Watt's linkage

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Animated depiction of Watt's linkage Watts linkage.gif
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. The Kinematics of Machinery Fig 1.png
Hand-drawn diagram by James Watt (1808) in a letter to his son, describing how he arrived at the design.

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. It was described in Watt's patent specification of 1784 for the Watt steam engine. It is also used in automobile suspensions, allowing the axle of a vehicle to travel vertically while preventing sideways motion.

James Watt British engineer

James Watt was a Scottish inventor, mechanical engineer, and chemist who improved on Thomas Newcomen's 1712 Newcomen steam engine with his Watt steam engine in 1776, which was fundamental to the changes brought by the Industrial Revolution in both his native Great Britain and the rest of the world.

Watt steam engine

The Watt steam engine, alternatively known as the Boulton and Watt steam engine, was the first practical steam engine and was one of the driving forces of the industrial revolution. James Watt developed the design sporadically from 1763 to 1775 with support from Matthew Boulton. Watt's design saved significantly more fuel compared to earlier designs that they were licensed based on the amount of fuel they would save. Watt never ceased developing the steam engine, introducing double-acting designs and various systems for taking off rotary power. Watt's design became synonymous with steam engines, and it was many years before significantly new designs began to replace the basic Watt design.



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.

Four-bar linkage

A four-bar linkage, also called a four-bar, is the simplest movable closed-chain linkage. It consists of four bodies, called bars or links, connected in a loop by four joints. Generally, the joints are configured so the links move in parallel planes, and the assembly is called a planar four-bar linkage. Spherical and spatial four-bar linkages also exist and are used in practice.


Figure 9 from James Watt's patent application (top left part) showing the straightline linkage James Watt's straight-line linkage.jpg
Figure 9 from James Watt's patent application (top left part) showing the straightline linkage

The idea of its genesis using links is contained in a letter Watt wrote to Matthew Boulton in June 1784.

Matthew Boulton English industrialist, business partner of James Watt

Matthew Boulton 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 mechanisation of factories and mills. Boulton applied modern techniques to the minting of coins, striking millions of pieces for Britain and other countries, and supplying the Royal Mint with up-to-date equipment.

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]

This type of linkage is one of several types described in Watt's 28 April 1784 patent specification. However, in his letter to Boulton he was actually describing a development of the linkage which was not included in the patent. The slightly later design, called a parallel motion linkage, led to a more convenient space-saving design which was actually used in his reciprocating (or rotary) beam engines. [3]

Parallel motion mechanical engineering

The parallel motion is a mechanical linkage invented by the Scottish engineer James Watt in 1784 for the double-acting Watt steam engine. It allows a rod moving practically straight up and down to transmit motion to a beam moving in an arc, without putting significant sideways strain on the rod.

Reciprocating engine heat engine that uses one or more reciprocating pistons to convert pressure into a rotating motion

A reciprocating engine, also often known as a piston engine, is typically a heat engine that uses one or more reciprocating pistons to convert pressure into a rotating motion. This article describes the common features of all types. The main types are: the internal combustion engine, used extensively in motor vehicles; the steam engine, the mainstay of the Industrial Revolution; and the niche application Stirling engine. Internal combustion engines are further classified in two ways: either a spark-ignition (SI) engine, where the spark plug initiates the combustion; or a compression-ignition (CI) engine, where the air within the cylinder is compressed, thus heating it, so that the heated air ignites fuel that is injected then or earlier.

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. The efficiency of the engines was improved by engineers including James Watt who added a separate condenser, Jonathan Hornblower and Arthur Woolf who compounded the cylinders, and William McNaught who devised a method of compounding an existing engine. Beam engines were first used to pump water out of mines or into canals, but could be used to pump water to supplement the flow for a waterwheel powering a mill.

The context of Watt's innovation has been described by C. G. Gibson:

During the Industrial Revolution, mechanisms for converting rotary into linear motion were widely adopted in industrial and mining machinery, locomotives and metering devices. Such devices had to combine engineering simplicity with a high degree of accuracy, and the ability to operate at speed for lengthy periods. For many purposes approximate linear motion is an acceptable substitute for exact linear motion. Perhaps the best known example is the Watt four bar linkage, invented by the Scottish engineer James Watt in 1784. [4]

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

Watts curve

In mathematics, Watt's curve is a tricircular plane algebraic curve of degree six. It is generated by two circles of radius b with centers distance 2a apart (taken to be at. A line segment of length 2c attaches to a point on each of the circles, and the midpoint of the line segment traces out the Watt curve as the circles rotate. It arose in connection with James Watt's pioneering work on the steam engine.

Lemniscate figure-eight-shaped curve

In algebraic geometry, a lemniscate is any of several figure-eight or -shaped curves. The word comes from the Latin "lēmniscātus" meaning "decorated with ribbons", from the Greek λημνίσκος meaning "ribbons", or which alternatively may refer to the wool from which the ribbons were made.

Antiparallelogram quadrilateral with two pairs of opposite equal-length sides, the longer two of which are crossed

In geometry, an antiparallelogram is a quadrilateral having, like a parallelogram, two opposite pairs of equal-length sides, but in which the sides of one pair cross each other. The longer of the two pairs will always be the one that crosses. Antiparallelograms are also called contraparallelograms or crossed parallelograms.

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, Hart's inversor, and other straight line mechanisms 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.


Double-acting piston

The earlier single-action beam engines used a chain to connect the piston to the beam and this worked satisfactorily for pumping water from mines, etc. However, for rotary motion a linkage that works both in compression and tension provides a better design and allows a double-acting cylinder to be used. Such an engine incorporates a piston acted upon by steam alternately on the two sides, hence doubling its power. The linkage actually used by Watt (also invented by him) in his later rotary beam engines was called the parallel motion linkage, a development of "Watt's linkage", but using the same principle. The piston of the engine is attached to the central point of the linkage, allowing it to act on the two outer beams of the linkage both by pushing and by pulling. The nearly linear motion of the linkage allows this type of engine to use a rigid connection to the piston without causing the piston to bind in its containing cylinder. This configuration also results in a smoother motion of the beam than the single-action engine, making it easier to convert its back-and-forth motion into rotation. [3] [6]

An example of Watt's linkage can be found on the high and intermediate pressure piston rod of the 1865 Crossness engines. In these engines, the low pressure piston rod uses the more conventional parallel motion linkage, but the high and intermediate pressure rod does not connect to the end of the beam so there is no requirement to save space.

Vehicle suspension

Watt's linkage automobile suspension Wattslinkage.svg
Watt's linkage automobile suspension
Watt's linkage in a 1998 Ford Ranger EV suspension Watt's Linkage Rear Suspension.gif
Watt's linkage in a 1998 Ford Ranger EV suspension
Watt's linkage train suspension Alstom link diameter 762mm FS075.jpg
Watt's linkage train suspension

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 are intended to prevent relative sideways motion between the axle and body of the car. Watt’s linkage approximates a vertical straight-line motion much more closely, and it does so while consistently locating the centre of the axle at the vehicle's longitudinal centreline, rather than toward one side of the vehicle as would be the case if a simple Panhard rod were used. [7]

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 largely balance each other in 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 arrangement was used on Australian V8 Supercars until the end of the 2012 season.

Watt's linkage can also be used to prevent axle movement in the longitudinal direction of the car. This application involves two Watt's linkages on each side of the axle, mounted parallel to the driving direction, but just a single 4-bar linkage is more common in racing suspension systems

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Straight line mechanism

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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. 1 2 Ferguson, Eugene S. (1962). "Kinematics of Mechanisms from the Time of Watt". United States National Museum Bulletin. 228: 185–230. Retrieved 12 May 2013.. Also available at https://www.gutenberg.org/files/27106/27106-h/27106-h.htm
  4. C. G. Gibson (1998) Elementary Geometry of Algebraic Curves, pp 12, 13, Cambridge University Press ISBN   0-521-64140-3
  5. Bryant, John; Sangwin, Christopher J. (2008), How round is your circle? Where Engineering and Mathematics Meet, Princeton University Press, pp. 58–59, ISBN   978-0-691-13118-4 .
  6. Hills, Richard (2006). James Watt, vol 3: Triumph through Adversity, 1785-1819. LandmarkPublishing Ltd. pp. 34–38.
  7. Adams, Herb (1993), Chassis Engineering, Penguin, p. 62, ISBN   978-1-55788-055-0 .