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Chebyshev lambda linkage

Summary

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]

See also edit

References edit

  • Design of Machinery – esp' p134
  1. ^ "Chebyshev's Lambda Mechanism – Wolfram Demonstrations Project". demonstrations.wolfram.com.
  2. ^ Design of Machinery. 2011.
  3. ^ a b "Tchebyshev's plantigrade machine — Mathematical Etudes". Archived from the original on 2017-07-28. Retrieved 2014-11-16.
  4. ^ DOM p134 Hoecken linkage (PDF).
  5. ^ "Dzenushko Dainis: Walking mechanisms survey – Department of Theoretical and Applied Mechanics".
  6. ^ Barlas, Fırat (June 2004). Design of a Mars Rover suspension mechanism (Master Thesis). Izmir Institute of Technology. hdl:11147/3449. Retrieved 3 April 2021.
  7. ^ Moxie Video Intro It, retrieved 2022-11-17

External links edit

 
Wikimedia Commons has media related to Chebyshev's Lambda Mechanism.
  • Hoeckens approximate straight-line mechanism (diagram and table of lengths)
  • Hoeckens straight line linkage Archived 2011-07-06 at the Wayback Machine (Homemade example)
  • Video of computer simulation of Tchebychev walking machine (Стопоход Чебышева).
  • alexdenouden.nl – Rectilinear motion after "Tchebychev"
  • A simulation Archived 2011-07-25 at the Wayback Machine using the Molecular Workbench software
  • How does a Hoecken's Linkage Work? (Interactive Flash Animation)