Watt's linkage is a type of mechanical linkage invented by James Watt

James Watt

James Watt, FRS, FRSE was a Scottish inventor and mechanical engineer whose improvements to the Newcomen steam engine were fundamental to the changes brought by the Industrial Revolution in both his native Great Britain and the rest of the world.While working as an instrument maker at the...

 (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.

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

Matthew Boulton

Matthew Boulton, FRS was an English manufacturer and business partner of Scottish engineer James Watt. In the final quarter of the 18th century the partnership installed hundreds of Boulton & Watt steam engines, which were a great advance on the state of the art, making possible the...

 in June 1784.

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 a lemniscate

Lemniscate

In algebraic geometry, a lemniscate refers to any of several figure-eight or ∞ shaped curves. It may refer to:*The lemniscate of Bernoulli, often simply called the lemniscate, the locus of points whose product of distances from two foci equals the square of half the interfocal distance*The...

; when the lengths of its bars and its base are chosen to form a crossed square

Antiparallelogram

An antiparallelogram is a quadrilateral in which, like a parallelogram, the pairs of nonadjacent sides are congruent, but in which two opposite sides intersect and are therefore not parallel.-Properties:Every antiparallelogram has an axis of symmetry through its crossing point...

, it traces the lemniscate of Bernoulli

Lemniscate of Bernoulli

In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F1 and F2, known as foci, at distance 2a from each other as the locus of points P so that PF1·PF2 = a2. The curve has a shape similar to the numeral 8 and to the ∞ symbol. Its name is from lemniscus, which is...

. In a letter to Boulton on 11 September 1784 Watt describes the linkage as follows.
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

Chebyshev linkage

The Hoekens linkage is a four-bar mechanism that converts rotational motion to approximate straight-line motion. The Hoekens linkage is a cognate linkage of the Chebyshev linkage.-See also:*Straight line mechanism*Peaucellier–Lipkin 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.

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

Beam engine

A beam engine is a type of steam engine where a pivoted overhead beam is used to apply the force from a vertical piston to a vertical connecting rod. This configuration, with the engine directly driving a pump, was first used by Thomas Newcomen around 1705 to remove water from mines in Cornwall...

, 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. This configuration also resulted in a smoother motion of the beam, facilitating its adaptation to rotative motion.

Automobile suspension

Watt's linkage is used in the rear axle

Beam axle

A beam axle is a suspension system, also called a solid axle, in which one set of wheels is connected laterally by a single beam or shaft...

 of some car suspensions

Suspension (vehicle)

Suspension is the term given to the system of springs, shock absorbers and linkages that connects a vehicle to its wheels. Suspension systems serve a dual purpose — contributing to the car's roadholding/handling and braking for good active safety and driving pleasure, and keeping vehicle occupants...

 as an improvement over the Panhard rod

Panhard rod

A Panhard rod is a component of a car suspension system that provides lateral location of the axle...

, 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.

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.

External links

• How round is your circle? Contains a chapter explaining the history of Watt's linkage.
• Watt Beam Engine
• How to draw a straight line, by A.B. Kempe, B.A.
• Lemniscoidal (figure 8 curved) linkage of the first kind by Watt
• Lemniscoidal linkage of the second and third kind by Watt
• A simulation using the Molecular Workbench software