An optimal design method of reproducing a given trajectory for planar four-bar linkage

This paper researched on how to realize a given trajectory more accurately by designing a planar four-bar linkage. In order to reproducing a given curve accurately, analytical synthesis and optimal algorithm were used in this paper. Mathematical model was established at first, the dimension of each link, location of the fixed hinge center and some angles between the links were taken as design variables. Then the objective function is established by calculating the root mean square error between the coupler curve and the given curve at the specified N points. According to Grashof Criteria and the minimum value of the transmission angle, the constraints of the design were determined. The iterative method is used to find the optimal solution of the objective function. Thirdly, an optimal design program were written through the use of Matlab Software to achieve the method. Finally, an example is given to verify the feasibility of the optimization program.