Klann linkage

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Underwater walking robot, using Klann leg linkages in laser-cut and anodised aluminium.[1]

The Klann linkage is a planar mechanism designed to simulate the gait of legged animal and function as a wheel replacement. The linkage consists of the frame, a crank, two grounded rockers, and two couplers all connected by pivot joints.

The proportions of each of the links in the mechanism are defined to optimize the linearity of the foot for one-half of the rotation of the crank. The remaining rotation of the crank allows the foot to be raised to a predetermined height before returning to the starting position and repeating the cycle. Two of these linkages coupled together at the crank and one-half cycle out of phase with each other will allow the frame of a vehicle to travel parallel to the ground.

The Klann linkage provides many of the benefits of more advanced walking vehicles without some of their limitations. It can step over curbs, climb stairs, or travel into areas that are currently not accessible with wheels but does not require microprocessor control or multitudes of actuator mechanisms. It fits into the technological space between these walking devices and axle-driven wheels.


These figures show a single linkage in the fully extended, mid-stride, retracted, and lifted positions of the walking cycle. These four figures show the crank (rightmost link in the first figure on the left with the extended pin) in the 0, 90, 180, and 270 degree positions.
This is a repeating animation of the legs in motion with the near legs of each set outlined in blue. A reasonable understanding of the functioning of the linkage can be gained by focusing on a specific point and following it through several cycles. Each of the pivot points is displayed in green. The three positions grounded to the frame for each leg are stationary. The upper and lower rockers move back and forth along a fixed arc and the crank traces out a circle.
Movement paths of each point

Example Leg[edit]

example leg illustrated

In US Patent 6,260,862 there is a set of coordinates for an example leg:

Point X Y Description
9 1.366 1.366 first rocker arm axle
11 1.009 0.574 second rocker arm axle
15 1.599 0.750 crank shaft
fully extended ground stride position
27X 0.741 0.750 elbow joint
29x 1.331 0.750 crank
33x 0.000 0.000 foot
35x 0.232 0.866 knee joint/axle
37x 0.866 1.500 hip joint
grounded gait position
27Y 1.277 0.750 elbow joint
29y 1.867 0.750 crank
33y 1.000 0.000 foot
35y 0.768 0.866 knee joint/axle
37y 1.000 1.732 hip joint


The Klann linkage was developed by Joe Klann in 1994 as an expansion of Burmester curves which are used to develop four-bar double-rocker linkages such as harbor crane booms.[2] It is categorized as a modified Stephenson type III kinematic chain.

  • U.S. Provisional Application Ser. No. 60/074,425, was filed on Feb. 11, 1998
  • US Patent 6,260,862,[3] issued July 17, 2001
  • US Patent 6,364,040,[4] issued April 2, 2002
  • US Patent 6,478,314,[5] issued November 12, 2002

See also[edit]


  1. ^ Rooney, T., Pearson, M., Welsby, J., Horsfield, I., Sewell, R. and Dogramadzi, S. (6–8 September 2011), Artificial active whiskers for guiding underwater autonomous walking robots (PDF), CLAWAR 2011, Paris, France 
  2. ^ Enable Text, linkage design notes.
  3. ^ U.S. Patent 6,260,862
  4. ^ U.S. Patent 6,364,040
  5. ^ U.S. Patent 6,478,314

External links[edit]