Abstract
Abstract This paper describes a generalisation of straight-line mechanisms of Tchebycheff-type. Tchebycheff considered symmetric four-bar mechanisms for which the part of the coupler curve used as an approximation for a straight line oscillates between two lines, so that one line is a tangent of the coupler curve in three points and the other is a tangent of the coupler curve in two points and intersects the coupler curve in two further points. The described synthesis methods allow the calculation of unsymmetric mechanisms which have the same characteristic oscillation and are also optimal in the sense of the approximation theory developed by Tchebycheff. The use of continuation methods not only enabled the solution of a classical kinematic problem and the possibility to synthesize straight-line mechanisms with desired characteristic values but also offers new possibilities for user-friendly software for kinematic synthesis.
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