Figure ig. — Pafnutu L'vovich Chebyshev 

 (1821-1894), Russian mathematician active in 

 analysis and synthesis of straight-line mecha- 

 nisms. From Ouvres de P. L. Tchebychef (St. 

 Petersburg, 1907, vol. 2, frontispiece). 



Figure 20. — Chebyshev's combination 

 (about 1867) of Watt's and Evans' 

 linkages to reduce errors inherent in 

 each. Points C, C, and C" are fixed; 

 A is the tracing point. From Oeuvres 

 de P. L. Tchebychef (St. Petersburg, 

 1907, vol. 2, p. 93). 



reputation abroad, Chebyshev's interest amounted 

 to an obsession. 



Pafnutii L'vovich Chebyshev was born in 1821, 

 near Moscow, and entered the University of Moscow 

 in 1837. In 1853, after visiting France and England 

 and observing carefully the progress of applied me- 

 chanics in those countries, he read his first paper on 

 approximate straight-line linkages, and over the 

 next 30 years he attacked the problem with new vigor 

 at least a dozen times. He found that the tvv'o 

 principal straight-line linkages then in use were 

 Watt's and Evans'. Chebyshev noted the departure 

 of these linkages from a straight line and calculated 

 the deviation as of the fifth degree, or about 0.0008 

 inch per inch of beam length. He proposed a 

 modification of the Watt linkage to refine its accu- 

 racy but found that he would have to more than 

 double the length of the working beam. Chebyshev 

 concluded ruefully that his modification would 

 "present great practical difficulties." ^"^ 



At length an idea occurred to Chebyshev that 

 would enable him to approach if not quite attain a 

 true straight line. If one mechanism was good, he 

 reasoned, two would be better, et cetera, ad infinitum. 

 The idea was simply to combine, or compound, four- 

 link approximate linkages, arranging them in such a 

 way that the errors would be successively reduced. 

 Contemplating first a combination of the Watt and 

 Evans linkages (fig. 19), Chebyshev recognized that 

 if point D of the Watt linkage followed nearly a 

 straight line, point A of the Evans linkage would 

 depart even less from a straight line. He calculated 

 the deviation in this case as of the 11th degree. He 

 then replaced Watt's linkage by one that is usually 

 called the Chebyshev straight-line mechanism (fig. 

 20), with the result that precision was increased to 

 the 13th degree.^* The steam engine that he dis- 

 played at the Vienna Exhibition in 1873 employed 

 this linkage — the Chebyshev mechanism compounded 

 with the Evans, or approximate isosceles, linkage. 

 An English visitor to the exhibition commented that 



3' Oeuvres de P. L. Tchebychef, 2 vols., St. Petersburff, 1899- 

 1907, vol. 1, p. 538; vol. 2, pp. 57, 85. 



I Ibid., vol. 2, pp. 93, 94. 



PAPER 27: KINEMATICS FROM THE TIME OF WATT 



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