Jansen linkage walker

A hand-cranked walking machine with twelve legs on one crankshaft, after the linkage Theo Jansen devised for his Strandbeesten. Each leg is his thirteen published numbers in laser-cut 4 mm birch and walnut-faced plywood; six pairs of legs hang from a row of frame ribs and are driven by a keyed brass crankshaft. One turn of the crank is one step of every leg, and a floor of dark boards rolls back under the feet by exactly one board, so the motion loops without a jump.

What it shows

• Many closed loops in one solve. 87 moving instances, 141 revolute, fixed and slider joints, and one crank drive (the floor has its own slide): t turns the crank (joint.set on the mate Drive) and everything else follows. assembly.solve reports 0 degrees of freedom.
• A leg as a flexible subassembly (instance.add with "mode": "flexible"), placed twelve times from one source, its scale and sheet sizes passed through params. The aft legs are the same subassembly turned half a turn about z.
• One bar part in several configurations: bar is placed 48 times in four lengths, its length coming through params (bar_length). Ribs, crank segments and the two triangles are configurations too.
• Phase in the part. Each journal rod is a configuration with its own key_angle: the turn between the flats at its two ends. Its far flat and the datum the next throw mates to are drawn at that angle, so a throw's phase is in the geometry of its rod and not in a mate value. See Platform notes for what was tried first.
• Closed form against the solve: variable.measure of a joint position (position), and the linkage's own circle intersections written as document variables, compared at every sample by assert.add.
• Measured contact, balance and slip as outputs (variable.output) of the measured feet and the measured centre of mass (centerOfMass, from the materials of body.material).
• The foot's path as a trace (view.trace, see The motion).

The real thing

The linkage. Theo Jansen found the proportions of his leg by an evolutionary search and published them; the bars are the numbers below, in his units, with m the crank and (a, l) the offset of the fixed pivot from the axle.

What was read: Wang (2026), Table 1 and equations 1 to 3 (the numbers and the joints as circle intersections); the Wikipedia table Jansen Linkage Ratios; the OpenSCAD manual's Strandbeest example, whose code gives the numbers and a fixed choice of each intersection. Jansen's own book and site were not read for the numbers (his site's front page holds no text about them); that he published them is from those secondary sources. "Eleven holy numbers" is the phrase Wang uses while listing thirteen values, a to m; Wikipedia does not use it, and what the eleven count is not explained in the sources read.

Which intersection. Two circles meet twice, and thirteen numbers fit more than one leg. This model uses the branches of the OpenSCAD example (mirrored, as its fixed pivot is on the other side), with joint C above the fixed pivot. Own calculation, at 15 mm crank: this branch has a stride of 67.9 mm and 22.5 mm of lift, and its foot stays within 0.1 mm of its lowest height for 98 degrees of the crank. The other branch for C has a stride of 82.9 mm and stays that flat for far less of the turn; Wang's figures 1 and 2 show that other assembly (joint J2 below the pivot, foot x from about -60 to +25). A flat stance is the whole point of the linkage, so the flat branch is the one built, and that choice is this model's judgement, not a statement in Wang.

Sheet parts, laser cut. Bars, crank webs and frame ribs are 4 mm birch plywood. The two triangles are 4 mm walnut-faced birch plywood, not solid walnut: at 131 mm spans with 3.9 mm of web beside the pin holes a solid 4 mm walnut plate would split along the grain. Grain direction is free in the plywood; the walnut face runs along one side of each triangle, as nested. The drawn holes and outlines are finished sizes: the laser's kerf is compensated by its own offset (about 0.2 mm on a typical machine; not modelled). The smallest hole is the 4.2 mm pin hole in 4 mm sheet, so no hole is smaller than the sheet, as the bar and the rib assert. Every sheet part has rounded corners and a 0.5 mm chamfer (sanded after cutting).

The key. The phase of the crankshaft is in its geometry. Each crank web has a D-shaped journal bore, and each brass journal rod has a flat at both ends (rod_flat 2.5 mm from the axis, a 1.5 mm deep flat filed or milled); the turn between a rod's two flats is the phase between its two throws, and each rod carries its own turn (key_angle), one of -120 or 180 degrees here. The rod's flat lies 0.1 mm from the bore's flat, and the bore's round part 0.2 mm from the rod, so the flat is the tightest fit; a wrong angle makes the rod overlap the web, and eight clearance assertions see that at every sample. The hand crank is keyed to the last rod the same way, by a D-bore in its arm.

Turned and bought parts. Pins are 4 mm brass rod in 4.2 mm holes (0.1 mm radial play, which the model checks at three joints). Journal rods are 8 mm brass rod: they run in the 8.4 mm rib bearings with 0.2 mm of radial play and are seated, keyed and glued, in the 8.4 mm D bores of the webs and the hand crank's arm: 0.2 mm radial play on the round part and 0.1 mm at the flat. Washers are M4 to DIN 125-1 A (4.3 x 9 x 0.8 mm, as listed by Fabory and Westfield Fasteners). The crank-pin and hip spacers are brass tube of 7 mm outside diameter with a 4.3 mm bore, turned from 7 mm rod (no stock tube of that size is claimed). The longerons are 12 mm walnut dowels, and the foot pads 18 mm rubber discs glued to the tips. Masses come from assigned densities: birch and walnut-faced plywood 680, walnut dowels and knob 640, brass 8440 and rubber 1100 kg/m³, typical values and this model's assumption; they matter only for the centre of mass.

Sources read. Jichao Wang, Durability-Aware Multi-Objective Optimization of the Jansen Linkage, arXiv:2606.22129 (2026), Table 1, eq. 1 to 3, figures 1 and 2, read in the PDF; Jansen's linkage, Wikipedia, the ratio table; OpenSCAD User Manual, Strandbeest example, the numbers and the code of the joints. The washer sizes come from the listings of Fabory and Westfield Fasteners, seen as search results; the standard itself was not read. The linkage is Theo Jansen's; "Strandbeest" is his name for his works.

Own judgement. Module pitch, rib shape, bar width (12 mm), layer gap (1 mm) and the dark floor are design choices checked by this model, not taken from a source. This is a kinetic model: no load, no drive torque and no strength of the plywood are modelled or claimed.

Parts and assembly order

Layers, measured from the middle of a throw along the shaft (1 mm between layers, a washer in each gap between moving bars; between a web and its rib there is 1 mm of bare clearance, no washer, and the shaft's end float lets birch touch birch there, so wax those faces):

Three layers are enough because only bars j and k ever pass over the shaft, so they run between the webs, where the shaft is interrupted, and the journals start at the webs. Parts sharing a layer stay at least 11 mm apart over the turn at the default scale (own calculation at every 2 degrees of crank, confirmed by the collision check below).

To build it. The crankshaft is strung up first, the frame is closed round it, the legs go in, and the crank pins go in last. (Each pin points towards the middle of its throw, so a layer goes on by sliding it outwards.)

1. Cut the sheet parts and sand the chamfers. Cut the seven journal rods and file a flat on each end (the far flat is turned from the near flat by the rod's key_angle; a paper index glued round the rod sets it). Turn the spacers.
2. Glue a hip pin into each rib and the pins C, D, E and F into the triangles.
3. For each of the five inner rods, thread two ribs on its round middle (one rib's hip pin pointing to each end) and press a crank web onto each flat, flat into the D bore, until the shoulder of the rod meets the web; glue the webs to the rod. That makes five rod units; the two end rods make shorter units with one web and one rib each. Each rib turns freely on its rod. Hold each rod's flat against its bore's flat while the glue sets: the round part of the bore has 0.2 mm of play.
4. Lay the seven units in a line and pass the two walnut dowels through the top holes of all twelve ribs. Set the 31 mm between the webs of each throw with a spacer, and glue the ribs to the dowels.
5. Build the legs from each rib towards the middle of the throw: on the hip pin a spacer, the hip triangle, a washer and bar c, whose far hole goes on the foot triangle's knee pin (a washer first); bar f on the pins D and F; bar j on pin C; bar k on the knee pin. The crank ends of j and k hang free.
6. For each throw, turn it so that the crank pin's place lies clear of the rib (the rib's stem and beam cover only part of the turn). Line up the holes of the two webs, j and k, and slide a crank pin in from the gap outside one web: web, spacer, j, washer, k, the centre washer, then the other leg's k, washer, j, spacer and web. Glue it in the webs only.
7. Fit the hand crank's D bore onto the last rod's flat and glue it.
8. Secure the free ends of the triangle pins with a drop of adhesive on a washer or a light peen (this retention is not modelled). Wax the faces of the webs and ribs, which may touch in the shaft's 1 mm of end float.

The motion

The timeline t is one crank turn: the drive joint is -(crank_start + 360 deg * t). Everything else follows through the mates. The whole machine stands still; the floor deck slides along x by floor_board * t, in the direction a foot in stance moves, so that the feet stand on it. That slide is exactly one board per turn, and the board seams are one board apart, so the deck looks the same at t = 1 as at t = 0; the fixed platforms cover both ends of the deck, so no edge jumps either. The phases of the six throws are 0, 120, 240, 60, 180 and 300 degrees along the shaft (the order that keeps at least four feet on the floor with the centre of mass inside them). There are no free motions.

To see the path of a foot: view.trace {"point": "Fore[1]/Foot/Foot tip", "samples": 121, "grow": true} (a trace is view state and is not saved in the file, A-005).

Parameters

Checks

At rest: document.check is ok; assembly.solve is ok with 0 degrees of freedom.

Over the motion (motion.check, tools/assemblies.py check), at the defaults and at the corners of the ranges, at 73 samples of t (every 5 degrees of crank). It holds at the samples; what happens between them is not checked by these assertions.

A pin that fits too loosely (a 4.3 mm hole, 0.15 mm radial) can come back as notProven from motion.check rather than failed, because the clearance on near-coaxial bodies is proven only coarsely; a key flat too far from its bore (2.8 mm) comes back the same way. tools/assemblies.py check counts both as a failure.

Measured over the turn at the default size, by motion.check and view.trace: the foot's path is closed, 297.9 mm long (121 samples), with a stride of 135.8 mm and a lift of 44.9 mm (Jansen's numbers at crank 15 give 67.9 and 22.5, twice that here at scale 2). The machine's mass is 1.25 kg, the output machine_mass (measured over every body but the floor, from the stated densities); its centre of mass stays within 0.82 mm of the shaft in x and at y = 5.9 mm (the hand crank sits at one end). The fine-grained maximum of the slip is 3.64 mm (closed form, every eighth of a degree, own calculation), inside the 3.8 mm bound. The assertions hold at the corners of the public ranges too, and check-range passes for the assembly and for every part that has public sizes.

Collisions: tools/assemblies.py check asks for named collisions at 121 moments of the turn over the whole assembly (no pair may collide but the listed contacts, and none is listed). Nothing touches: the pins sit in their holes with their radial play, the feet come down to 0.1 mm above the deck.

What the samples do not cover: the crank angles between samples; no strength, friction, torque or power is modelled. The stance is a rigid-model statement: a foot counts as on the floor when it is within 0.375 × the scale (0.75 mm at the default) of its lowest height, because a rigid plywood walker cannot put all its feet on one plane at once.

The README in the model's repository has the rest (Files, Rebuild, Difficulty, Platform notes, Licence): the whole README on GitHub.