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قراءة كتاب Kinematics of Mechanisms from the Time of Watt
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Kinematics of Mechanisms from the Time of Watt
pull. It was in the solution of this problem that Watt's originality and sure judgment were most clearly demonstrated.
A rack and sector arrangement (fig. 8) was used on some engines. The first one, according to Watt, "has broke out several teeth of the rack, but works steady."[15] A little later he told a correspondent that his double-acting engine "acts so powerfully that it has broken all its tackling repeatedly. We have now tamed it, however."[16]
[15] James Watt, March 31, 1783, quoted in Dickinson and Jenkins, op. cit. (footnote 5), p. 140.
[16] Watt to De Luc, April 26, 1783, quoted in Muirhead, op. cit. (footnote 3), vol. 2, p. 174.
Figure 8.—Watt engine of 1782 (British Patent 1321, March 12, 1782) showing the rack and sector used to guide the upper end of the piston rod and to transmit force from piston to working beam. This engine, with a 30-inch cylinder and an 8-foot stroke, was arranged for pumping. Pump rod SS is hung from sector of the working beam. From James P. Muirhead, The Origin and Progress of the Mechanical Inventions of James Watt (London, 1854, vol. 3, pl. 15).
It was about a year later that the straight-line linkage[17] was thought out. "I have started a new hare," Watt wrote to his partner. "I have got a glimpse of a method of causing the 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, or untowardly frictions, arch-heads, or other pieces of clumsiness.... I have only tried it in a slight model yet, so cannot build upon it, though I think it a very probable thing to succeed, and one of the most ingenious simple pieces of mechanism I have contrived...."[18]
[17] Watt's was a four-bar linkage. All four-bar straight-line linkages that have no sliding pairs trace only an approximately straight line. The exact straight-line linkage in a single plane was not known until 1864 (see p. 204). In 1853 Pierre-Frédéric Sarrus (1798-1861), a French professor of mathematics at Strasbourg, devised an accordion-like spatial linkage that traced a true straight line. Described but not illustrated (Académie des Sciences, Paris, Comptes rendus, 1853, vol. 36, pp. 1036-1038, 1125), the mechanism was forgotten and twice reinvented; finally, the original invention was rediscovered by an English writer in 1905. For chronology, see Florian Cajori, A History of Mathematics, ed. 2, New York, 1919, p. 301.
[18] Muirhead, op. cit. (footnote 3), vol. 2, pp. 191-192.
Watt's marvelously simple straight-line linkage was incorporated into a large beam engine almost immediately, and the usually pessimistic and reserved inventor was close to a state of elation when he told Boulton that the "new central perpendicular motion answers beyond expectation, and does not make the shadow of a noise."[19] This linkage, which was included in an extensive patent of 1784, and two alternative devices are illustrated here (fig. 9). One of the alternatives is a guided crosshead (fig. 9, top right).
[19] Ibid., p. 202.
Figure 9.—Watt's mechanisms for guiding the upper end of the piston rod of a double-acting engine (British Patent 1432, April 28, 1784). Top left, straight-line linkage; top right, crosshead and guide arrangement; lower left, piston rod A is guided by sectors D and E, suspended by flexible cords. From James P. Muirhead, The Origin and Progress of the Mechanical Inventions of James Watt (London, 1854, vol. 3, pls. 21, 22).
Brilliant as was the conception of this linkage, it was followed up by a synthesis that is very little short of incredible. In order to make the linkage attached to the beam of his engines more compact, Watt had plumbed his experience for ideas; his experience had yielded up the work done much earlier on a drafting machine that made use of a pantograph.[20] Watt combined his straight-line linkage with a pantograph, one link becoming a member of the pantograph.
[20] "It has only one fault," he had told a friend on December 24, 1773, after describing the drafting machine to him, "which is, that it will not do, because it describes conic sections instead of straight lines." Ibid., p. 71.
The length of each oscillating link of the straight-line linkage was thus reduced to one-fourth instead of one-half the beam length, and the entire mechanism could be constructed so that it would not extend beyond the end of the working beam. This arrangement soon came to be known as Watt's "parallel motion" (fig. 10).[21] Years later Watt told his son: "Though I am not over anxious after fame, yet I am more proud of the parallel motion than of any other mechanical invention I have ever made."[22]