Synthesis of four-bar mechanisms by Freudenstein–Chebyshev

A new dimensional synthesis method is described in the paper. The position function of the four-bar mechanism is presented by the Freudenstein’s equation and it is minimized by the Chebyshev’s best approximation theory. The target function is used as an exactly satisfied equation and the Freudenstein’s equation is considered as a Chebyshev’s polynomial. In some cases the method provides possibilities to find simple solutions of the synthesis tasks. These solutions are known as the best Chebyshev’s approach of the weighted target function. This approach is near the best one for the original target function. A numerical example given here explains the essence of the method.