. Bulletin. Science. 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 Mo
. Bulletin. Science. 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 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 ; ^"^ 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 E
Size: 1345px × 1859px
Photo credit: © Library Book Collection / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthorunitedstatesdepto, bookcentury1900, booksubjectscience
