The Klann linkage uses a crank, two rockers, a connecting member and a bent leg to turn rotary motion into a stepping path. The animation follows the pivot coordinates in Table 1 of Joseph C. Klann’s walking-device patent. Change crank radius to scale the whole leg, or change speed to follow the same path at a different rate.
Klann Linkage Interactive Calculator
Explore the calculated foot path while the frame stays fixed. The travel factor is a separate assumption about body advance per cycle; it does not change the links or predict traction. Compare that assumption with the actual path dimensions shown in the animation.
Equation Used
Table 1 provides rounded pivot coordinates for one Klann arrangement. The model derives rigid lengths and member angles from its extended position, then solves their motion by circle intersections. All dimensions scale with crank radius. Foot excursion is the full vertical range relative to the stationary frame, not obstacle clearance. The animation runs at one tenth of the entered RPM. At zero RPM the leg stops and cycle time is undefined. No slip, ground-contact, stability, load or skipping-risk model is included.
One crank, two rockers and a bent leg
The frame holds three fixed pivots: upper-rocker pivot A, lower-rocker pivot B and crank shaft O. The crank turns pin C. The rigid connecting member carries C, elbow E and knee K; the lower rocker joins B to E. This constrains the motion of the knee as the crank turns.
The upper rocker joins A to hip H. Hip H, knee K and foot F belong to one rigid bent leg. Solving the two rocker constraints therefore determines the foot position. The upper and lower rockers both oscillate while the crank completes full turns.
The green curve joins the calculated foot positions. The frame stays still so the shape is easy to inspect. The shallow lower part and raised return come from the linkage geometry; the drawing does not hold the foot artificially on a horizontal line.
Geometry from the patent’s Table 1
The example starts with these coordinates, in the table’s reference units: A=(1.366,1.366), B=(1.009,0.574), O=(1.599,0.750), C=(1.331,0.750), E=(0.741,0.750), K=(0.232,0.866), H=(0.866,1.500) and F=(0,0). These correspond to patent points 9, 11, 15, 29x, 27x, 35x, 37x and 33x respectively.
The reference crank radius is |O−C|=0.268. For an entered radius r in millimetres, multiply every coordinate and link dimension by s=r/0.268. The connecting member retains all three distances between C, E and K; the bent leg retains all three distances between H, K and F.
For each crank angle, the elbow is the intersection of circles about B and C. The rigid connecting member then locates K. The hip is found from circles about A and K, and the rigid bent leg locates F. Path extrema are refined numerically from 1,440 equally spaced crank angles.
A 20 mm crank at 60 rpm
With r=20 mm, the table geometry gives a foot path approximately 75.3 mm wide and 39.4 mm high relative to the frame. One crank cycle takes 1 second at 60 rpm; the slowed display takes 10 seconds.
If you separately assume body advance of four crank radii per cycle, S=4×20=80 mm and ideal speed is 80×60/60=80 mm/s. That result follows from the entered assumption. The 80 mm assumed advance is not the calculated 75.3 mm foot-path width, and neither establishes actual ground speed.
Changing the factor from 4 to 3 changes assumed advance to 60 mm and ideal speed to 60 mm/s. The leg dimensions and foot path remain the same. Doubling crank radius, by contrast, scales every geometric length and the path dimensions by two.
Walking mechanisms and kinematics studies
Klann’s patent describes single-leg motion and arrangements of multiple legs on a common frame. The mechanism is useful for studying how a rotary drive and two rocker constraints can shape an end-point trajectory. Repeated legs and their relative phases can support a walking-machine concept.
A pair phased half a revolution apart does not, by itself, establish a stable machine. The number and placement of supporting feet, centre of mass and contact with the ground determine whether a walker tips or slips. This illustration solves one leg relative to its frame.
What the geometric model can tell you
Uniform scaling preserves the ideal path shape. It does not preserve structural strength, joint loading or drive requirements. The diagram shows separate axial layers for links that cross in projection; it does not specify bar thickness, bearing fits or fabrication tolerances.
The patent coordinates are rounded, so the model is an approximation to that tabulated geometry. The shallow portion of the computed path is not exactly horizontal. No universal four-to-one advance ratio or fixed skipping-speed threshold follows from the linkage alone.
Use measured advance per cycle in the travel-factor comparison when it is available for a particular walker and surface. Drive torque and motor choice require loads, friction, speed, inertia and contact forces in addition to the geometry.
Frequently asked questions
Why are there three fixed pivots?
The crank and both rockers are attached to the frame. Each rocker constrains a different point on the moving connecting member or leg.
Is the green foot path calculated?
Yes. It is obtained from fixed link lengths and rigid member shapes derived from Table 1 of the Klann patent.
Why does changing the travel factor leave the leg unchanged?
The factor is an assumed body advance per cycle divided by crank radius. It is used only in the travel and ideal-speed comparison; it is not a link dimension.
Does the foot-path height equal obstacle clearance?
No. It is the vertical excursion relative to the fixed frame. Body motion and ground contact must also be considered for obstacle clearance.
Does a 180-degree phase difference guarantee stability?
No. Stability also depends on how many feet support the body, their positions, the centre of mass and the ground.
What happens at zero speed?
The leg stays still and assumed forward speed is zero. Cycle time is undefined because the crank does not complete a revolution.
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