The Klann Linkage is a 6-bar planar mechanism that converts continuous rotary input from a single crank into a foot-path curve mimicking an animal's leg stride. It sits at the heart of small legged robots and educational walking toys, where wheels are off the table but full servo-driven legs are overkill. The linkage uses fixed link-length ratios to lift, swing forward, plant, and push back the foot in one revolution. A pair of legs phased 180? apart gives a stable two-point stance throughout the cycle.
Klann Linkage Interactive Calculator
Vary crank size, crank speed, and stride ratio to see the walking foot path, stride length, and forward speed.
Equation Used
The calculator uses the article's practical Klann approximation: one crank revolution produces one stride, and standard geometry gives stride length of about four times the crank length. Forward speed is stride length multiplied by crank revolutions per second.
- Standard Klann geometry gives stride length about 4 times crank length.
- One crank revolution produces one complete foot stride.
- Forward speed ignores slip, scrub, and compliance losses.
- Skipping risk increases above the article's 70 to 90 RPM caution range.
Operating Principle of the Klann Linkage
The Klann Linkage, also called the Klann walking linkage in robotics literature, works by chaining six rigid bars and seven pivots so that one continuous crank rotation produces a closed foot-path curve with a flat bottom and a tall arch. Joe Klann patented it in 1994 as a wheel-free alternative for uneven terrain. The crank rotates at constant speed, but the foot tip traces a stride: it lifts at the back of the cycle, swings forward through the air, plants at the front, then sweeps back along the ground while supporting the body. That ground sweep is roughly straight and roughly horizontal, which is the whole point - the body doesn't bob up and down the way a simple four-bar foot would make it.
Link-length ratios are tight. If you scale every bar from Klann's original ratios proportionally the foot path stays correct, but if you mis-scale even one bar by 5% you lose the flat ground-stroke and the walker starts limping or scrubbing. The two most common build mistakes you would see in a classroom kit: pivot holes drilled 0.3 mm oversize, which lets the foot lift mid-stance and produces a wobble; and leg-pair phasing off by more than 10°, which means one foot is still in swing phase while the other is already lifting - the walker face-plants. Pivot bushings, usually brass or PTFE on a 3 mm steel pin, need to run with under 0.05 mm diametral clearance to keep the foot-path curve repeatable over thousands of cycles.
Why six bars and not four? A four-bar linkage can give you a curved coupler path, but it cannot give you a long flat ground stroke combined with a tall swing arch from a single crank. Klann's extra two bars and the grounded rocker are what break that constraint. The trade is mechanical complexity - more pivots means more places for slop to accumulate.
Key Components
- Crank: The single rotary input, typically driven by a small DC gearmotor at 30-90 RPM. One full crank rotation produces one full foot-path stride. Crank length sets the overall scale - a 20 mm crank in a desktop walker yields roughly 80 mm of stride.
- Frame (ground link): The fixed reference holding the two grounded pivots - the crank pivot and the rocker pivot. Spacing between these two pivots is the most safety-critical dimension; tolerance must be held within ±0.2 mm on a 100 mm-class build or the foot path distorts.
- Rocker: Grounded swing arm that constrains one end of the upper coupler. Oscillates back and forth across roughly 60° per cycle. Rocker pivot bushing wear is the first thing to fail in a high-cycle build - expect inspection at 50,000 cycles.
- Coupler bars (upper and lower): Two rigid bars connecting the crank, rocker, and the leg-shaped foot member. These transfer the crank motion through the rocker constraint to produce the characteristic foot-path. Hole-to-hole length tolerance ±0.1 mm on a laser-cut acrylic build.
- Leg (foot link): The output bar carrying the foot tip. Its shape is usually a downward-pointing triangle, with the foot tip at the apex. The tip traces the closed walking curve; the rest of the leg is structural and sets the moment arm to the ground.
- Pivot pins and bushings: Seven pivots total. Typical build uses 3 mm steel shoulder bolts with brass or PTFE bushings. Diametral clearance under 0.05 mm or the foot-path repeatability collapses after a few hundred cycles.
Industries That Rely on the Klann Linkage
The Klann Linkage shows up wherever a designer wants legged motion driven by a single motor, with no microcontroller, no sensors, and no servo per joint. It splits the difference between Theo Jansen's 8-bar Strandbeest (smoother but bigger) and a simple four-bar wobbler (cheaper but useless on rough ground). Most real-world deployments are educational kits, robotics demos, and small toys, but it has also shown up in concept rovers and physical-computing art pieces.
- Educational robotics: Laser-cut Klann walker kits sold by EMSL (Evil Mad Scientist Labs) and various STEM suppliers - used in middle-school and high-school robotics programs to teach kinematic chains without requiring code.
- Toys and hobby kits: The Tamiya Mechanical Spider and similar wind-up walker toys use the Klann walking linkage geometry scaled down to roughly 60 mm leg length, running at 40-60 RPM from a small DC motor.
- Concept rovers: Small all-terrain prototype rovers built by university teams as wheel-free alternatives where wheels would clog with debris - typically 4-leg or 8-leg configurations at 200-400 mm leg length.
- Kinetic art and museum exhibits: Gallery walking sculptures and crank-driven kinetic pieces where visitors see one motor producing lifelike walking motion - the Klann linkage is preferred over Jansen for its smaller footprint.
- Animatronics and stage props: Low-budget creature-effect rigs where a single hidden motor must produce visible leg motion - used in some indie film and theatre productions for spider and insect props.
- Mechanism teaching at university level: Mechanical engineering kinematics courses use Klann linkage CAD models in SolidWorks Motion or PTC Creo as a worked example of a 6-bar with one degree of freedom.
The Formula Behind the Klann Linkage
The most useful closed-form result for a Klann walker is forward speed as a function of crank RPM and stride length. Stride length itself comes from the foot-path geometry - for the standard Klann ratios it works out to roughly 4? the crank length. At the low end of typical operating range (30 RPM) the walker creeps and the foot-path tracks cleanly with no scuffing. At the high end (above ~90 RPM in a 100 mm leg build) the foot starts skipping because swing-phase time drops below the time the leg needs to clear the ground. The sweet spot sits around 50-70 RPM for desktop-scale builds.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| vfwd | Forward walking speed of the body | m/s | ft/s |
| Ncrank | Crank rotational speed | RPM | RPM |
| Lstride | Stride length per crank revolution (? 4 ? crank length for standard Klann ratios) | m | ft |
| Lcrank | Crank arm length | m | ft |
Worked Example: Klann Linkage in a battery-powered desktop Klann walker for a maker-faire demo
You are building a small 4-leg desktop Klann walker to display on a maker-faire booth. Crank length is 20 mm, giving a stride of roughly 80 mm. You plan to run it from a 6V DC gearmotor with a no-load output of 60 RPM at the crank. You want to know how fast it will cross a 600 mm display table, and where the realistic operating ceiling sits before the walking gait breaks down.
Given
- Lcrank = 20 mm
- Lstride = 80 mm (= 0.080 m)
- Ncrank (nominal) = 60 RPM
Solution
Step 1 - at the nominal crank speed of 60 RPM, convert to revolutions per second:
Step 2 - multiply by stride length to get nominal forward speed:
That is 80 mm per second - the walker crosses the 600 mm table in about 7.5 seconds. Quick enough to look alive, slow enough that visitors can study the leg motion.
Step 3 - at the low end of the typical operating range, 30 RPM:
At 40 mm/s the foot-path tracks cleanly, the gait looks deliberate, and the walker covers the table in 15 seconds. This is where you would run it for a slow-motion demo - the legs look almost biological.
Step 4 - at the high end, 120 RPM, theoretical speed:
In theory the walker covers the table in under 4 seconds. In practice you will not get there. Above roughly 90 RPM in a 20 mm-crank build, the swing phase compresses below the time the leg needs to clear the ground, the foot starts scuffing during what should be the lift phase, and the walker pitches forward. You will hear it before you see it - a tick-tick-tick of the foot tip catching the surface.
Result
The walker travels at a nominal 0. 080 m/s (80 mm/s) at 60 RPM, crossing the 600 mm table in roughly 7.5 seconds. At 30 RPM it creeps at 0.040 m/s with a clean gait - ideal for slow-motion viewing. At 120 RPM theoretical speed is 0.160 m/s but the gait breaks down above ~90 RPM and you get foot-scuffing instead of forward motion, so the realistic ceiling is around 70-80 RPM. If you measure noticeably less than 0.080 m/s at the bench, the most likely causes are: (1) crank-shaft set screw slipping on the motor output, dropping effective RPM; (2) foot-tip rubber pad worn smooth so the support foot slides backward during ground-stroke instead of pushing the body forward; or (3) frame flex in a thin acrylic baseplate, which lets the grounded pivot spacing breathe under load and distorts the foot path.
When to Use a Klann Linkage and When Not To
Klann is one of three popular single-DOF walking linkages a designer would actually consider. The other two are the Jansen linkage (the Strandbeest mechanism, 8 bars) and a basic crank-rocker four-bar with a curved coupler point. Each one is a different point on the same trade curve: bar count vs gait quality vs build complexity.
| Property | Klann Linkage | Jansen Linkage (Strandbeest) | Four-bar crank-rocker |
|---|---|---|---|
| Bar count / pivots | 6 bars, 7 pivots | 8 bars, 11 pivots | 4 bars, 4 pivots |
| Typical operating RPM | 30-90 RPM (desktop scale) | 20-60 RPM | 30-120 RPM |
| Forward speed at nominal scale | 0.04-0.12 m/s | 0.05-0.15 m/s | varies, often poor |
| Gait quality (flat ground stroke) | Good - long flat stroke | Excellent - longest flat stroke | Poor - coupler curve only |
| Build complexity | Moderate - 7 pivots to align | High - 11 pivots, tight ratios | Low - 4 pivots |
| Tolerance sensitivity | ±0.1 mm on link lengths | ±0.05 mm - very sensitive | ±0.3 mm acceptable |
| Best application fit | Educational kits, small robots, art | Large kinetic sculptures, beach walkers | Toy wobblers, novelty motion only |
| Cost (laser-cut hobby build) | $15-40 per leg pair | $25-60 per leg pair | $5-15 per leg pair |
Frequently Asked Questions About Klann Linkage
Yes - they are the same 6-bar mechanism. Robotics textbooks and STEM kit suppliers usually call it the Klann walking linkage to distinguish it from other linkages by Joe Klann, while the Wikipedia mechanism index and most CAD libraries list it as Klann Linkage. Same geometry, same ratios, same patent.
Phasing is only half of it. The other half is leg-length symmetry between the two sides. If the foot-tip pivot on one leg sits even 0.5 mm lower than the other when the crank is at top-dead-centre, that side carries more weight and drags through the swing phase. Lay the walker on a flat sheet of glass with both cranks at TDC and check that both foot tips clear the glass by the same amount. If they don't, the asymmetry is in the leg link, not the phasing.
The other common cause is a bent crank pin - a 3 mm steel pin pressed into laser-cut acrylic will bend under repeated impact landings, dropping the effective stroke on that side.
Scale every bar uniformly by the same factor. The foot-path geometry depends on the ratios, not the absolute lengths, so a 2? build doubles every link, every pivot spacing, and every offset. What you cannot scale linearly is bar stiffness - a 2? longer bar bends 8? more under the same load, so you need to thicken the bars or move from acrylic to aluminium above roughly 200 mm leg length. Pivot clearance also has to stay absolute, not scaled - 0.05 mm clearance at 100 mm leg is good, and 0.05 mm at 400 mm leg is still good. Don't proportionally widen it.
Klann, almost always. Jansen has 11 pivots and ratios held to ±0.05 mm - that is a hard build for laser-cut classroom material. Klann has 7 pivots and ratios that tolerate ±0.1 mm without visible gait change. For a one-class-period assembly, Klann finishes; Jansen frustrates. Pick Jansen only if the gait quality matters more than buildability, which is rarely true in a teaching context.
The 4? rule assumes the standard Klann link-length ratios and zero pivot slop. Two things shorten effective stride in practice. First, oversize pivot holes - a 3.2 mm hole on a 3.0 mm pin gives 0.2 mm of slop per pivot, and across 7 pivots that adds up to several millimetres of foot-path shrinkage. Second, foot compliance: a soft rubber foot tip compresses on ground contact and the leg pivots forward through the contact patch instead of the body translating, which steals stride. Measure foot-path on the bench with the walker held off the ground first - if that matches 4? crank, the problem is on the floor, not in the linkage.
You can, but you usually shouldn't. The crank torque demand is highly non-uniform across one revolution - peak demand is right at the foot-plant transition, sometimes 3-4? the average. A stepper sized for the average torque will skip steps at the peak, and a stepper sized for the peak is heavy and expensive. A DC gearmotor with a flywheel-like rotor inertia smooths through the peak naturally. Use a stepper only if you specifically need positional control of the crank angle for a synchronised art piece.
Less than people expect. A 100 mm-leg laser-cut acrylic walker tops out around 200-300 g of payload before the bars start visibly flexing on each step and the foot path distorts. The limiting member is usually the lower coupler - it sees a bending moment equal to payload weight times leg length at the worst point in the cycle. If you need to carry more, go to 3 mm aluminium bars or laminated plywood, and accept that build weight will roughly triple.
References & Further Reading
- Wikipedia contributors. Klann linkage. Wikipedia
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