Watt's linkage

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Animated depiction of Watt’s linkage
Hand-drawn diagram by James Watt (1808) in a letter to his son, describing how he arrived at the design.[1]

Watt's linkage (also known as the parallel linkage) is a type of mechanical linkage invented by James Watt (19 January 1736 – 25 August 1819) in which the central moving point of the linkage is constrained to travel on an approximation to a straight line. Its applications include doubling the power of a piston engine by allowing two pistons to connect to a single beam, and, in automobile suspensions, allowing the axle of a vehicle to travel vertically while preventing sideways motion.

Contents

Description

Watt's linkage consists of a chain of three rods, two longer and equal length ones on the outside ends of the chain, connected by a short rod in the middle. The outer endpoints of the long rods are fixed in place relative to each other, and otherwise the three rods are free to pivot around the joints where they meet. Thus, counting the fixed-length connection between the outer endpoints as another bar, Watt's linkage is an example of a four-bar linkage.

History

The idea of its genesis using links is contained in a letter Watt 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.[2]

Shape traced by the linkage

This linkage does not generate a true straight line motion, and indeed Watt did not claim it did so. Rather, it traces out Watt's curve, a lemniscate or figure eight shaped curve; when the lengths of its bars and its base are chosen to form a crossed square, it traces the lemniscate of Bernoulli.[3] In a letter to Boulton on 11 September 1784 Watt describes the linkage as follows.

The convexities of the arches, lying in contrary directions, there is a certain point in the connecting-lever, which has very little sensible variation from a straight line.

Although the Peaucellier–Lipkin linkage and Hart's inversor generate true straight-line motion, Watt's linkage has the advantage of much greater simplicity than these other linkages. It is similar in this respect to the Chebyshev linkage, a different linkage that produces approximate straight-line motion; however, in the case of Watt's linkage, the motion is perpendicular to the line between its two endpoints, whereas in the Chebyshev linkage the motion is parallel to this line.

Applications

Double piston

Watt intended his linkage to enable a piston acted upon by steam on alternate sides of it (double acting) to be connected to the beam of a beam engine, doubling its power. This required replacing the chain, used in the single piston configuration, in which steam acted only on one side of the piston (only pulling). Watt's linkage used rigid connectors that prevented the piston binding in its containing cylinder.[4] This configuration also resulted in a smoother motion of the beam, facilitating its adaptation to rotative motion.

Automobile suspension

Watt's linkage as part of an automobile suspension
Watt's linkage used in a 1998 Ford Ranger EV
The above image with the linkage movement animated

Watt's linkage is used in the rear axle of some car suspensions as an improvement over the Panhard rod, which was designed in the early twentieth century. Both methods intend 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 centre of the axle rather than toward one side of the vehicle, as more commonly used when fitting a long Panhard rod.[5]

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.

In a way, Watt’s linkage can be seen as two Panhard rods mounted opposite each other. In Watt’s arrangement, however, the opposing curved movements introduced by the pivoting Panhard rods are compensated by the short vertical rotating bar.

The linkage can be inverted, in which case the centre P is attached to the body, and L1 and L3 mount to the axle. This reduces the unsprung mass and changes the kinematics slightly. This is used on Australian V8 Supercars.

Watt's linkage can also be used to prevent axle movement in the longitudinal direction of the car; however, this is more common in racing suspension systems. This application usually involves two Watt's linkages on each side of the axle, mounted parallel to the driving direction.

See also

References

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  1. Franz Reuleaux, The Kinematics of Machinery (1876), page 4.
  2. As quoted in the 1890 Encyclopædia Britannica, "James Watt", Vol. 24, p. 413.
  3. Bryant, John; Sangwin, Christopher J. (2008), How round is your circle? Where Engineering and Mathematics Meet, Princeton University Press, pp. 58–59, ISBN 9780691131184, http://books.google.com/books?id=iIN_2WjBH1cC&pg=PA58 .
  4. Hills, Richard (2006). James Watt, vol 3: Triumph through Adversity, 1785-1819. LandmarkPublishing Ltd. pp. 34–38. 
  5. Adams, Herb (1993), Chassis Engineering, Penguin, p. 62, ISBN 9781557880550, http://books.google.com/books?id=rY2ujnNrhf0C&pg=PA62 .

External links

ar:وصلة وات

cs:Wattův přímovod ru:Механизм Ватта

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