Chebyshev lambda linkage

In kinematics, the Chebyshev Lambda Linkage[1] is a four-bar linkage that converts rotational motion to approximate straight-line motion with approximate constant velocity.[2] It is so-named because it looks like a lowercase Greek letter lambda (λ).[3] The precise design trades off straightness, lack of acceleration, and the proportion of the driving rotation that is spent in the linear portion of the full curve.[4]

Animation of the Chebyshev Lambda Linkage
Dimensions (unit length a):

  Link 2: a

  Link 4: 2.5a

  Link 3: 2.5a + 2.5a

Link 1 (horizontal distance between ground joints): 2a

Chebyshev's plantigrade machine.

A Chebyshev Translating Table Linkage, which combines together two cognate linkages: the Chebyshev Linkage and Chebyshev Lambda Linkage.

The example to the right spends over half of the cycle in the near straight portion. Coupler (link 3) point stays within 1% positional tolerance with intersecting the ideal straight line 6 times.

The linkage was first shown in Paris on the Exposition Universelle (1878) as "The Plantigrade Machine".[5][3] The Chebyshev Lambda Linkage is a cognate linkage of the Chebyshev linkage.

The Chebyshev Lambda Linkage is used in vehicle suspension mechanisms, walking robots and rover wheel mechanisms. In 2004, a study completed as a Master of Science Thesis at Izmir Institute of Technology introduced a new mechanism design by combining two symmetrical Lambda linkages to distribute the force evenly on to ground with providing the straight vertical wheel motion.[6] It was then designed, manufactured and tested in the Earth Rover Project of Los Angeles City College Electronics Club.[7]