Chebyshev lambda linkage: Difference between revisions

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In [[kinematics]], the '''Chebyshev Lambda Linkage'''<ref name="Wolfram">{{Cite web|url=http://demonstrations.wolfram.com/ChebyshevsLambdaMechanism/|title=Chebyshev's Lambda Mechanism – Wolfram Demonstrations Project|website=demonstrations.wolfram.com}}</ref> is a [[four-bar linkage]] that converts [[rotational motion]] to approximate [[straight-line motion]] with approximate constant velocity.<ref name=DOM>{{Cite book |url=http://www.designofmachinery.com/DOM/ |title=Design of Machinery |year=2011}}</ref> It is so-named because it looks like a lowercase Greek letter [[lambda]] (λ).<ref name=etudes /> 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.<ref name=DOM134>{{Cite book |url=http://www.designofmachinery.com/DOM/Chap_03_3ed_p134.pdf |title=DOM p134 Hoecken linkage }}</ref>

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

The linkage was first shown in Paris on the [[Exposition Universelle (1878)]] as "The Plantigrade Machine".<ref>{{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}}</ref><ref name=etudes>{{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 }}</ref> The Chebyshev Lambda Linkage is a [[cognate linkage]] of the [[Chebyshev linkage]].

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 introduced by combining two symmetrical Lambda linkages to distribute the force evenly on to ground with providing the straight vertical wheel motion.<ref>{{Cite webthesis |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 }}</ref> It was then designed, manufactured, and tested in the Earth Rover Project of Los Angeles City College Electronics Club.<ref>{{Citation|title=Moxie Video Intro It|url=https://vimeo.com/117774490|language=en|access-date=2022-11-17}}</ref>

== See also ==

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*[https://web.archive.org/web/20141129015429/http://www.etudes.ru/en/etudes/stopohod/ Video of computer simulation of Tchebychev walking machine] (Стопоход Чебышева).

*[http://www.alexdenouden.nl/artikelen2/vierstangen.htm alexdenouden.nl] – Rectilinear motion after "Tchebychev"

*[http://mw.concord.org/modeler1.3/mirror/mechanics/peaucellier.html A simulation] {{Webarchive|url=https://web.archive.org/web/20110725190957/http://mw.concord.org/modeler1.3/mirror/mechanics/peaucellier.html |date=2011-07-25 }} using the Molecular Workbench software

*[http://www.mekanizmalar.com/hoekens_linkage.html How does a Hoecken's Linkage Work?] (Interactive Flash Animation)