Physics:Parallel motion linkage

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Short description: Six-bar straight-line mechanism
This page is about parallel motion in mechanics. For parallel motion in musicsee Parallel motion (music).
Animation of the parallel motion linkage.
Dimensions (unit lengths ab):
  Link 2: a + a
  Links 3 & 5: b + b2b
  Links 4 & 6: a
Vertical distance between ground joints ≈ 2b
Horizontal distance between ground joints ≈ 2a
Thuslink 1 (total distance between ground joints) ≈4a2+4b2

In kinematicsthe 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 arcwithout putting significant sideways strain on the rod.

Description

Watt's parallel motion on a pumping engine

In previous engines built by Newcomen and Wattthe piston pulled one end of the walking beam downwards during the power stroke using a chainand the weight of the pump pulled the other end of the beam downwards during the recovery stroke using a second chainthe alternating forces producing the rocking motion of the beam. In Watt's new double-acting enginethe piston produced power on both the upward and downward strokesso 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 verticallyparallel to one another.

Hand-drawn diagram in James Watt's letter to his son.[1]

In a letter to his son in 1808 describing how he arrived at the designJames Watt wrote "I am more proud of the parallel motion than of any other invention I have ever made."[1] 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shows what is now known as Watt's linkage which was a linkage described in Watt's 1784 patent but it was immediately superseded by the parallel motion.[2]

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.[2]

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 pistonthus almost doubling the powerand also delivering the power more evenly through the cyclean advantage when converting the reciprocating motion to rotary motion (whether through a crank or through a Sun and planet gear system).

Principle of operation

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.

See the diagram on the right. A is the journal (bearing) of the walking beam KACwhich rocks up and down about A. H is the pistonwhich is required to move vertically but not horizontally. The heart of the design is the four-bar linkage consisting of ABBE and EG and the base link is AGboth joints on the framework of the engine. As the beam rockspoint F (which is drawn to aid this explanationbut is not a marked point on the machine itself) describes an elongated figure-eight (more preciselya lemniscate of Bernoulli) in mid-air. Since the motion of the walking beam is constrained to a small angleF describes only a short section of the figure-eightwhich is quite close to a vertical straight line. The figure-eight is symmetrical as long as arms AB and EG are equal in lengthand straightest when the ratio of BF to FE matches that of AB to EG. If the stroke length (that isthe maximum travel of F) is Sthen the straight section is longest when BE is around ⅔ S and AB is 1.5 S.[3]

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 shapewith G a long way from the end of the walking beam. To avoid thisWatt added the parallelogram linkage ▱BCDE to form a pantograph. This guarantees that F always lies on a straight line between A and Dand 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 notedthe path of F is not a perfect straight linebut merely an approximation. Watt's design produced a deviation of about one part in 4000 from a straight line. Laterin the 19th centuryperfect straight-line linkages were inventedbeginning with the Peaucellier–Lipkin linkage of 1864.

See also

References

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  1. ↑ 1.0 1.1 Franz ReuleauxThe Kinematics of Machinery (1876)page 4.
  2. ↑ 2.0 2.1 FergusonEugene S. (1962). Contributions from the Museum of History and Technology: Paper 27 Kinematics of Mechanisms from the Time of Watt. United States National Museum Bulletin. 228. pp. 185–230. https://ebooks.library.cornell.edu/cgi/t/text/text-idx?c=kmoddl;cc=kmoddl;view=toc;subview=short;idno=kmod009.  Also available at https://www.gutenberg.org/files/27106/27106-h/27106-h.htm
  3. ↑ Neil Sclater and Nicholas P. ChironisMechanisms and Mechanical Devices Sourcebook Third Edition (2001)page 136.
General

Further reading

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