Chebyshev lambda linkage

{{Short description|Four-bar straight-line mechanism}}

[[File:Chebyshev Lambda Linkage.gif|thumb|Animation of the Chebyshev Lambda Linkage

Dimensions (unit length {{mvar|a}}):

{{legend-line|solid cyan|Link 2: {{mvar|a}}}}

{{legend-line|solid green|Link 4: {{math|2.5a}}}}

{{legend-line|solid yellow|Link 3: {{math|2.5a + 2.5a}}}}

Link 1 (horizontal distance between ground joints): {{math|2a}}]]

File:Tchebyshevs plantigrade machine.gif

File:Chebyshev Table Linkage.gifs: the Chebyshev Linkage and Chebyshev Lambda Linkage.]]

In kinematics, the Chebyshev Lambda Linkage{{Cite web|url=http://demonstrations.wolfram.com/ChebyshevsLambdaMechanism/|title=Chebyshev's Lambda Mechanism – Wolfram Demonstrations Project|website=demonstrations.wolfram.com}} is a four-bar linkage that converts rotational motion to approximate straight-line motion with approximate constant velocity.{{Cite book |url=http://www.designofmachinery.com/DOM/ |title=Design of Machinery |year=2011}} It is so-named because it looks like a lowercase Greek letter lambda (λ). 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.{{Cite book |url=http://www.designofmachinery.com/DOM/Chap_03_3ed_p134.pdf |title=DOM p134 Hoecken linkage }}

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

The linkage was first shown in Paris on the Exposition Universelle (1878) as "The Plantigrade Machine".{{Cite web|url=http://mech.spbstu.ru/Dzenushko_Dainis:_Walking_mechanisms_survey#The_Chebyshev_Walking_Mechanism|title = Dzenushko Dainis: Walking mechanisms survey – Department of Theoretical and Applied Mechanics}}{{Cite web |url=https://etudes.ru/en/etudes/chebyshev-plantigrade-machine/ |title=Tchebyshev's plantigrade machine — Mathematical Etudes |accessdate=2014-11-16 |url-status=dead |archive-url=https://web.archive.org/web/20170728024836/http://www.etudes.ru/en/etudes/chebyshev-plantigrade-machine |archivedate=2017-07-28 }} 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.{{Cite thesis |last1=Barlas |first1=Fırat |title=Design of a Mars Rover suspension mechanism |url=https://openaccess.iyte.edu.tr/xmlui/handle/11147/3449 |publisher=Izmir Institute of Technology |access-date=3 April 2021 |date=June 2004 |hdl=11147/3449|type=Master Thesis }} It was then designed, manufactured, and tested in the Earth Rover Project of Los Angeles City College Electronics Club.{{Citation|title=Moxie Video Intro It|url=https://vimeo.com/117774490|language=en|access-date=2022-11-17}}