valve gear | Steam engines, IC engines, high-speed reciprocators |
Frequently Asked Questions About Haven's Planetary Crank Gear
The 2:1 ratio is not just tooth count — it is pitch diameter. If the ring and planet were cut on slightly different centre-distance assumptions, or if the planet was re-bored off-centre, the pitch circles no longer roll cleanly and the planet rotates fractionally fast or slow per crank revolution. That phase drift opens the trace into a long thin ellipse.
The diagnostic check: rotate the crank by hand one full turn and mark the pin's extreme positions on a piece of card. The two extremes should lie on a single straight line passing through the ring centre. If they form a narrow ellipse with a minor axis of even 1–2 mm, your effective ratio is off by roughly 0.5–1%. Re-cut the planet on the correct pitch or shim the carrier to restore true centre distance.
Bearing reaction at the planet pin is dominated by the centripetal load of the planet's own mass orbiting the ring centre. That load scales with Nrpm2, so going from 60 to 110 RPM nearly quadruples the dynamic component of the bearing load. L10 bearing life then drops with the cube of load, which compounds to roughly a 50× life reduction — exactly consistent with what you measured.
The fix is either to drop the speed back, lighten the planet (a steel hub with bronze tooth ring instead of solid steel), or step up to a needle roller bearing rated for the new dynamic load. Plain bronze bushings rarely survive sustained service above ~80 RPM on planetary crank gears with cast-iron planets.
For 200 mm stroke at 90 RPM, both will work mechanically, so the decision is service life and rod stuffing-box wear. Scotch yokes wear their slot oval at any non-trivial side load, and pump-rod packings always introduce some side load through misalignment. Plan on slot rework every 4,000–6,000 hours.
Haven's gear runs the same duty for 20,000+ hours with no slot to wear. The cost premium is the precision internal ring gear — typically 3–5× the cost of a Scotch yoke build. If the pump is heritage equipment or runs continuously, Haven's pays back inside 18 months. For an intermittent duty cycle of a few hours per week, the Scotch yoke is the smarter buy.
That tick is almost always backlash at the gear mesh combined with a connecting-rod load that reverses sign at dead centre. When the rod load flips from pull to push, all the backlash takes up at once and the planet jumps through the slack. You hear it as a discrete click.
Measure backlash with a dial indicator on the planet rim while holding the carrier still. Anything over 0.15 mm on a 200 mm pitch diameter is too much for quiet running. The cure is either re-shim the carrier centre distance closer to the ring (within manufacturer's recommended mesh), or fit a lightly preloaded scissor planet — a split planet gear with a torsion spring between the halves that takes up backlash on both flanks.
You can, but you lose the straight-line trace property. The geometric straight line only exists when the ring is fixed and the carrier is the input — that is the kinematic condition that makes the pitch-circle point trace a diameter of the ring. Drive any other member as input and you get a regular hypocycloidal curve, not a line.
If you have a constraint that forces a different input configuration, you can rebase the kinematics by fixing a different member, but the gear ratios change and you lose the simplicity. For 99% of designs, fix the ring, drive the carrier, take the output from the trace pin. That is the only configuration that gives you the Haven's straight-line output.
Two likely causes, neither of which is the trace itself. First, check that your trace pin sits exactly on the planet's pitch circle. A radial position error of even 0.3 mm on a 200 mm planet bows the trace into a shallow figure-of-eight, which loads the small end transversely twice per revolution. The wear pattern from that is a distinct oval aligned vertical to the rod axis.
Second, the connecting-rod alignment to the driven load matters. If the pump rod and the trace pin are not coplanar — say the pump axis is offset 2 mm out of the gear's plane of motion — the small end carries a constant cocking moment that wears the bushing oval along the rod axis. Sight along the rod with a straightedge to the pin centre; any visible offset is too much.
References & Further Reading
- Wikipedia contributors. Hypocycloid. Wikipedia
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
