Parallel motion linkage
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Dimensions (unit lengths Template:Mvar): Template:Legend-line Template:Legend-line Template:Legend-line Vertical distance between ground joints Template:Math
Horizontal distance between ground joints Template:Math
Thus, link 1 (total distance between ground joints) <math>\approx \sqrt{4a^2 + 4b^2}</math>
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.
DescriptionEdit
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."<ref name="watt1808">Franz Reuleaux, The Kinematics of Machinery (1876), page 4.</ref> 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shows what is now known as Watt's linkage which was a linkage described in Watt's 1784 patent but it was immediately superseded by the parallel motion.<ref name=ferguson>Template:Cite book Also available at https://www.gutenberg.org/files/27106/27106-h/27106-h.htm</ref>
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.<ref name=ferguson />
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 operationEdit
See the diagram on the right. Template:Mvar is the journal (bearing) of the walking beam Template:Mvar, which rocks up and down about Template:Mvar. Template:Mvar is the piston, which is required to move vertically but not horizontally. The heart of the design is the four-bar linkage consisting of Template:Mvar, Template:Mvar and Template:Mvar and the base link is Template:Mvar, both joints on the framework of the engine. As the beam rocks, point Template:Mvar (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, Template:Mvar 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 Template:Mvar and Template:Mvar are equal in length, and straightest when the ratio of Template:Mvar to Template:Mvar matches that of Template:Mvar to Template:Mvar. If the stroke length (that is, the maximum travel of Template:Mvar) is Template:Mvar, then the straight section is longest when Template:Mvar is around Template:Math and Template:Mvar is Template:Math.<ref name="mechanisms2001">Neil Sclater and Nicholas P. Chironis, Mechanisms and Mechanical Devices Sourcebook Third Edition (2001), page 136.</ref>
It would have been possible to connect Template:Mvar directly to the piston rod (the "Watt's linkage" design), but this would have made the machine an awkward shape, with Template:Mvar a long way from the end of the walking beam. To avoid this, Watt added the parallelogram linkage Template:Mvar to form a pantograph. This guarantees that Template:Mvar always lies on a straight line between Template:Mvar and Template:Mvar, and therefore that the motion of Template:Mvar is a magnified version of the motion of Template:Mvar. Template:Mvar is therefore the point to which the piston rod Template:Mvar 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 Template:Mvar 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 alsoEdit
- Pantograph, part of what the Parallel motion linkage uses.
- Straight line mechanism
- Watt's linkage, the core of how the Parallel motion linkage works.
ReferencesEdit
- 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 readingEdit
- How Round Is Your Circle? (Bryant and Sangwin, 2008) contains a chapter about James Watt's parallel motion mechanism
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