Sunday, December 19, 2010

Chebyschev Straight-line Mechanism

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

It was invented by the 19th century mathematician Pafnuty Chebyschev 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. (Read more info about Watt Straight-line Mechanism)
The straight-line linkage of Chebyschev confines the point P — the midpoint on the link AB — 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

O2O4 : O2A : AB = 200 : 250 : 100 = 4 : 5 : 2

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


No comments: