Optimum synthesis of four-bar mechanisms considering clearance-induced uncertainty

This paper presents a multi-objective optimization model for the motion synthesis of four-bar mechanisms considering the effects of revolute joint clearances. A geometric method is proposed to compute the maximum clearances-induced positioning and orientation errors. The proposed error modeling method is validated using a simple example, and the results reveal its advantages of high accuracy and fast computation compared with the widely used existing methods. A multi-objective optimization model is developed to design the four-bar mechanism with the best accuracy. The positioning and orientation errors are modeled separately and equally. Moreover, three constraints are included in the optimization to ensure that the synthesized mechanism is a compact crank-rocker or double-crank mechanism free from branch and order defects. A study case of synthesizing a four-bar mechanism passing through 6 motion points is investigated to illustrate the proposed method. Finally, conclusions and a brief discussion are given.