Jansen's Linkage is a 12-bar planar linkage driven by a single rotating crank that converts continuous rotation into a foot-path approximating a flattened D-shape, giving a walking machine smooth ground contact and a fast aerial return. Kinetic-sculpture builders and educational-robot designers rely on it because it walks without wheels, axles, or active control. Each leg's lower pivot traces the same closed curve every revolution, so a pair of legs 180° out of phase produces continuous forward motion. Theo Jansen's Strandbeest sculptures use it to walk on Dutch beaches powered by wind alone.
Jansen's Linkage Interactive Calculator
Vary the leg scale, crank radius, and leg-pair phase to see the predicted D-shaped foot path and build checks.
Equation Used
This calculator uses the worked example scale relationship: a 100 mm classroom Jansen leg with a 15 mm crank gives an approximately 80 mm long by 30 mm tall D-shaped foot path. Keeping the holy-number linkage proportions means those path dimensions scale directly with leg size. The crank match and phase error show how close the entered crank and paired-leg phase are to the article reference values.
- Uses the article's typical 100 mm classroom Jansen leg as the reference scale.
- Theo Jansen holy-number proportions are assumed, so foot path dimensions scale linearly with leg size.
- Crank match compares the entered crank radius with the 15 percent of leg length reference.
- Best paired-leg phasing is 180 deg.
Operating Principle of the Jansen's Linkage
A Jansen leg is built from 11 fixed-length bars and one rotating crank, all pivoting in a single plane. The crank turns at constant speed, and the linkage forces the foot pivot to trace a closed path roughly 80 mm long and 30 mm tall in a typical 100 mm-leg classroom build. The bottom of that path is nearly flat — that's the ground-contact phase, where the foot pushes the body forward. The top of the path is a fast arc — that's the swing phase, where the foot lifts and resets. Because the curve is closed and repeatable, you only need a crank, a frame, and gravity. No clutches, no cams, no electronics.
The geometry only works because the 11 bar lengths sit in a very specific ratio Theo Jansen called the "holy numbers" — 38, 41.5, 39.3, 40.1, 55.8, 39.4, 36.7, 65.7, 49, 50, 61.9, plus a 15 mm crank. Drift even 2-3% on any one of them and the foot path stops being flat at the bottom. You'll see the sculpture rocking up and down with each step instead of gliding. If the lower triangle's bars come out 5% long, the foot drags during what should be the swing phase and the walker scuffs the ground every cycle. Pivot bushings matter too — slop above roughly 0.2 mm at any joint compounds across the chain and the foot path opens out into a sloppy oval.
Failure modes are predictable. Most home builds fail because the crank stalls near top-dead-centre — peak torque demand swings hard through the cycle, and an undersized gearmotor will hesitate on the upswing. Worn pivot holes are the second most common issue: the multi-bar kinematic chain amplifies any one bushing's wear into visible foot wobble. Phasing between leg pairs is the third — if your two cranks aren't locked at exactly 180°, one foot lifts before the other lands and the body drops.
Key Components
- Crank: The single rotating input. In Jansen's holy numbers it has a 15 mm radius. The crank converts motor rotation into the orbital input that drives the rest of the chain. Crank-shaft concentricity must hold within ±0.1 mm or the foot path wobbles visibly.
- Upper triangle (bars a, b, c): Three bars forming a rigid triangle near the frame pivot. They constrain the upper portion of the linkage and translate crank motion into a controlled upper-knee position. Bar lengths 38, 41.5, and 39.3 mm in the canonical scale.
- Lower triangle (bars g, h, i): The triangle directly above the foot. It controls the foot's swing geometry and is the most sensitive group — a 1 mm error here visibly changes the height of the swing arc. Lengths 36.7, 65.7, and 49 mm.
- Connecting bars (d, e, f, j, k): The five bars that couple the upper and lower triangles to the crank and frame. They carry most of the cyclic stress and are where pin-hole wear shows up first in long-running Strandbeest builds.
- Frame pivot (point O): The fixed point on the chassis where the upper triangle hinges. Must be rigid relative to the crank-shaft mount — any flex between O and the crank centre directly distorts the foot path.
- Foot pivot: The endpoint of the chain that traces the working curve. This is the point you measure when verifying the linkage geometry. In a 100 mm-leg build the foot traces an ~80 mm × 30 mm closed path.
Who Uses the Jansen's Linkage
Jansen's Linkage shows up wherever a designer needs walking motion from a single rotary input without wheels or active control. It is most famous in kinetic art, but the same geometry has crossed into education, soft robotics, and a handful of niche off-road platforms. The mechanism's appeal is simple: one motor, multiple legs, no electronics, and a foot path that already approximates clean walking before any tuning.
- Kinetic sculpture: Theo Jansen's Strandbeest series — wind-powered walking sculptures on the beaches of Scheveningen and Ijmuiden, Netherlands, walking since 1990.
- Educational robotics: The EK Japan Mechanical Spider kit and similar classroom builds using a single 60 RPM gearmotor to drive 8 or 12 legs in paired phasing.
- Toy manufacturing: Hasbro's Cleverbot and various Strandbeest-licensed mini-kits sold by the Theo Jansen workshop, scaled to 80-120 mm legs.
- Mobile robotics research: University walking-platform prototypes — TU Delft and Wageningen have published Jansen-based rovers for low-disturbance soil traversal.
- Soft robotics and prosthetics study: Bench rigs at Harvard's Wyss Institute have used scaled Jansen legs to study passive-dynamic gait without active feedback control.
- Architectural installations: Museum atrium kinetic displays — the Exploratorium in San Francisco has hosted multiple Strandbeest-style walking exhibits.
The Formula Behind the Jansen's Linkage
Forward walking speed is the most useful number to compute for a Jansen build because it tells you whether your motor and gearbox choice will actually move the machine at the pace you want. The formula multiplies stride length (the horizontal distance the foot travels during ground contact) by crank rotational speed. At the low end of typical operating range — around 30 RPM — the walker creeps and looks almost stalled to a casual observer. The sweet spot sits near 60 RPM for a 100 mm-leg build, where the foot tracks cleanly and the motion looks deliberate. Past 90-120 RPM the math still gives you a higher number but the foot starts scuffing because swing-phase time drops below the time the leg needs to clear the ground.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| vwalk | Forward walking speed of the chassis | m/s | ft/s |
| Lstride | Horizontal stride length per crank revolution (the flat-bottom segment of the foot path) | m | ft |
| N | Crank rotational speed | RPM | RPM |
Worked Example: Jansen's Linkage in a desktop Strandbeest classroom kit
A maker-education studio in Porto is building a 6-leg Jansen walker for primary-school workshops. The legs use the canonical holy numbers scaled to a 15 mm crank, giving a measured stride length of 80 mm at the foot. The drive is a 6 V gearmotor running nominally at 60 RPM, with the kit specifying an operating window of 30-120 RPM via a PWM controller the kids use to vary speed. The studio needs to know how fast the walker actually moves at each end of that range so they can plan the workshop floor space.
Given
- Lstride = 0.080 m
- Nnom = 60 RPM
- Nlow = 30 RPM
- Nhigh = 120 RPM
Solution
Step 1 — at nominal 60 RPM, convert crank speed to revolutions per second:
Step 2 — multiply by stride length to get nominal forward speed:
That's about 8 cm per second — slow, deliberate, easy for a child to track with their eye and easy to film without motion blur. This is the sweet spot for the holy-numbers geometry.
Step 3 — at the low end of the operating range, 30 RPM:
4 cm per second is a creep. The walker covers a workshop tabletop in a couple of minutes and looks almost stalled to a casual observer. Useful for demonstrating the foot path slowly but boring as a continuous-run exhibit.
Step 4 — at the high end, 120 RPM:
The math says 16 cm/s. In practice you won't get there. Above roughly 90 RPM on a 100 mm-leg build the swing phase compresses below the time the leg needs to lift, swing forward, and land — and the foot starts scuffing the ground every cycle. You'll hear it before you see it: a soft scraping on each step. Practical maximum for clean walking is around 0.12 m/s.
Result
Nominal forward speed at 60 RPM is 0. 080 m/s, or about 8 cm per second. At that pace the walker moves at a deliberate, watchable speed — the foot path is clearly visible and the motion looks intentional rather than frantic. The 30 RPM low end gives 0.040 m/s (a slow creep, almost stalled-looking) and the 120 RPM high end gives a theoretical 0.160 m/s but practically tops out around 0.12 m/s before the foot starts scuffing during the swing phase. If your measured speed is well below 0.080 m/s at 60 RPM, the most likely causes are: (1) crank shaft eccentricity above 0.1 mm shortening the effective stride, (2) lower-triangle bar lengths drifted 3-5% from the holy numbers so the flat-bottom ground-contact segment is no longer flat, or (3) frame flex between the crank-shaft mount and frame pivot O letting the chassis bob up and down instead of moving forward.
When to Use a Jansen's Linkage and When Not To
Jansen's Linkage is one of three common ways to get walking motion from a single rotary input. The Klann linkage and a Chebyshev-driven leg are its main competitors for hobbyist and educational walkers. The decision usually comes down to how clean a foot path you need, how much fabrication tolerance you can hold, and whether the build is statically driven or has to handle uneven terrain.
| Property | Jansen's Linkage | Klann Linkage | Chebyshev Lambda Linkage |
|---|---|---|---|
| Bars per leg | 12 (11 fixed + 1 crank) | 8 (7 fixed + 1 crank) | 4 (3 fixed + 1 crank) |
| Foot-path quality (flat ground-contact segment) | Excellent — long, flat bottom | Very good — slightly arched | Fair — noticeably curved bottom |
| Sensitivity to bar-length tolerance | High — 3% drift visibly degrades gait | Moderate — 5% drift tolerable | Low — quite forgiving |
| Typical operating speed range | 30-90 RPM clean, scuffs above 90 | 30-120 RPM | 30-150 RPM |
| Build complexity | High — 11 unique bar lengths | Medium — 7 unique bars | Low — 3 unique bars |
| Obstacle clearance per stride | ~30% of leg length | ~40% of leg length (steps over taller obstacles) | ~15% of leg length |
| Best application fit | Smooth-ground kinetic sculpture, classroom kits | Mobile robots crossing small obstacles | Simple toys, demonstration models |
Frequently Asked Questions About Jansen's Linkage
The flat-bottom segment of the foot path has lost its flatness. That happens when the lower triangle's bar lengths (g, h, i in the holy numbers — 36.7, 65.7, 49) drift more than about 2-3% from spec. The foot stops tracing a flat line during ground contact and instead traces a shallow arc, so the chassis lifts and drops on each step.
Quick diagnostic: pull the crank by hand and watch the foot pivot against a ruler held horizontally. If the foot rises more than 1 mm during the bottom third of its travel, your lower triangle is out of spec. Re-measure each of those three bars to within 0.2 mm.
Yes, but only by uniform scaling — every one of the 11 bar lengths and the crank radius must scale by the same factor. Theo Jansen designed the ratios as a set and they only produce the correct foot path when held in proportion. Doubling all 12 lengths gives you a 200 mm-leg walker with a foot path twice as long and twice as tall, and a stride of roughly 160 mm.
What does NOT scale is bar stiffness. Double the length and bending deflection under load goes up roughly 8× for the same cross-section. Big Strandbeest builds use thicker tubing and triangulated bars precisely because the geometric scaling outruns the structural scaling.
Minimum is 4 legs in two pairs, with each pair driven by one crank and the two cranks locked 180° out of phase. That guarantees at least one leg from each side is always in ground contact. For 6 or 8 legs you stagger the cranks at 120° or 90° intervals respectively.
The common build mistake is gluing both cranks to a single shaft without indexing them. You think they're at 180°, you measure later, and they're at 165° because the set-screw slipped during assembly. Always pin or key the cranks to the shaft, and verify the phase angle with a digital protractor before final assembly. 5° off is enough to make the walker limp.
Klann. The Jansen foot path lifts roughly 30% of leg length above the ground at peak swing — fine for a flat beach, marginal for a desk with cable clutter. Klann's foot lifts closer to 40% and has a more pronounced step-over arc, which is exactly why Joe Klann patented it as an alternative for terrain where a leg needs to clear bumps.
The trade is fabrication: Klann uses 8 bars with 7 unique lengths, Jansen uses 12 bars with 11 unique lengths. If you're cutting bars on a laser or waterjet the build cost difference is small. If you're filing them by hand, Klann is meaningfully faster to build.
Peak torque demand swings hard through the cycle — the linkage is most loaded when the leg is near top-dead-centre on the upswing. Sizing on average torque will leave you with a motor that stalls there. Rule of thumb: size the motor for 2.5-3× the average computed torque to handle the peak.
For a typical 100 mm-leg desktop walker weighing 200-400 g, a 6 V gearmotor with 0.5-1.0 N·cm continuous output running at 60 RPM is comfortable. Anything below 0.3 N·cm and you'll hear the motor hesitate at top-dead-centre on every revolution. The hesitation looks like a brief stutter in the gait — it's not a foot-path problem, it's a torque problem.
Three usual suspects beyond the obvious bar-length errors. First, joint slop: total clearance across 11 pivots compounds, and 0.2 mm of play per joint becomes visible foot-path distortion. Use bushings or precision pins, not loose pop-rivets through oversized holes.
Second, out-of-plane wobble: if the leg can flex sideways (out of the kinematic plane) the foot pivot describes a 3D path and the projected forward stride shrinks. Add a guide bushing or a parallel stiffener bar to constrain the leg to its plane.
Third, ground compliance: on carpet or foam, the foot sinks during ground contact and the effective stride drops. Test the walker on a hard, flat surface before blaming the linkage.
References & Further Reading
- Wikipedia contributors. Jansen's linkage. Wikipedia
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