kinematics In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion such as linked machine parts are also described as kinematics. Kinematics is concerned with s ...

, the Chebyshev Lambda Linkage is a

four-bar linkage In the study of Mechanism (engineering), mechanisms, a four-bar linkage, also called a four-bar, is the simplest closed-Kinematic chain, chain movable linkage (mechanical), linkage. It consists of four Rigid body, bodies, called ''bars'' or ''link ...

that converts

rotational motion Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis interse ...

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

lambda Lambda (; uppercase , lowercase ; , ''lám(b)da'') is the eleventh 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 Phoen ...

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

acceleration In mechanics, acceleration is the Rate (mathematics), rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are Euclidean vector, vector ...

, 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. The coupler (link 3) point stays within 1% positional tolerance while intersecting the ideal straight line 6 times. The linkage was first shown in Paris on the

Exposition Universelle (1878) The 1878 Universal Exposition (, ), also known as the 1878 Paris Exposition, 1878 World Fair, or 1878 World Expo, was a world's fair held in Paris, French Third Republic, France, from 1 May to 10 November 1878, to celebrate the recovery of Franc ...

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 Mechanism ...

. 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