Analytic synthesis of a four-bar mechanism as part of a reclining mechanism

The method presented in this paper is based on the synthesis of the four-bar mechanism considering two or three imposed positions for the coupler link of the mechanism and its length and determining the required lengths of the other links and the positions of the fixed revolute joint in order to achieve the prescribed position. This method represents an analytical approach of the geometrical method used for the mechanism synthesis. A numerical example was developed, and the geometrical synthesis problem was studied using Dassault System Solidworks and compared with analytical method that was computed using MathWorks MATLAB. The obtained mechanism represents a part of a complex structure representing a reclining mechanism for an armchair, for which desired positions of the seat, backrest and footrest are imposed.