This paper provides a new robust design method to dimension a mechanism and to synthesize its dimensional tolerances. The general issue is to find a robust mechanism for a given task, and to compute its optimal dimensional tolerances. For that purpose, the developed approach follows two consecutive steps, which are independent and complementary. First, the dimensions of the mechanism are computed by means of an appropriate robustness index, which is used to minimize the sensitivity of its performances to variations. These robust dimensions are obtained independently of the amount of variations, and tolerate globally the largest variations. Thus, knowing the acceptable performance error of the mechanism, the second step aims at computing the optimal dimensional tolerances of the mechanism by means of the new tolerance synthesis method. This method is used to find the best distribution of the error between the dimensions of the mechanism. Two serial manipulators are studied to illustrate the theory.