Jansen’s linkage converts a rotating crank into the stepping motion used in Theo Jansen’s Strandbeest sculptures. Two rigid triangular members and connecting bars guide the foot around a closed path. This calculator solves the link positions and plots the resulting foot trajectory relative to a stationary frame.
Jansen’s Linkage Interactive Calculator
Scale the leg, vary its crank radius, and compare two identical leg views with a chosen phase difference. Each bar retains its length. A combination that cannot complete a crank turn shows no foot-path result.
Equation Used
At L=100 mm, the listed link lengths below are in millimetres. All lengths except the independently entered crank radius scale by s. Circle intersections determine the joints on the illustrated assembly branch. Path extrema are numerically refined from 1,440 crank positions. Each view has its own stationary frame; the drawings are separated for clarity and do not specify spacing on a walker. The animation takes 5 seconds per turn. No ground contact, body travel, stability or drive torque is calculated.
Two rigid triangles shape the foot path
The fixed leg pivot B and crank shaft O are attached to the frame. Crank OC drives pin C. Connecting rods CD and CF move the upper and lower parts of the leg. Triangle BDE rocks about B; the other rigid triangle FGH carries the foot H. Link EG joins the two triangular members, and BF supports their lower junction.
Only marked circular joints connect links. A projected crossing without a joint is not a connection: separate bars can occupy different parallel planes. The filled triangles show rigid bodies, not flexible panels.
The two animated views use the same dimensions. View B is advanced by the entered phase angle. Changing this angle changes their relative timing but does not change either individual foot path.
Link dimensions and position calculation
The dimensioned diagram in Cleveland State University’s The Jansen Linkage gives the following proportions. At the 100 mm scale setting they become millimetres: BD=41.5, BE=40.1, DE=55.8, EG=39.4, BF=39.3, FG=36.7, GH=65.7, FH=49.0, CD=50.0 and CF=61.9. The shaft offset from B is 38.0 horizontally and 7.8 vertically. The reference crank is 15.0.
For scale s=L/100, multiply those dimensions and the fixed offsets by s. The crank radius r remains the entered value. The next joint is found at the intersection of two circles whose centres are known pivots and whose radii are the adjoining link lengths. The selected intersection follows the assembly shown in the drawing.
The foot path is the sequence of H positions for a complete crank turn. Its horizontal span and total vertical excursion come from the extrema of that curve. The fixed-pivot distance is s√(38²+7.8²), approximately 38.7923s mm. The scale reference is not the overall leg height.
Example with the reference crank
At L=100 mm and r=15 mm, the computed foot path spans approximately 67.9 mm horizontally and 22.5 mm vertically. Fixed-pivot spacing is approximately 38.8 mm. At a 180-degree phase offset, the two views are half a crank revolution apart.
Double L to 200 mm and r to 30 mm to scale the complete geometry uniformly: both path dimensions double. Doubling L alone changes the crank-to-link proportions, so the path shape also changes.
From a leg path to a walking machine
Jansen uses repeated leg mechanisms in his walking sculptures. A single crank can coordinate several legs, while their phase offsets determine when each foot traverses the lower or upper part of its path. The geometry is also useful in teaching linkage closure and studying alternative foot trajectories.
The lower part of this foot path is relatively shallow, but it is not a perfectly straight line. A full walker adds a moving body, multiple feet and ground interaction. This fixed-frame illustration does not establish stride length, support stability, obstacle clearance or motor size.
Crank changes can prevent a complete turn
A circle-intersection solution exists only when the distance between its centres lies between the difference and the sum of the two radii. A crank setting can satisfy that condition at one position yet fail elsewhere in the revolution.
The calculator checks the selected assembly through a complete turn before displaying its path. When it cannot complete the turn, path dimensions are blank and the linkage drawing is withheld. Fixed-pivot spacing and the entered phase remain available. Reduce the crank radius or increase the scale to explore another combination.
Joint clearance, bar thickness, flexibility, inertia and collisions between physical parts require additional design checks. The diagram places crossing links in separate axial layers; it is not a fabrication drawing or a load-capacity calculation.
Frequently asked questions
Is the green curve calculated from the links?
Yes. It joins foot positions obtained by solving the rigid-link geometry through a full crank revolution. It is not a prescribed path imposed on the foot.
Why do some settings show no path?
The selected link lengths and crank cannot complete a full revolution on the illustrated assembly branch. Drawing the leg through those positions would require a link to change length or a joint to disconnect.
Does the phase slider change the path shape?
No. It advances the second leg by the selected crank angle. The two views follow the same path at different times.
Is vertical excursion the clearance over an obstacle?
No. It is the full vertical range of the foot relative to the fixed frame. Real obstacle clearance depends on body motion and the ground-contact conditions.
How do I scale the same path?
Multiply both the scale reference and crank radius by the same factor. All link lengths and the foot path then scale by that factor.
Can this calculator select a motor?
No. Motor sizing requires loads, speed, inertia, friction and ground-contact forces that are outside this geometric calculation.
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