Abstract: A robust design method of planar linkage mechanism is proposed when the length errors of links and the kinematic pair clearances are taken into account. The offset between the socket center and the pin center caused by the clearance in a pin joint is calculated and its effect on the positional posture of a planar linkage mechanism is analyzed. The position vector equation is used to represent the positional posture of a planar linkage mechanism with kinematic pair clearances. According to the pair elements of pin joints at the both ends of links, the links of a mechanism are classified into three types: the link with two sockets, the link with two pins, the link with one socket and one pin. The value and the direction of the offset in a pin joint are viewed as two random variables. Three effective length models corresponding to three link types are proposed and three calculation formulas of effective lengths are derived by using the complex number vector method. The calculation accuracy of the proposed effective length models is validated by simulations and it is showed that the calculation accuracy of the derived formulas is satisfactory to engineering design. Based on the proposed models, an example is given to achieve the robust design optimization of a slider-crank mechanism generating a given function. The example shows that the proposed method is practical and effective.

Key words: Effective length model, Kinematic pair with clearance, Planar linkage mechanism, Robust design optimization