This paper proposes an analytical design method for the quick-return mechanisms such as the four-bar linkage and the offset slider crank and developes an optimum design method for those mechanisms in which the time-ratio and the minimum transmission angle are given simultaneously. Using this method,the maximum value of the time-ratio is given only. The quick-return mechanisms in which the minimum transmission angle should be the maximum can be designed easily using the proportion of the links presented in the tables in this paper.