XVIII. On a general method of producing exact rectilinear motion by linkwork

Abstract

Since the invention by James W att, in 1784, of the 3-bar linkwork known as “Watt’s Parallel Motion,” which gives an approximate rectilinear motion, many attempts have been made to obtain a more perfect solution of the problem how to obtain accurate rectilinear motion by means of linkwork. Professor Tchebicheff succeeded in obtaining a 3-bar link-work giving a much closer approximation to a true result; but in his case, as in that of others, the solution is only approximate, and it may be, in fact, shown that with 3 bars an accurate result cannot be obtained. It was not until 1864 that the problem was solved; in that year M. Peaucellier made his memorable discovery of an accurate 7-bar solution; and in 1874, when the subject was brought prominently forward in England by Professor Sylvester, Mr. Hart, in a paper read before the British Association, gave a solution by means of 5 bars. Both these linkworks, as is now well known, depended upon the inversion of a circle with respect to a point on its circumference.