Chebyshev lambda linkage: Difference between revisions

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{{Short description|Linkage that generates approximateFour-bar straight-line motionmechanism}}

[[ImageFile:Chebyshev Lambda Linkage.gif|thumb|'''Animation of the Chebyshev's Lambda Linkage'''<br><br>Dimensions:<br>Cyan Link = a<br>Green Link = 2.5a<br>Yellow Link = 2.5a + 2.5a<br>Horizontal Distance between Ground Joints = 2a<br>]]

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

[[File:Tchebyshevs plantigrade machine.gif|thumb|Chebyshev's plantigrade machine]]

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

[[File:Chebyshev Table Linkage.gif|thumb|Chebyshev's Translating Table Linkage, which combines together two [[Cognate linkage|cognate linkages]]: [[Chebyshev linkage|Chebyshev's Linkage]] and Chebyshev's Lambda Linkage]]

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

[[File:Lambda mechanism.svg|upright=0.5|thumb|Lambda Mechanism]]

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

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

[[File:Tchebyshevs plantigrade machine.gif|thumb|Chebyshev's plantigrade machine.]]

[[File:Chebyshev Table Linkage.gif|thumb|A Chebyshev's Translating Table Linkage, which combines together two [[Cognatecognate linkage|cognate linkages]]s: the [[Chebyshev linkage|Chebyshev's Linkage]] and Chebyshev's Lambda Linkage.]]

TheIn [[kinematics]], the '''Chebyshev's 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 mechanismlinkage]] that converts [[rotational motion]] to approximate [[straight-line motion]] with approximate constant velocity.<ref name=DOM>{{citeCite 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>{{citeCite 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>{{citeCite web |url=https://etudes.ru/en/etudes/chebyshev-plantigrade-machine/ |title=Tchebyshev's plantigrade machine — Mathematical Etudes |accessdate=2014-11-16 |url-status=dead |archiveurlarchive-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's Lambda Mechanism is a [[cognate linkage]] of the [[Chebyshev linkage]].

The Chebyshev's Lambda MechanismLinkage 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 Mechanismlinkages to distribute the force evenly on to ground with providing the straight vertical wheel motion.<ref>{{citeCite 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>

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 |archiveurl=https://web.archive.org/web/20170728024836/http://www.etudes.ru/en/etudes/chebyshev-plantigrade-machine |archivedate=2017-07-28 }}</ref>

== See also ==

The Chebyshev's Lambda Mechanism is so-named because it looks like a lowercase Greek letter [[lambda]].<ref name=etudes/>

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The *[[Chebyshev's Lambdalinkage]], Mechanism is athe [[cognateCognate linkage|cognate]] of the [[Chebyshev lambda linkage]].

Chebyshev's Lambda Mechanism 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]], a new mechanism design introduced by combining two symmetrical Lambda Mechanism to distribute the force evenly on to ground with providing the straight vertical wheel motion.<ref>{{cite web |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}}</ref>

*[[Hoeckens linkage]], a linkage that produces a very similar locus using one less link but an additional slider.

*[[Leg mechanism]]

Double Lambda Chebyshev Mechanism rover suspension design manufactured and tested in Earth Rover Project of Los Angeles City College Electronics Club<ref>https://vimeo.com/117774490 Video of The Earth Rover Moxie</ref>

==See also==

*[[Straight line mechanism]]

*[[Peaucellier–Lipkin linkage]] (an 8-bar linkage)

*[[Chebyshev linkage]]

*[[Four-bar linkage]]

*[[Hoeckens linkage]]

*[[Leg mechanism]]

== References ==

*[http://www.designofmachinery.com/DOM/ Design of Machinery -– esp' p134]

{{reflistReflist}}

== External links ==

{{commonsCommons category|Chebyshev's Lambda Mechanism}}

*[http://www.designofmachinery.com/DOM/Chap_03_3ed_p134.pdf Hoeckens approximate straight-line mechanism] (diagram and table of lengths)

*[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)

*[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)

[[Category:Straight line mechanisms]]

[[Category:Linkages (mechanical)]]

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[[Category:Straight line mechanisms]]