Chebyshev linkage
From Wikipedia, the free encyclopedia
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. Between those points, point P deviates slightly from a perfect straight line. The proportions between the links are: L1:L2:L3 = 2:2.5:1. 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]
Mathematical relationship:
For example:
5 = 2 + 3
[edit] References
- ^ Cornell university - Cross link straight-line mechanism
- ^ Brock institute for advanced studies - Tchebicheff's linkage
[edit] See also
[edit] External links
- Cornell university, "How to draw a straight line, by A.B. Kempe, B.A."
- A simulation using the Molecular Workbench software
