In kinematics, the Chebyshev Lambda Linkage is a

four-bar linkage In the study of mechanisms, a four-bar linkage, also called a four-bar, is the simplest closed-chain movable linkage. It consists of four bodies, called ''bars'' or ''links'', connected in a loop by four joints. Generally, the joints are configu ...

that converts

rotational motion Rotation, or spin, is the circular movement of an object around a ''axis of rotation, central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A t ...

to approximate

straight-line motion Linear motion, also called rectilinear motion, is one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension. The linear motion can be of two types: uniform linear motion, with ...

with approximate constant velocity. It is so-named because it looks like a lowercase Greek letter

lambda Lambda (}, ''lám(b)da'') is the 11th letter of the Greek alphabet, representing the voiced alveolar lateral approximant . In the system of Greek numerals, lambda has a value of 30. Lambda is derived from the Phoenician Lamed . Lambda gave ris ...

(λ). The precise design trades off straightness, lack of

acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...

, and the proportion of the driving rotation that is spent in the linear portion of the full curve. The example to the right spends over half of the cycle in the near straight portion. Coupler (link 3) point stays within 1% positional tolerance with intersecting the ideal straight line 6 times. The linkage was first shown in Paris on the

Exposition Universelle (1878) The third Paris World's Fair, called an Exposition Universelle in French, was held from 1 May to 10 November 1878. It celebrated the recovery of France after the 1870–71 Franco-Prussian War. Construction The buildings and the fairgroun ...

as "The Plantigrade Machine". The Chebyshev Lambda Linkage is a

cognate linkage In kinematics, cognate linkages are linkages that ensure the same coupler curve geometry or input-output relationship, while being dimensionally dissimilar. In case of four-bar linkage coupler cognates, the Roberts–Chebyshev Theorem, after ...

of the

Chebyshev linkage In kinematics, Chebyshev's linkage is a four-bar linkage that converts rotational motion to approximate linear motion. It was invented by the 19th-century mathematician Pafnuty Chebyshev, who studied theoretical problems in kinematic mechani ...

. 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. It was then designed, manufactured and tested in the Earth Rover Project of Los Angeles City College Electronics Club.

References

Design of Machinery – esp' p134

External links

Hoeckens approximate straight-line mechanism
(diagram and table of lengths)
Hoeckens straight line linkage
(Homemade example)
Video of computer simulation of Tchebychev walking machine
(Стопоход Чебышева).

– Rectilinear motion after "Tchebychev"

using the Molecular Workbench software

(Interactive Flash Animation) Straight line mechanisms Linkages (mechanical) {{technology-stub

See also

References

External links