The Ghassaei walking linkage is a single degree of freedom planar leg mechanism that converts continuous rotary input into a flat-bottomed walking foot trajectory. Unlike the Klann or Jansen linkages it draws inspiration from, it uses a smaller bar count and a re-tuned pivot layout designed by Amanda Ghassaei for laser-cut fabrication. The mechanism produces a near-straight ground stroke and a high swing arc, so a small DC gearmotor at 30-90 RPM drives a stable walking gait suitable for desktop kinetic sculptures and educational robots.
Ghassaei Walking Linkage Interactive Calculator
Vary leg length and pivot tolerance to see the allowable pivot error, recommended crank range, and an animated walking-linkage diagram.
Equation Used
The worked example scales the allowable pivot-location error directly from leg length: a 1% tolerance on a 100 mm leg gives +/-1 mm. The crank range shown uses the article guideline that the driven crank is usually 15-25% of total leg length.
- Calculator follows the worked-example scaling rule that pivot tolerance is a percentage of leg length.
- Recommended crank length uses the article range of 15-25% of leg length.
- A scaled Ghassaei layout is assumed; this does not solve the full linkage coordinate synthesis.
How the Ghassaei Walking Linkage Actually Works
The Ghassaei walking linkage takes a single rotating crank and routes its motion through a chain of pinned bars so the foot end traces a closed curve — flat along the bottom, arcing high above. While the crank turns at a constant RPM, the foot spends roughly the bottom third of its cycle pressed against the ground moving rearward at a near-constant horizontal speed, then lifts and loops forward through the swing phase. Pair two of these linkages 180° out of phase on a common crankshaft and the body translates forward in a steady waddle. Run four legs in two phased pairs and you have a stable static walker that never tips, because at any instant at least two feet are in their ground stroke.
The geometry is the whole game. Each pivot location and bar length sits at coordinates Ghassaei optimised numerically — shift any pivot by more than about 1% of the leg length and the bottom of the foot path bows upward, which means the foot lifts mid-stride and scuffs the ground instead of pushing the body forward. For a 100 mm leg-length build, that 1% tolerance means pivot holes must be drilled within ±1 mm of the called-out coordinates. Laser-cut acrylic or plywood at 0.1 mm kerf accuracy hits this comfortably; hand-drilled cardboard prototypes do not, which is why first-time builders see legs that hop instead of walk.
Failure modes are predictable. Floppy pivots — bushings worn or holes drilled oversize — let the foot drift vertically by a few millimetres, which is enough to break the flat-bottom condition. Phasing errors between leg pairs above ~10° cause the body to pitch fore-and-aft each cycle. And running the linkage too fast — past about 90 RPM on a typical 100 mm leg — means the swing-phase foot does not have time to clear the ground before the next stroke, so it drags. Slow it down, tighten the pivots, and the linkage walks cleanly.
Key Components
- Crank: The driven input bar rotating at constant angular velocity, typically 30-90 RPM from a small DC gearmotor. Its length sets the overall scale of the foot path — longer crank means taller swing arc and longer stride. Crank length is usually 15-25% of the total leg length.
- Coupler bar: The intermediate floating bar that connects the crank to the rocker and carries the upper foot pivot. This bar sees the highest dynamic loads in the linkage because it transfers torque from the crank into the foot lever; bushings here wear first if pivot clearance exceeds about 0.1 mm on a 100 mm-leg build.
- Rocker / ground link: The pivoting bar grounded to the chassis that constrains the coupler's motion and sets the angular envelope of the foot. Its mounting pivot location relative to the crank centre is the most sensitive dimension in the whole linkage — within ±1% of nominal or the foot path collapses.
- Foot bar: The output bar carrying the contact tip. The lower portion traces the flat ground stroke; the upper portion arcs high. Foot tip is usually a rubber bumper or laser-cut foot pad to prevent slipping on smooth surfaces during the ground-stroke push.
- Leg-pair phasing collar: On the common crankshaft, two cranks are fixed exactly 180° apart so one leg lifts as the other pushes. Phasing tolerance is ±5°; beyond 10° the chassis pitches visibly each rotation.
- Frame / chassis: Holds the rocker pivots and crankshaft bearings rigidly. Frame rigidity matters — a flexing chassis adds parasitic motion that shows up as foot wobble, so most builders use 3-5 mm laser-cut plywood or acrylic with bolted standoffs rather than glued joints.
Where the Ghassaei Walking Linkage Is Used
The Ghassaei linkage lives almost entirely in the educational, kinetic-art, and hobby-robotics space. It exists because Amanda Ghassaei published the geometry as a freely-downloadable laser-cut template, which means anyone with access to a laser cutter and a 3 mm sheet of plywood can build one in an afternoon. That accessibility, combined with a cleaner foot path than the simpler four-bar walkers, makes it a go-to mechanism for teaching planar linkage kinematics and for small kinetic sculpture work where Strandbeest scale is overkill.
- Education: Mechanical engineering kinematics courses use laser-cut Ghassaei walker kits as a hands-on lab — students measure foot path deviation as a function of pivot tolerance, typically on 80-120 mm leg builds running at 45 RPM.
- Kinetic Art: Tabletop kinetic sculpture pieces shown at maker faires and gallery installations, often paired with a hand crank or a 6 V gearmotor, where the visible bar motion is part of the aesthetic appeal.
- Hobby Robotics: DIY walking robot builds documented on Instructables and Hackaday using the original Ghassaei files, typically scaled to 150 mm leg length with an Arduino-driven N20 gearmotor.
- STEM Outreach: Museum and library mechanism demonstration tables — e.g. the Exploratorium-style hands-on exhibits where visitors turn a crank and watch four phased legs translate the chassis across a track.
- Product Photography & Stop-Motion: Slow-walking platform for stop-motion animation rigs needing repeatable forward motion at 1-2 cm per crank revolution, where the flat ground stroke gives clean per-frame translation.
- Maker Education: High school robotics clubs and FIRST teams using the linkage as an introduction to coupler curves and single-DOF walking before moving to servo-driven gaits.
The Formula Behind the Ghassaei Walking Linkage
The most useful formula for a Ghassaei walker is forward speed as a function of crank RPM and stride length per cycle. Stride length is fixed by the linkage geometry — typically 35-45% of the leg length for a Ghassaei layout. At the low end of the practical range (25-30 RPM) the walker creeps and looks deliberate, which is what kinetic-art installations want. At the high end (90+ RPM) the swing-phase clearance time drops below what the linkage can deliver and the foot scuffs. The sweet spot for a 100 mm-leg build sits around 45-60 RPM, where the gait is visually steady and the foot tracks cleanly.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| vfwd | Forward chassis translation speed | m/s | in/s |
| NRPM | Crankshaft input speed | RPM | RPM |
| Lstride | Net forward distance per crank revolution (≈ 0.4 × leg length for Ghassaei geometry) | m | in |
Worked Example: Ghassaei Walking Linkage in a tabletop kinetic art Ghassaei walker
You are building a 4-leg tabletop Ghassaei walker as a kinetic art piece for a gallery installation, with leg length 120 mm, stride length 48 mm per crank revolution, driven by a 6 V N20 gearmotor with a target nominal speed of 60 RPM at the crankshaft. You want to know how fast the chassis will translate across the gallery plinth and what speeds bracket the usable range.
Given
- Lleg = 120 mm
- Lstride = 48 mm (0.048 m)
- Nnom = 60 RPM
- Nlow = 30 RPM
- Nhigh = 120 RPM
Solution
Step 1 — convert nominal crank RPM to revs per second:
Step 2 — multiply by stride length to get nominal forward chassis speed:
That's a deliberate, watchable walking pace — about the speed of a slow snail and exactly what a gallery visitor expects from a kinetic sculpture. The legs cycle once per second so the gait reads clearly to the eye.
Step 3 — at the low end of the typical operating range, 30 RPM:
At 24 mm/s the walker creeps — a bystander glancing at it for two seconds might assume it has stalled. Useful for long-duration installations where you want the piece to take 10+ minutes to cross the plinth.
Step 4 — at the high end, 120 RPM:
96 mm/s is the theoretical number. In practice, on a 120 mm-leg Ghassaei build, the foot starts scuffing the ground above roughly 90 RPM because the swing-phase clearance time drops below the time the linkage needs to lift the foot clear. You'll see the chassis hop slightly each cycle and forward progress drops below the predicted value. Stay under 80 RPM for clean gait.
Result
At nominal 60 RPM the chassis translates at 0. 048 m/s (48 mm/s) — a deliberate, sculpture-paced walk that crosses a 600 mm plinth in about 12 seconds. The full operating range gives you roughly 2× speed control: 24 mm/s at 30 RPM for slow installations, up to a practical ceiling near 70-80 mm/s before scuffing sets in. If you measure 30 mm/s instead of the predicted 48 mm/s at 60 RPM, the most likely causes are: (1) crank-pivot bushings drilled oversize so the foot lifts mid-stride and the effective stride drops, (2) battery sag pulling the gearmotor below its rated RPM under load — check actual crank speed with a tachometer or a phone strobe app, or (3) chassis flex letting the rocker pivots shift under load, which collapses the bottom of the foot curve.
When to Use a Ghassaei Walking Linkage and When Not To
The Ghassaei sits between the simple Klann walker and the geometrically heavier Jansen Strandbeest. Pick between them based on bar count, foot-path quality, and the scale you want to build at.
| Property | Ghassaei Walking Linkage | Klann Linkage | Jansen Strandbeest Linkage |
|---|---|---|---|
| Bar count per leg | 6 bars | 6 bars | 8 bars |
| Practical RPM range | 30-90 RPM | 30-120 RPM | 20-60 RPM |
| Foot path flatness (ground stroke deviation as % of leg length) | ≈1.5% | ≈3-4% | ≈0.5% |
| Pivot-position tolerance for clean gait | ±1% of leg length | ±2% of leg length | ±0.5% of leg length |
| Typical build cost (materials, 4-leg desktop) | $20-40 laser-cut plywood | $15-30 laser-cut plywood | $60-150 PVC or laser-cut, more bars |
| Best application fit | Kinetic sculpture, classroom kits | Robotics teaching, hobby walkers | Large-scale outdoor sculpture |
| Build complexity (assembly time, 4-leg) | 2-3 hours | 1-2 hours | 6-10 hours |
| Load capacity (chassis mass / leg) | ≈100-200 g | ≈100-300 g | ≈300-1000 g |
Frequently Asked Questions About Ghassaei Walking Linkage
Veering on a different surface almost always points to asymmetric foot-ground friction or a phasing error you couldn't see on the slick bench. On a smooth bench the feet slip during the push stroke, masking the problem; on a higher-friction floor the slip disappears and the asymmetry shows up as steering bias.
Check that both crank pairs are pinned exactly 180° from each other — even a 5° phase error gives one side a longer effective stride than the other. Also check foot pad wear: if one rubber tip is harder or smaller than the others, the chassis pitches toward the high-friction side each cycle.
Move to Jansen above roughly 200 mm leg length. The Ghassaei geometry was numerically optimised for the small laser-cut desktop scale, and its foot-path flatness tolerance (~1.5% of leg length) means a 300 mm leg has 4-5 mm of vertical wander during the ground stroke — visible and bouncy.
Jansen tolerates larger scale because its 8-bar geometry produces a flatter ground stroke (~0.5%) and the extra bars distribute load better. The Strandbeest sculptures Theo Jansen builds run at 2 m+ leg length for exactly this reason. If you want to stay with Ghassaei past 200 mm, use thicker frame stock (6-8 mm ply) and oilite bushings instead of bare holes to keep pivot slop under control.
The bottom of the foot curve has bowed upward, which means a pivot location is off. The Ghassaei foot path is acutely sensitive to the rocker-pivot-to-crank-centre distance — if your CAD said 42 mm and the laser cut came out at 43.5 mm because of kerf compensation, you've shifted the curve by ~3.5% and the flat bottom collapses into a shallow arch.
Re-measure pivot-to-pivot distances with calipers, not from the CAD file. The most common offender is forgetting to compensate for laser kerf (typically 0.1-0.2 mm) when cutting pivot holes — the holes come out larger than nominal and the bars sit at the wrong centres once pinned.
The crank is starting at or near top-dead-centre, where torque demand at the foot is highest because the linkage has minimum mechanical advantage there. A small N20 gearmotor that handles steady-state load fine can stall at TDC because peak starting torque is 2-3× the running torque.
Two fixes: either offset the two crank pairs so at least one leg starts mid-stroke (this is automatic if pairs are 180° phased and you start with one crank at 90°), or step up to a gearmotor with more stall torque. As a quick check, rotate the crank by hand through one full revolution and feel for the stiffest point — that's where the motor is failing to start.
Yes, and it's a good choice for gallery installations where you want exact, repeatable speed. A NEMA 11 or NEMA 14 stepper geared down to deliver the crank torque at 10-60 RPM gives you smooth speed control via step rate, and you can stop the chassis at exactly the foot position you want for staged photography.
The catch is current draw at low speeds — a stepper holds full current even when stationary, which heats the motor. Use a driver with idle-current reduction, and be aware that stepper cogging at very low speeds (under 5 RPM) can cause the chassis to jerk forward in visible steps rather than walking smoothly. Below that speed, microstepping at 1/16 or finer becomes essential.
A 20% stride loss is too much to blame on a single tolerance — it's almost always the foot slipping during the push stroke. The Ghassaei ground stroke pushes the foot rearward through air friction with the ground; if the foot pad has too little grip, the foot slides instead of the chassis translating, and your measured forward distance is less than the geometric stride.
Check the foot pads first — bare laser-cut wood on smooth tabletop typically loses 15-25% of stride. Add adhesive-backed rubber feet or a strip of 220-grit sandpaper to the foot tip and re-measure. If stride still falls short after that, look at chassis mass: if the walker is too light the foot doesn't load the ground enough to grip during the push.
References & Further Reading
- Wikipedia contributors. Linkage (mechanical). Wikipedia
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