http://debianws.lexgopc.com/wiki143/index.php?action=history&feed=atom&title=Chebyshev_lambda_linkageChebyshev lambda linkage - Revision history2026-05-04T21:33:19ZRevision history for this page on the wikiMediaWiki 1.43.1http://debianws.lexgopc.com/wiki143/index.php?title=Chebyshev_lambda_linkage&diff=2636449&oldid=previmported>LucasBrown at 06:12, 9 December 20242024-12-09T06:12:14Z<p></p>
<p><b>New page</b></p><div>{{Short description|Four-bar straight-line mechanism}}<br />
[[File:Chebyshev Lambda Linkage.gif|thumb|'''Animation of the Chebyshev Lambda Linkage'''<br><br />
Dimensions (unit length {{mvar|a}}):<br />
{{legend-line|solid cyan|Link 2: {{mvar|a}}}}<br />
{{legend-line|solid green|Link 4: {{math|2.5''a''}}}}<br />
{{legend-line|solid yellow|Link 3: {{math|2.5''a'' + 2.5''a''}}}}<br />
Link 1 (horizontal distance between ground joints): {{math|2''a''}}]]<br />
[[File:Tchebyshevs plantigrade machine.gif|thumb|Chebyshev's plantigrade machine.]]<br />
[[File:Chebyshev Table Linkage.gif|thumb|A Chebyshev Translating Table Linkage, which combines together two [[cognate linkage]]s: the [[Chebyshev linkage|Chebyshev Linkage]] and Chebyshev Lambda Linkage.]]<br />
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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><br />
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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.<br />
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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]].<br />
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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.<ref>{{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 }}</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><br />
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== See also ==<br />
<!-- New links in alphabetical order please --><br />
*[[Chebyshev linkage]], the [[Cognate linkage|cognate]] of the Chebyshev lambda linkage.<br />
*[[Hoeckens linkage]], a linkage that produces a very similar locus using one less link but an additional slider.<br />
*[[Leg mechanism]]<br />
*[[Straight line mechanism]]<br />
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== References ==<br />
*[http://www.designofmachinery.com/DOM/ Design of Machinery – esp' p134]<br />
{{Reflist}}<br />
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== External links ==<br />
{{Commons category|Chebyshev's Lambda Mechanism}}<br />
*[http://www.designofmachinery.com/DOM/Chap_03_3ed_p134.pdf Hoeckens approximate straight-line mechanism] (diagram and table of lengths)<br />
*[http://flash.lakeheadu.ca/~kliu/hoekens.jpg Hoeckens straight line linkage] {{Webarchive|url=https://web.archive.org/web/20110706184142/http://flash.lakeheadu.ca/~kliu/hoekens.jpg |date=2011-07-06 }} (Homemade example)<br />
*[https://web.archive.org/web/20141129015429/http://www.etudes.ru/en/etudes/stopohod/ Video of computer simulation of Tchebychev walking machine] (Стопоход Чебышева).<br />
*[http://www.alexdenouden.nl/artikelen2/vierstangen.htm alexdenouden.nl] – Rectilinear motion after "Tchebychev"<br />
*[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<br />
*[http://www.mekanizmalar.com/hoekens_linkage.html How does a Hoecken's Linkage Work?] (Interactive Flash Animation)<br />
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[[Category:Straight line mechanisms]]<br />
[[Category:Linkages (mechanical)]]<br />
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