kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, Physical object, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause ...

, Watt's linkage (also known as the parallel linkage) is a type of

mechanical linkage A mechanical linkage is an assembly of systems connected to manage forces and movement. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. The connections between links are modeled as providing i ...

invented by

James Watt James Watt (; 30 January 1736 (19 January 1736 OS) – 25 August 1819) 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 fun ...

in which the central moving point of the linkage is constrained to travel on a nearly straight line. It was described in Watt's patent specification of 1784 for the

Watt steam engine The Watt steam engine design became synonymous with steam engines, and it was many years before significantly new designs began to replace the basic Watt design. The first steam engines, introduced by Thomas Newcomen in 1712, were of the "at ...

. Today it is used in automobile suspensions, allowing the axle of a vehicle to travel vertically while preventing sideways motion.

Description

Watt's linkage consists of three bars bolted together in a chain. The chain of bars consists of two end bars and a middle bar. The middle bar is bolted at each of its ends to one of the ends of each outer bar. The two outer bars are of equal length, and are longer than the middle bar. The three bars can pivot around the two bolts. The outer endpoints of the long bars are fixed in place relative to each other, but otherwise the three bars are free to pivot around the two joints where they meet. In linkage analysis there is an imaginary fixed-length bar connecting between the outer endpoints. Thus Watt's linkage is an example of a

four-bar linkage In the study of mechanisms, a four-bar linkage, also called a four-bar, is the simplest closed- chain movable linkage. It consists of four bodies, called ''bars'' or ''links'', connected in a loop by four joints. Generally, the joints are configu ...

History

Its genesis is contained in a letter Watt wrote to

Matthew Boulton Matthew Boulton (; 3 September 172817 August 1809) 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 engine ...

in June 1784. 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 In kinematics, the parallel motion linkage is a six-bar 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 moti ...

linkage, led to a more convenient space-saving design which was actually used in his reciprocating, and his rotary,

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 Newco ...

s.. Also available at https://www.gutenberg.org/files/27106/27106-h/27106-h.htm The context of Watt's innovation has been described by C. G. Gibson: :During the

Industrial Revolution The Industrial Revolution was the transition to new manufacturing processes in Great Britain, continental Europe, and the United States, that occurred during the period from around 1760 to about 1820–1840. This transition included going f ...

, 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.

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 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 2''a'' apart (taken to be at (±''a'', 0)). A line segment of length 2''c'' attaches to a p ...

, a

lemniscate 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 alternativel ...

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 In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points and , known as foci, at distance from each other as the locus of points so that . The curve has a shape similar to the numeral 8 and to the ∞ symbol. I ...

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

Peaucellier–Lipkin linkage The Peaucellier–Lipkin linkage (or Peaucellier–Lipkin cell, or Peaucellier–Lipkin inversor), invented in 1864, was the first true planar straight line mechanism – the first planar linkage (mechanical), linkage capable of trans ...

, Hart's inversor, and other

straight line mechanism A straight-line mechanism is a Mechanism (engineering), mechanism that converts any type of rotary or angular motion to perfect or near-perfect straight-line motion, or ''vice-versa''. Straight-line motion is linear motion of definite length ...

s 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 In kinematics, Chebyshev's linkage is a four-bar linkage that converts rotational motion to approximate linear motion. It was invented by the 19th-century mathematician Pafnuty Chebyshev, who studied theoretical problems in kinematic mechanism ...

, 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-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 In mechanical engineering, the cylinders of reciprocating engines are often classified by whether they are single- or double-acting, depending on how the working fluid acts on the piston. Single-acting A single-acting cylinder in a reciprocat ...

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

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. 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

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 is used in the rear

axle An axle or axletree is a central shaft for a rotating wheel or gear. On wheeled vehicles, the axle may be fixed to the wheels, rotating with them, or fixed to the vehicle, with the wheels rotating around the axle. In the former case, bearing ...

of some car

suspensions In chemistry, a suspension is a heterogeneous mixture of a fluid that contains solid particles sufficiently large for sedimentation. The particles may be visible to the naked eye, usually must be larger than one micrometer, and will eventually ...

as an improvement over the

Panhard rod A Panhard rod (also called Panhard bar, track bar, or track rod) is a suspension link that provides lateral location of the axle. Originally invented by the Panhard automobile company of France in the early twentieth century, this device has been ...

, 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.. 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 The Supercars Championship is a touring car racing category in Australia, running as an International Series under Fédération Internationale de l'Automobile (FIA) regulations, governing the sport. Supercars events take place in all Australian ...

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.

References

External links

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

using the Molecular Workbench software. {{Chassis control systems Automotive suspension technologies Linkages (mechanical) Scottish inventions

Linkage Linkage may refer to: * ''Linkage'' (album), by J-pop singer Mami Kawada, released in 2010 *Linkage (graph theory), the maximum min-degree of any of its subgraphs *Linkage (horse), an American Thoroughbred racehorse * Linkage (hierarchical cluster ...

Linear motion Straight line mechanisms