Chebyshev linkage

Chebyshev linkage
Chebyshev linkage

The Chebyshev linkage is a mechanical linkage that converts rotational motion to approximate straight-line motion.

It was invented by the 19th century mathematician Pafnuty Chebyshev who studied theoretical problems in kinematic mechanisms. One of the problems was the construction of a linkage that converts a rotary motion into an approximate straight line motion. This was also studied by James Watt in his improvements to the steam engine.[1]

The straight line linkage confines the point P — the midpoint on the link L3 — on a straight line at the two extremes and at the center of travel. (L1, L2, L3, and L4 are as shown in the illustration.) Between those points, point P deviates slightly from a perfect straight line. The proportions between the links are

L_1 : L_2 : L_3 = 2 : 2.5 : 1 = 4 : 5 : 2. \,

Point P is in the middle of L3. This relationship assures that the link L3 lies vertically when it is at the extremes of its travel.[2]

The lengths are related mathematically as follows:

L_4=L_3+\sqrt{L_2^2 - L_1^2}. \,

See also

References

  1. ^ Cornell university - Cross link straight-line mechanism
  2. ^ Brock institute for advanced studies - Tchebicheff's linkage

External links


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Linkage (mechanical) — This article is about assemblies of links designed to manage forces and movement. For other uses, see Linkage. Variable stroke engine (Autocar Handbook, Ninth edition) A mechanical linkage is an assembly of bodies connected together to manage… …   Wikipedia

  • Chebyshev — Pafnouti Tchebychev Pafnouti Tchebychev Pafnouti Lvovitch Tchebychev (en russe : Пафнутий Львович Чебышёв) (4 mai 1821 à Okatovo, près de Boro …   Wikipédia en Français

  • Pafnuty Chebyshev — Chebyshev redirects here. For other uses, see Chebyshev (disambiguation). Pafnuty Chebyshev Pafnuty Lvovich Chebyshev Born May 16, 1821 …   Wikipedia

  • Chebyshev, Pafnuty Lvovich — ▪ Russian mathematician born May 4 [May 16, New Style], 1821, Okatovo, Russia died November 26 [December 8], 1894, St. Petersburg  founder of the St. Petersburg mathematical school (sometimes called the Chebyshev school), who is remembered… …   Universalium

  • Sarrus linkage — The Sarrus linkage, invented in 1853 by Pierre Frédéric Sarrus, is a mechanical linkage to convert a limited circular motion to a linear motion without reference guideways. The linkage uses two perpendicular hinged rectangular plates positioned… …   Wikipedia

  • Pafnuty Chebyshev — Pafnouti Tchebychev Pafnouti Tchebychev Pafnouti Lvovitch Tchebychev (en russe : Пафнутий Львович Чебышёв) (4 mai 1821 à Okatovo, près de Boro …   Wikipédia en Français

  • Механизм Чебышева — Механизм Чебышева  это механизм, преобразующий вращательное движение в приближённое к прямолинейному движение. Был изобретён в 19 м веке математиком Пафнутием Чебышевым, проводившим исследования теоретических проблем кинематических… …   Википедия

  • Straight line mechanism — In the late seventeenth century, before the development of the milling machine, it was extremely difficult to machine straight, flat surfaces. For this reason, good prismatic pairs without backlash were not easy to make. During that era, much… …   Wikipedia

  • Cheval de Tchebychev — Le cheval de Tchebychev est une liaison mécanique qui convertit un mouvement de rotation en un mouvement proche de la ligne droite. Il a été inventé au XIXe siècle par le mathématicien Pafnouti Tchebychev qui a étudié les problèmes de la… …   Wikipédia en Français

  • Chebychev — Pafnouti Tchebychev Pafnouti Tchebychev Pafnouti Lvovitch Tchebychev (en russe : Пафнутий Львович Чебышёв) (4 mai 1821 à Okatovo, près de Boro …   Wikipédia en Français

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”