A method of optimum synthesis of plane mechanisms for the generation of paths and rigid-body positions is presented. The method is developed for the four-bar plane mechanism with six and eight unknown dimensions. Dimensions of the optimum mechanism are determined by minimizing the error in the loop-closure equations for N design points on the path, along with the loop-closure equation of the linkage, where N is not limited by the number of the unknown dimensions of the system. Design equations are linearized by the method of linear superposition. Solution of design equations requires no iterations, and it leads to a series of optimum mechanisms of different efficiency of approximation. Numerical examples are given.

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