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.


Saturday, December 4, 2010

Watt Straight-Line Mechanism

Watt's linkage (also known as the parallel linkage) is a type of mechanical linkage invented by James Watt to constrain the movement of a steam engine piston in a straight line. The idea of its genesis using links is contained in a letter he wrote to Matthew Boulton in June 1784.
"I have got a glimpse of a method of causing a piston rod to move up and down perpendicularly by only fixing it to a piece of iron upon the beam, without chains or perpendicular guides [...] and one of the most ingenious simple pieces of mechanics I have invented."
This linkage does not generate a true straight line motion, and indeed Watt did not claim it did so.

Watt's straight-line mechanism is used in the rear axle of some car suspensions. It intends to prevent relative sideways motion between the axle and body of the car. Watt’s linkage approximates a vertical straight line motion more closely, and does so while locating the center of the axle rather than toward one side of the vehicle.

It consists of two horizontal rods of equal length mounted at each side of the chassis. In between these two rods, a short vertical bar is connected. The center of this short vertical rod – the point which is constrained in a straight line motion - is mounted to the center of the axle. All pivoting points are free to rotate in a vertical plane.

Here is the video of Watt straight-line mechanism in Solid Edge ST 2D model.