A method for optimal path synthesis of four-link planar mechanisms

The paper deals with the optimal synthesis of planar mechanisms as path generators. The formulation of the synthesis problem enables decreasing the number of design parameters. The angular position of the floating link (coupling link) connecting input and output links is described by function sine. The coupler link is treated as a free body which generates precisely desired motion. The objective is to determine the coupler dimensions for which the coupler joints approximate with a prescribed accuracy the trajectories which these joints trace in the assembled mechanism. The structural error for most typical kinematic pairs was derived in order to apply the method to a wide spectrum of four-link planar mechanisms. Compared with classical path synthesis approach, this technique measures the deviation of the paths of the coupler joints from their paths in the assembled mechanisms, not the deviation of the coupler path from the prescribed trajectory. Various modifications of the method were discussed to widen the range of possible applications. The problem was formulated as an optimization task. An objective function was constructed and minimized in searching for generators of desired motion using an evolutionary algorithm. Test paths were chosen to verify the effectiveness of the method. Numerical tests addressed also practical linkage applications. The technique was verified in the synthesis of four-bar linkage, crank-slider mechanism and mechanism with slotted link. The method was also applied to solve chosen motion synthesis tasks combining the positions and angular orientations of the link.