The dimension variables of a mechanism vary randomly within their tolerance ranges. Likewise, the positions of the pins in joints also vary randomly, and the joint distribution of the position coordinates of a pin is usually unknown. In traditional robust mechanism synthesis, however, dimension variables are usually considered as unbounded random variables, and the joint distributions of the clearance variables are commonly assumed to be known. This work intends to make robust mechanism synthesis more practical by treating dimension variables as truncated random variables and clearance variables as interval variables. A new robust methodology is then proposed to accommodate truncated dimension variables and interval clearance variables. A quality loss function is created with the mean and standard deviation of the maximal motion error with respect to interval clearance variables. Then minimizing the expected quality loss function leads to reductions in both nominal motion error and the variation of the motion error. This ensures that the mechanism is robust against uncertainties in both dimension variables and clearance variables. The robust synthesis methodology is applied to a four-bar function generating mechanism. ► New mechanism synthesis methodology that can handle both truncated random variables and interval clearance variables ► Accurate analysis for the robustness of function generating mechanisms ► New robust design model for mechanism synthesis with both truncated random variables and interval clearance variables