The present work entitled "Synthesis of a four-link mechanism for a rest chair using the Newton-Raphson method", was developed using the Freudenstein equation to obtain the optimal dimensions of a four-bar mechanism in a rest chair, and ensure stability in the extreme positions of the chair. The angles 1, 2 and 4 of the links of the mechanism were taken based on the ergonomics of a resting chair and taking into account the anatomy of the human body (back, legs and arms) The synthesis of the mechanism was proposed in the Freudenstein equation for a fourlink mechanism, to which the least-squares method was applied to minimize the error in the desired positions (2 and 4) of the links. A system of non-linear equations is obtained by applying the partial derivative with respect to the k constants of Freudenstein to the function that defines the positions of the mechanism. This system of nonli...