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Parallel motion linkage

Parallel motion linkage is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Parallel motion linkage rather than just read about it. In short: 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 motion to a beam moving in an arc, without putting significant sideways strain on the rod.

Parallel motion linkage — main illustration
Parallel motion linkage — illustration

Key takeaways

  • Parallel motion linkage belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Parallel motion linkage to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Parallel motion linkage from memory before moving on to harder problems.

Reference excerpt

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 motion to a beam moving in an arc, without putting significant sideways strain on the rod.

Description

In previous engines built by Newcomen and Watt, the piston pulled one end of the walking beam downwards during the power stroke using a chain, and the weight of the pump pulled the other end of the beam downwards during the recovery stroke using a second chain, the alternating forces producing the rocking motion of the beam. In Watt's new double-acting engine, the piston produced power on both the upward and downward strokes, so a chain could not be used to transmit the force to the beam. Watt designed the parallel motion to transmit force in both directions whilst keeping the piston rod very close to vertical. He called it "parallel motion" because both the piston and the pump rod were required to move vertically, parallel to one another.

In a letter to his son in 1808 describing how he arrived at the design, James Watt wrote "I am more proud of the parallel motion than of any other invention I have ever made." The sketch he included actually shows what is now known as Watt's linkage which was a linkage described in Watt's 1784 patent but it was immediately superseded by the parallel motion. The parallel motion differed from Watt's linkage by having an additional pantograph linkage incorporated in the design. This did not affect the fundamental principle but it allowed the engine room to be smaller because the linkage was more compact. The Newcomen engine's piston was propelled downward by the atmospheric pressure. Watt's device allowed live steam to be used for direct work on both sides of the piston, thus almost doubling the power, and also delivering the power more evenly through the cycle, an advantage when converting the reciprocating motion to rotary motion (whether through a crank or through a Sun and planet gear system).

Principle of operation

See the diagram on the right. A is the journal (bearing) of the walking beam KAC, which rocks up and down about A. H is the piston, which is required to move vertically but not horizontally. The heart of the design is the four-bar linkage consisting of AB, BE and EG and the base link is AG, both joints on the framework of the engine. As the beam rocks, point F (which is drawn to aid this explanation, but is not a marked point on the machine itself) describes an elongated figure-eight (more precisely, a lemniscate of Bernoulli) in mid-air. Since the motion of the walking beam is constrained to a small angle, F describes only a short section of the figure-eight, which is quite close to a vertical straight line. The figure-eight is symmetrical as long as arms AB and EG are equal in length, and straightest when the ratio of BF to FE matches that of AB to EG. If the stroke length (that is, the maximum travel of F) is S, then the straight section is longest when BE is around ⅔ S and AB is 1.5 S. It would have been possible to connect F directly to the piston rod (the "Watt's linkage" design), but this would have made the machine an awkward shape, with G a long way from the end of the walking beam. To avoid this, Watt added the parallelogram linkage ▱BCDE to form a pantograph. This guarantees that F always lies on a straight line between A and D, and therefore that the motion of D is a magnified version of the motion of F. D is therefore the point to which the piston rod DH is attached. The addition of the pantograph made the mechanism shorter and so the building containing the engine could be smaller. As already noted, the path of F is not a perfect straight line, but merely an approximation. Watt's design produced a deviation of about one part in 4000 from a straight line. Later, in the 19th century, perfect straight-line linkages were invented, beginning with the Peaucellier–Lipkin linkage of 1864.

See also Pantograph, part of what the Parallel motion linkage uses. Straight line mechanism Watt's linkage, the core of how the Parallel motion linkage works.

References

General Linkages article in Encyclopædia Britannica, 1958. Parallel Motion article in Encyclopædia Britannica, 1911. Robert Stuart, A Descriptive History of the Steam Engine, London, J. Knight and H. Lacey, 1824.

Further reading

How Round Is Your Circle? (Bryant and Sangwin, 2008) contains a chapter about James Watt's parallel motion mechanism

Illustrations

Parallel motion linkage: Animation of the parallel motion linkage. Dimensions (unit lengths a, b): .mw-parser-output .legend{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .legend-color{display:inline-block;min-width:1.25em;height:1.25em;line-height:1.25;margin:1px 0;text-align:center;border:1px solid black;background-color:transparent;color:black}.mw-parser-output .legend-text{}  Link 2: a + a   Links 3 & 5: b + b, 2b   Links 4 & 6: a Vertical distance between ground joints ≈ 2b Horizontal distance between ground joints ≈ 2a Thus, link 1 (total distance between ground joints) ≈ 4 a 2 + 4 b 2 {\displaystyle \approx {\sqrt {4a^{2}+4b^{2}}}}
Animation of the parallel motion linkage. Dimensions (unit lengths a, b): .mw-parser-output .legend{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .legend-color{display:inline-block;min-width:1.25em;height:1.25em;line-height:1.25;margin:1px 0;text-align:center;border:1px solid black;background-color:transparent;color:black}.mw-parser-output .legend-text{}  Link 2: a + a   Links 3 & 5: b + b, 2b   Links 4 & 6: a Vertical distance between ground joints ≈ 2b Horizontal distance between ground joints ≈ 2a Thus, link 1 (total distance between ground joints) ≈ 4 a 2 + 4 b 2 {\displaystyle \approx {\sqrt {4a^{2}+4b^{2}}}}
Parallel motion linkage: Watt's parallel motion on a pumping engine
Watt's parallel motion on a pumping engine
Parallel motion linkage: Hand-drawn diagram in James Watt's letter to his son.[1]
Hand-drawn diagram in James Watt's letter to his son.[1]
Parallel motion linkage: Schematic of Watt's parallel motion: A and G are fixed hinge joints while F is not a joint but merely signifies the point on the linkage which follows a lemniscate. Its motion is magnified in D by the parallelogram ▱BCDE.
Schematic of Watt's parallel motion: A and G are fixed hinge joints while F is not a joint but merely signifies the point on the linkage which follows a lemniscate. Its motion is magnified in D by the parallelogram ▱BCDE.

Worked examples

Example 1 — a first encounter with Parallel motion linkage

Start with the simplest possible case. Write down what Parallel motion linkage claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Parallel motion linkage before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Parallel motion linkage ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Parallel motion linkage

In research
Parallel motion linkage appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Parallel motion linkage in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Parallel motion linkage is common in secondary-school and first-year university syllabi. It links to neighbouring topics Beam engines, Linkages (mechanical), Scottish inventions, so understanding it makes those chapters shorter.
In everyday life
Look for Parallel motion linkage outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Parallel motion linkage in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Parallel motion linkage means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Parallel motion linkage out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Parallel motion linkage in simple terms?

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 motion to a beam moving in an arc, without putting significant…

Why does Parallel motion linkage matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Parallel motion linkage?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Parallel motion linkage.

Tags

  • Beam engines
  • Linkages (mechanical)
  • Scottish inventions
  • Straight line mechanisms
  • Technical drawing

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