Watt's linkage

Last updated
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.

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.

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.

History

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.

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 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

Related Research Articles

Machine tool using energy to perform an intended action

A machine is a mechanical structure that uses power to apply forces and control movement to perform an intended action. Machines can be driven by animals and people, by natural forces such as wind and water, and by chemical, thermal, or electrical power, and include a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement. They can also include computers and sensors that monitor performance and plan movement, often called mechanical systems.

Panhard rod

A Panhard 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 widely used ever since.

In mechanical engineering, an eccentric is a circular disk solidly fixed to a rotating axle with its centre offset from that of the axle.

Linkage (mechanical) assembly of bodies connected to manage forces and movement

A mechanical linkage is an assembly of bodies 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 ideal movement, pure rotation or sliding for example, and are called joints. A linkage modeled as a network of rigid links and ideal joints is called a kinematic chain.

Sun and planet gear

The sun and planet gear is a method of converting reciprocating motion to rotary motion and was used in the first rotative beam engines.

Beam axle

A beam axle, rigid axle or solid axle is a dependent suspension design, in which a set of wheels is connected laterally by a single beam or shaft. Beam axles were once commonly used at the rear wheels of a vehicle, but historically they have also been used as front axles in rear-wheel-drive vehicles. In most automobiles, beam axles have been replaced by front and rear independent suspensions.

Scott Russell linkage

A Scott Russell linkage gives a theoretically linear motion by using a linkage form with three portions of the links all equal, and a rolling or sliding connection. It can be used to form a right-angle change of motion, linear-to-linear.

Straight line mechanism

In the late seventeenth century, before the development of the planer and the milling machine, it was extremely difficult to machine straight, flat surfaces. For this reason, good prismatic pairs without backlash were not easy to make. During that era, much thought was given to the problem of attaining a straight-line motion as a part of the coupler curve of a linkage having only revolute connection. Probably the best-known result of this search is the straight line mechanism development by Watt for guiding the piston of early steam engines. Although it does not generate an exact straight line, a good approximation is achieved over a considerable distance of travel.

Chebyshev linkage

The Chebyshev linkage is a mechanical linkage that converts rotational motion to approximate straight-line motion.

Mechanism (engineering) device designed to transform input forces and movement into a desired set of output forces and movement

In engineering, a mechanism is a device that transforms input forces and movement into a desired set of output forces and movement. Mechanisms generally consist of moving components that can include:

Whitbread Engine

The Whitbread Engine preserved in the Powerhouse Museum in Sydney, Australia, built in 1785, is one of the first rotative steam engines ever built, and is the oldest surviving. A rotative engine is a type of beam engine where the reciprocating motion of the beam is converted to rotary motion, producing a continuous power source suitable for driving machinery.

Grasshopper beam engine

Grasshopper beam engines are beam engines that are pivoted at one end, rather than in the centre.

Return connecting rod engine

A return connecting rod, return piston rod or double piston rod engine or back-acting engine is a particular layout for a steam engine.

Lap Engine Watt engine, now in the Science Museum, London

The Lap Engine is a beam engine designed by James Watt, built by Boulton and Watt in 1788. It is now preserved at the Science Museum, London.

Slider-crank linkage

A slider-crank linkage is a four-link mechanism with three revolute joints and one prismatic, or sliding, joint. The rotation of the crank drives the linear movement the slider, or the expansion of gases against a sliding piston in a cylinder can drive the rotation of the crank.

References

  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 .