Synthesis and robust design of approximate straight-line mechanism with instantaneous center at infinity

For the synthesis problems of the approximate straight-line mechanism with instantaneous center at infinity, a universal synthesis method is proposed in this paper. Given the overall design requirements: the expected straight-line and one fixed pivot, the mathematical model is established to determine the mechanism with the offset as the design variables, through which the infinite straight-line mechanisms are generated with the offset change, including second-order and third-order osculation four-bar linkage. Moreover, the model is also suitable for the synthesis of mechanism with a sliding pair; the second-order osculation slider and rocking-block linkage and third-order osculation slider linkage are gained, which makes a beneficial exploration for the mechanism synthesis with a sliding pair. The robustness is one of the essential indicators to evaluate the motion output of mechanism in this paper, and a robust model of the approximate straight-line mechanism with instantaneous center at infinity is established. Then, the mechanisms are screened by geometric and kinematic constraints and robustness constraints, and the final optimal solution that meets all the constraints is found according to the optimization aim. This method allows the designer to rapidly discover the optimal robust mechanism from an infinite number of straight-line mechanisms, reducing design time substantially and making up for the deficiency of the current synthesis theory of approximate straight-line mechanism in the mechanism with instantaneous center at infinity.