A Leg Mechanism is a multi-bar linkage that converts continuous rotary input into a foot path resembling a biological walking gait. It solves the problem of moving a robot or toy across uneven ground without wheels or tracks. The crank drives a coupler point along a closed curve with a flat lower portion (stance phase) and an arched upper portion (swing phase), so the foot pushes the body forward then lifts clear. Klann and Jansen linkages use this principle in classroom walkers, kinetic art, and small-scale robots like Theo Jansen's Strandbeest.
Leg Mechanism Interactive Calculator
Vary crank radius, stride factor, and crank RPM range to see stride length, walking speed range, and high-speed scuff risk.
Equation Used
The calculator uses the article speed relation: walking speed equals stride length times crank revolutions per second. Stride length is estimated from crank radius using an empirical linkage factor k, with Klann mechanisms near 2.4 and Jansen mechanisms near 1.7.
- Stride factor k is empirical: about 2.4 for Klann and 1.7 for Jansen linkages.
- One crank revolution produces one walking stride for the modeled leg.
- No foot slip, chassis bounce, or terrain losses are included.
- High-speed scuff risk is estimated from the article note that problems begin around 90-100 RPM.
The Leg Mechanism in Action
A Leg Mechanism is a planar linkage — usually six or eight bars — arranged so one point on a coupler link traces a coupler curve that looks like a flattened D lying on its side. The flat bottom of that curve is the stance phase, where the foot is on the ground pushing the body forward. The arched top is the swing phase, where the foot lifts, returns, and resets for the next step. A single rotating crank drives the whole loop, so one motor and one shaft can power multiple legs phased 180° or 120° apart for a stable gait. That's why you can build a 12-leg Strandbeest with one wind-driven crankshaft and no electronics at all.
The geometry is unforgiving. Link lengths in a Jansen linkage follow Theo Jansen's eleven "holy numbers" — 38, 41.5, 39.3, 40.1, 55.8, 39.4, 36.7, 65.7, 49, 50, 61.9 mm in his canonical scale — and if you change one by even 2 mm the foot path collapses. Either the stance becomes too short and the walker shuffles, or the swing arc dips below ground level and the foot drags. Pivot bushings matter too: 0.3 mm of slop at each pin in a six-bar Klann adds up to roughly 2 mm of vertical wander at the foot, and you'll see one leg scuff while its mirror partner clears cleanly. Common failure modes are worn pin holes (the linkage gets noisy and the gait goes asymmetric), a leg-pair phasing error from a loose crank-pin (the walker yaws to one side), and gearmotor stall near top-dead-centre when peak torque demand isn't sized for the lift portion of the swing.
Why a closed coupler curve and not a cam or a four-bar? Because a four-bar can't generate a curve with both a long straight stance and a high swing arc from a single rotating input — you need at least six bars. A cam can produce the same foot path, but it forces sliding contact under load, wears fast, and can't be shared cleanly across multiple phased legs from one crankshaft. Six-bar linkages give you a coupler curve, a single-DOF mechanism, and revolute joints only — which means cheap pins, cheap bushings, and long life.
Key Components
- Crank: The continuously rotating input link, typically 15-40 mm long depending on scale. Its length sets the stride amplitude — double the crank radius and you roughly double the stride length, which is why classroom Klann kits use 25 mm cranks and Strandbeest installations use 150 mm or larger.
- Coupler links (the "thigh" and "shin"): Two or three rigid bars connecting the crank to the foot point. These set the shape of the coupler curve. Length tolerance is ±0.5 mm on a 100 mm-scale build — go beyond that and the foot path loses its flat stance segment.
- Rocker / ground link: A fixed-pivot link that constrains one end of the coupler chain to swing in an arc. In a Jansen linkage there are two rockers per leg. The ground-link pivot positions are fixed to the chassis and define the kinematic frame of the leg.
- Foot point: A specific point on the coupler link — not at a pin joint but at a defined offset — whose path through space is the coupler curve. Drilling this hole 2 mm off-position shifts the entire foot path and is the most common build error in classroom kits.
- Crankshaft: Couples multiple legs in correct phase. For a 4-leg walker, opposing legs are 180° out of phase. For a Strandbeest with 6 or more legs per side, the cranks are phased at 60° or 120° increments to keep at least three feet on the ground at all times for static stability.
- Pivot pins and bushings: Revolute joints at every link connection. Bronze bushings or PTFE-lined polymer bushings on a 4-6 mm steel pin are typical. Slop above 0.1 mm per joint compounds across the chain — by the foot point you can see 1-2 mm vertical error.
Who Uses the Leg Mechanism
Leg Mechanisms show up wherever wheels are wrong — soft beaches, classroom robotics, kinetic sculpture, and any application where the visual or mechanical character of legged motion matters more than peak speed. The mechanism is purely mechanical, runs from one motor, and survives sand, dust, and water far better than a wheeled drivetrain.
- Kinetic art: Theo Jansen's Strandbeest series — wind-powered multi-legged sculptures walking on Dutch beaches since 1990, using the canonical 11-link Jansen linkage.
- Educational robotics: Tamiya Mechanical Spider Kit (item 70112) and EK Japan Mechanical Walking Robot — both use Klann-style 6-bar linkages running at 40-60 RPM for primary-school workshops.
- Small mobile robotics: Strider walking-robot research platforms used at universities including Virginia Tech for legged-locomotion coursework, built on Chebyshev lambda linkages.
- Toy and hobby kits: Cardboard Strandbeest kits sold by Gakken (Japan) — a 12-leg crankshaft-driven walker assembled from laser-cut chipboard.
- Museum installations: The Exploratorium in San Francisco and NEMO Science Museum in Amsterdam both run hand-cranked Klann walker exhibits to demonstrate coupler-curve generation.
- Soft-terrain inspection: Prototype walking inspection robots for sand-dune and tidal-zone monitoring, where wheel-and-track designs bog down within a few metres.
The Formula Behind the Leg Mechanism
The single most useful number for sizing a leg mechanism is forward walking speed. Stride length is set by the linkage geometry — for a Klann it's roughly 2.4× the crank radius, for a Jansen closer to 1.7× the crank radius. Multiply stride by step rate (cranks per second) to get walking speed. At the low end of typical operating range, 20-30 RPM, the walker creeps and the gait looks deliberate — good for sculpture and demonstration. At the nominal 50-70 RPM range you get a walking-pace gait where the foot still tracks the coupler curve cleanly. Push above 90-100 RPM and the swing-phase clearance time drops below what the leg needs to lift over surface debris, and feet start scuffing.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| vwalk | Forward walking speed of the chassis | m/s | ft/s |
| Lstride | Stride length per crank revolution (length of the flat stance portion of the coupler curve) | m | ft |
| RPM | Crank rotational speed | rev/min | rev/min |
| kgeom | Stride-to-crank-radius ratio (≈2.4 for Klann, ≈1.7 for Jansen, ≈2.0 for Chebyshev lambda) | dimensionless | dimensionless |
Worked Example: Leg Mechanism in a vineyard-monitoring walking robot prototype
A precision-agriculture startup in Mendoza, Argentina is prototyping a 4-leg Klann walker to crawl between vine rows carrying a 1.2 kg multispectral camera. The chassis uses a 12 V gearmotor driving a single crankshaft. The crank radius is 35 mm, giving an expected stride length of 2.4 × 35 = 84 mm. The team needs to know walking speed at low, nominal, and high crank RPM to match the camera's frame-capture rate.
Given
- rcrank = 35 mm
- kgeom = 2.4 (Klann)
- Lstride = 0.084 m
- RPMnominal = 60 rev/min
Solution
Step 1 — convert nominal crank speed to revs per second:
Step 2 — multiply by stride length to get nominal forward speed:
That is roughly 5 m/min — a comfortable inspection-pace crawl, slow enough that the camera gets sharp frames at 10 fps and fast enough to cover a 50 m vine row in about 10 minutes.
Step 3 — at the low end of the typical operating range, 30 RPM:
At 0.042 m/s the walker creeps so slowly a casual observer will assume it has stalled. Useful only if the camera needs long-exposure or hyperspectral scans where motion blur matters.
Step 4 — at the high end of the typical operating range, 120 RPM:
The arithmetic says 0.168 m/s, but in practice the Klann's swing-phase clearance arc only gives the foot about 12 mm of ground clearance. Above roughly 90 RPM the leg's lift-and-return time drops below what's needed to clear a 5-10 mm clod of vineyard soil, and you'll see scuffing, stumbling, and a yaw drift to one side. The realistic upper bound for clean gait on this build is 80-90 RPM, giving 0.11-0.13 m/s.
Result
Nominal walking speed is 0. 084 m/s, or about 5 m/min. That feels like a deliberate, steady crawl — the body translates smoothly with no visible bobbing if the linkage is built well. Across the operating range the walker covers 0.042 m/s at 30 RPM (creep, almost imperceptible), 0.084 m/s at the 60 RPM sweet spot (clean gait, sharp camera frames), and a theoretical 0.168 m/s at 120 RPM that the mechanism cannot actually deliver because foot clearance time runs out around 90 RPM. If the team measures only 0.06 m/s instead of 0.084 m/s at 60 RPM, the most likely causes are: (1) crank radius drilled at 30 mm instead of 35 mm, shrinking stride proportionally; (2) the foot-point hole offset by 1-2 mm on the coupler link, flattening the coupler curve and shortening effective stride; or (3) one ground-link pivot mounted 3+ mm out of position, distorting the entire foot path so the stance segment no longer sits flat on the ground.
Leg Mechanism vs Alternatives
A Leg Mechanism is one of three competing approaches to legged locomotion at small scale. The other two are servo-articulated legs (multiple actuators per leg, software-controlled gait) and cam-driven legs. Each has a clear application window.
| Property | Leg Mechanism (Klann/Jansen) | Servo-articulated leg (Boston Dynamics-style) | Cam-driven walking leg |
|---|---|---|---|
| Typical crank speed / step rate | 20-90 RPM clean, 120 RPM theoretical max | 0.5-3 Hz step rate, software-limited | 30-150 RPM, limited by cam follower wear |
| Position accuracy at foot | ±1-2 mm at 100 mm scale (geometry-fixed) | ±0.1 mm with encoder feedback | ±0.5 mm if cam profile is ground accurately |
| Cost (single leg, prototype scale) | $5-30 in laser-cut acrylic or steel | $200-2000+ for servos plus controller | $50-150 for ground cam plus follower |
| Reliability / lifespan | 10,000+ hours on bronze bushings, no electronics to fail | Servo lifetime 1,000-5,000 hours, electronics MTBF lower | 2,000-5,000 hours, cam wear is the limiter |
| Load capacity per leg (typical small-scale) | 0.5-5 kg per leg with 4-6 mm pins | 1-50 kg per leg depending on servo class | 1-10 kg, limited by cam-follower contact stress |
| Best application fit | Kinetic art, classroom robots, low-power soft-terrain crawlers | Adaptive walking robots needing terrain feedback | Industrial walking machines with fixed gait pattern |
| Mechanical complexity | Single DOF, one motor drives all legs via crankshaft | Multiple DOF per leg, typically 3 servos per leg | Single DOF but precision cam grinding required |
Frequently Asked Questions About Leg Mechanism
The phasing is correct on the crank but the foot paths are not identical. Check the ground-link pivot positions on the dragging leg — if either fixed pivot is mounted even 2-3 mm out of position relative to the other leg, the coupler curve tilts and the stance segment no longer sits parallel to the chassis floor. One foot sits 1-2 mm lower at mid-stance and drags through the swing phase.
Quick check: lift the chassis, hand-rotate the crank, and watch each foot trace its path against a vertical ruler. If the two paths aren't mirror images at the same height, the pivot mount is the cause, not the linkage geometry.
You scaled the lengths but probably not the pivot positions of the two fixed ground-link points. Jansen's holy numbers include the spacing between the two fixed pivots as part of the geometry — it's not a free parameter. If you doubled link lengths but kept the original pivot spacing, the linkage is no longer in Jansen proportions and the coupler curve degenerates.
Scale every dimension uniformly, including the fixed-pivot offset. Verify by plotting the foot path in any kinematic simulator (Linkage by David Rector, or a quick GeoGebra sketch) before cutting parts.
Klann for a 4-leg build, every time. Jansen needs 6 or more legs per side to maintain static stability because of its narrower stance segment — try a 4-leg Jansen and the body pitches forward at every step transition. Klann's longer flat stance phase keeps two feet solidly grounded through the gait cycle, so a 4-leg quadruped pattern works.
Reserve Jansen for 8+ leg sculpture-style builds where the multi-leg phasing carries the body through stance gaps, like the Strandbeest configuration.
Peak torque demand on the crankshaft happens at the start of the lift portion of the swing phase, not during stance. Estimate it as Tpeak ≈ mleg+payload share × g × rcrank × 1.5, where the 1.5 factor covers acceleration and bushing friction.
For the Mendoza vineyard example — 35 mm crank, 1.2 kg camera plus 0.5 kg of leg mass per leg lifted, four legs sharing — you get roughly 0.1 N·m peak. A 12 V gearmotor rated 0.3 N·m continuous gives you the 3× safety margin you want, because if you size to peak the motor stalls at top-dead-centre on cold mornings when bushing drag is highest.
The pivot holes are wallowing out. Acrylic has a very low surface hardness, and a steel pin running directly in an acrylic hole will egg-shape the hole within a few hundred cycles under load. By 30 minutes of running you've put each joint through 1,800-3,600 cycles and the holes have grown from 4.0 mm to 4.3-4.5 mm.
The fix is to press a brass or PTFE bushing into every pivot hole. Drill the acrylic 6 mm, press in a 6 mm OD / 4 mm ID bushing, and run the steel pin in the bushing. Service life jumps from hours to thousands of hours.
Likely a crankshaft phasing error, not a linkage error. If the left and right cranks are off by 5-10° from true 180° opposition — easy to do with a set-screw crank coupler that slipped during assembly — one side completes its stance push fractionally before the other and the chassis rotates a small amount each cycle. Over 20 steps that's a noticeable yaw drift.
Mark top-dead-centre on both cranks with the chassis on a flat surface and verify they reach TDC at exactly the same shaft angle. A keyed shaft connection or a pinned crank coupler eliminates the slip that set-screws cause.
References & Further Reading
- Wikipedia contributors. Jansen's linkage. Wikipedia
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